Optical elements based on polymer structures incorporating inorganic materials

Abstract

To provide optical elements based on polymer structures incorporating suitable inorganic materials.SOLUTION: The present disclosure relates to display systems and, more particularly, to augmented reality display systems. In one aspect, a method of fabricating an optical element includes providing a substrate having a first refractive index and transparent in the visible spectrum. The method additionally includes forming on the substrate periodically repeating polymer structures. The method further includes exposing the substrate to a metal precursor followed by an oxidizing precursor. Exposing the substrate is performed under pressure and at a temperature such that an inorganic material including the metal of the metal precursor is incorporated into the periodically repeating polymer structures, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light. The optical structures have a second refractive index greater than the first refractive index.SELECTED DRAWING: Figure 10

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority to U.S. Provisional Patent Application No. 62 / 613,651, filed January 4, 2018, and entitled "OPTICAL ELEMENTS BASED ON POLYMERIC STRUCTURES INCORPORATING INORGANIC MATERIALS," the contents of which are incorporated herein by reference in their entirety.

[0002] (Incorporated by reference) This application is incorporated by reference into the following patent applications: U.S. Patent Application No. 14 / 555,585, filed November 27, 2014, published on July 23, 2015 as U.S. Patent Publication No. 2015 / 0205126; U.S. Patent Application No. 14 / 555,585, filed April 18, 2015, published on October 22, 2015 as U.S. Patent Publication No. 2015 / 0302652; No. 690,401, U.S. Patent Application No. 14 / 212,961, filed March 14, 2014, now U.S. Patent No. 9,417,452, issued August 16, 2016, and U.S. Patent Application No. 14 / 331,218, filed July 14, 2014, published October 29, 2015 as U.S. Patent Publication No. 2015 / 0309263, each of which is incorporated in its entirety.

[0003] The present disclosure relates to display systems, and more particularly to augmented reality display systems. [Background technology]

[0004] Modern computing and display technology has facilitated the development of systems for so-called "virtual reality" or "augmented reality" experiences, in which digitally reproduced images or portions thereof are presented to a user in a manner that appears or can be perceived as real. Virtual reality, or "VR," scenarios typically involve the presentation of digital or virtual image information without transparency to other actual real-world visual input, while augmented reality, or "AR," scenarios typically involve the presentation of digital or virtual image information as an augmentation to the user's visualization of the real world around them. Mixed reality, or "MR," scenarios are a type of AR scenario that typically involve virtual objects integrated into and responsive to the natural world. For example, MR scenarios may include AR image content that appears blocked by or is perceived to otherwise interact with objects in the real world.

[0005] Referring to FIG. 1 , an augmented reality scene 1 is depicted. A user of the AR technology sees a real-world, park-like setting 20 featuring people, trees, a building in the background, and a concrete platform 30. The user also perceives that they are "seeing" "virtual content," such as a robotic figure 40 standing on the real-world platform 1120 and a flying, cartoonish avatar character 50 that appears to be an anthropomorphic bumblebee. These elements 50, 40 are "virtual" in that they do not exist in the real world. Due to the complexity of the human visual perception system, producing AR technology that facilitates a comfortable, natural-feeling, and rich presentation of virtual image elements among other virtual or real-world image elements is challenging.

[0006] The systems and methods disclosed herein address various challenges associated with AR or VR technology. Summary of the Invention [Means for solving the problem]

[0007] In a first aspect, a method for fabricating an optical element includes providing a substrate having a first refractive index and transparency in the visible spectrum. The method additionally includes forming a periodically repeating polymer structure on the substrate. The method further includes exposing the substrate to a metal precursor and then to an oxidizing precursor. The exposing of the substrate is carried out under pressure and temperature such that inorganic material, including the metal of the metal precursor, is incorporated into the periodically repeating polymer structure, thereby forming a pattern of a periodically repeating optical structure configured to diffract visible light. The optical structure has a second refractive index greater than the first refractive index.

[0008] In a second aspect, an optical element includes a substrate having a first refractive index and transparency within the visible spectrum. The optical element additionally includes a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light. The optical structures include a polymeric material having a second refractive index greater than the first refractive index and having inorganic material incorporated therein.

[0009] In a third aspect, an optical system includes an optical element. The optical element includes a substrate having a first refractive index and transparency within the visible spectrum. The optical element additionally includes a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light. The optical structures include a polymer material having a second refractive index greater than the first refractive index and having an inorganic material incorporated therein. The periodically repeating optical structures include nanobeams arranged as a metasurface. The metasurface includes a plurality of repeating unit cells, each unit cell including a set of first nanobeams formed by one or more first nanobeams and a set of second nanobeams formed by one or more second nanobeams positioned adjacent to the one or more first nanobeams and separated from each other by subwavelength spacing. The one or more first nanobeams and the plurality of second nanobeams are elongated in different orientation directions.

[0010] In a fourth aspect, an optical system includes a waveguide configured to propagate visible light. The optical system includes a substrate having a first refractive index and transparency within the visible spectrum such that light can be guided therein by total internal reflection. The optical system additionally includes a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light. The optical structures include a polymeric material having a second refractive index greater than the first refractive index and having inorganic material incorporated therein. The periodically repeating optical structures are arranged to diffract light at a diffraction angle relative to the direction of the incident light and cause the diffracted light to propagate within the substrate under total internal reflection, or are arranged to diffract light guided within the substrate under total internal reflection at a diffraction angle relative to the direction of the light guided within the substrate.

[0011] In a fifth aspect, a head-mounted display device is configured to project light to a user's eye and display augmented reality image content. The head-mounted display device includes a frame configured to be supported on the user's head. The head-mounted display device also includes a display disposed on the frame, at least a portion of the display including one or more waveguides. The one or more waveguides are transparent and positioned in front of the user's eye such that, when the user wears the head-mounted display device, the transparent portion transmits light from a portion of the environment in front of the user to the user's eye, providing a view of the portion of the environment in front of the user. The head-mounted display device also includes one or more light sources and at least one diffraction grating configured to couple light from the light sources into or out of the one or more waveguides. The at least one diffraction grating includes a substrate having a first refractive index and transparency within the visible spectrum. The at least one diffraction grating also includes a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light. The optical structure includes a polymeric material having a second refractive index greater than the first refractive index and having an inorganic material incorporated therein.

[0012] In a sixth aspect, a method of fabricating an optical element includes providing a substrate transparent in the visible spectrum, forming a periodically repeating polymer structure on the substrate having a first refractive index, and exposing the substrate to a metal precursor and then to an oxidizing precursor, the exposing being carried out at a pressure and temperature such that inorganic material, including the metal of the metal precursor, becomes incorporated into the periodically repeating polymer structure, thereby increasing the refractive index of the periodically repeating polymer structure and forming a pattern of periodically repeating optical structures configured to diffract visible light.

[0013] In a seventh aspect, a method of fabricating an optical element includes providing a substrate having a first refractive index and transparency in the visible spectrum, the substrate having a periodically repeating polymer structure formed thereon. The method additionally includes exposing the substrate to a metal precursor and then to an oxidizing precursor. The exposing is carried out under pressure and temperature such that inorganic material, including the metal of the metal precursor, is incorporated into the periodically repeating polymer structure, thereby forming a pattern of a periodically repeating optical structure configured to diffract visible light, the optical structure having a second refractive index greater than the first refractive index. The present invention provides, for example, the following. (Item 1) 1. A method of fabricating an optical element, comprising: providing a substrate having a first refractive index and transparency within the visible spectrum; forming a periodically repeating polymer structure on the substrate; exposing the substrate to a metal precursor and then to an oxidizing precursor; Including, The exposing is carried out under pressure and temperature such that inorganic material comprising a metal of the metal precursor is incorporated into the periodically repeating polymer structure, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index. (Item 2) An optical element comprising: a substrate having a first refractive index and transparency within the visible spectrum; a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and comprising a polymeric material having an inorganic material incorporated therein; and An optical element comprising: (Item 3) 3. The optical element of claim 2, wherein the polymer material has a bulk refractive index less than the second refractive index and the inorganic material has a bulk refractive index greater than the second refractive index. (Item 4) 3. The optical element of claim 2, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. (Item 5) 3. The optical element of claim 2, wherein the substrate has a refractive index greater than 1.5. (Item 6) 3. The optical element of claim 2, wherein the polymer material comprises a photoresist. (Item 7) 3. The optical element according to item 2, wherein the inorganic material comprises a transition metal oxide. (Item 8) 8. The optical element according to item 7, wherein the inorganic material comprises a metal oxide. (Item 9) 8. The optical element according to item 7, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide and titanium oxide. (Item 10) 8. The optical element of claim 7, wherein the inorganic material is incorporated into a surface region of the optical structure and a core region of the optical structure does not have the inorganic material incorporated therein. (Item 11) 3. The optical element of claim 2, wherein adjacent ones of the periodically repeating optical structures are separated by a space, and a surface of the substrate within the space does not have the inorganic material disposed thereon. (Item 12) 3. The optical element of claim 2, wherein adjacent ones of the periodically repeating optical structures are separated by a space, and the surface of the substrate within the space has formed thereon a layer of polymeric material into which the inorganic material is incorporated, the layer having a thickness less than a height of the optical structures. (Item 13) Item 13. The optical element of item 12, wherein the layer of polymeric material formed in the space is incorporated with the inorganic material throughout its thickness. (Item 14) Item 13. The optical element of item 12, wherein the layer of polymeric material formed in the space is partially incorporated with the inorganic material in a surface region and partially not incorporated with the inorganic material. (Item 15) Item 3. The optical element of item 2, wherein the substrate is configured such that visible light diffracted by the periodically repeating optical structure propagates under total internal reflection. (Item 16) Item 3. The optical element of item 2, wherein the periodically repeating optical structure comprises a metasurface. (Item 17) Item 3. The optical element of item 2, wherein the substrate is configured such that visible light is guided therein under total internal reflection and diffracted out of the substrate by the periodically repeating optical structure. (Item 18) Item 3. The optical element of item 2, wherein the substrate is configured such that visible light is guided therein under total internal reflection, diffracted by the periodically repeating optical structure, and modifies the direction of the light beam propagating within the substrate by total internal reflection. (Item 19) 1. An optical system comprising: An optical element comprising: a substrate having a first refractive index and transparency within the visible spectrum; a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and comprising a polymeric material having an inorganic material incorporated therein; and Equipped with The periodically repeating optical structure comprises nanobeams arranged as a metasurface, the metasurface comprising a plurality of repeating unit cells, each unit cell comprising: a first nanobeam set formed by one or more first nanobeams; a set of second nanobeams formed by one or more second nanobeams, the one or more second nanobeams being disposed adjacent to the one or more first nanobeams and separated from each other by a sub-wavelength spacing; Equipped with the one or more first nanobeams and the plurality of second nanobeams are elongated in different orientation directions. An optical system comprising: (Item 20) 20. The optical system of item 19, wherein the unit cells repeat with a period of about 10 nm to 1 μm or less. (Item 21) 20. The optical system of item 19, wherein the one or more first nanobeams and the second nanobeam are oriented at an angle relative to each other that causes a phase difference between visible light diffracted by the one or more first nanobeams and visible light diffracted by the second nanobeam. (Item 22) 20. The optical system of claim 19, wherein the one or more first nanobeams and the second nanobeam are oriented in orientation directions that are rotated approximately 90 degrees relative to each other. (Item 23) 20. The optical system of claim 19, wherein the unit cells repeat with a period equal to or less than the wavelength, the wavelength being within the visible spectrum. (Item 24) 20. The optical system of claim 19, wherein the one or more first nanobeams and the second nanobeam have a height that is less than the wavelength. (Item 25) 1. An optical system comprising a waveguide configured to propagate visible light, the optical system comprising: a substrate having a first refractive index and transparency within the visible spectrum such that light may be guided therein by total internal reflection; a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and comprising a polymeric material having an inorganic material incorporated therein; and Equipped with an optical system, wherein the periodically repeating optical structures are arranged to diffract light at a diffraction angle relative to the direction of incident light and cause the diffracted light to propagate within the substrate under total internal reflection, or are arranged to diffract light guided within the substrate under total internal reflection at a diffraction angle relative to the direction of light guided within the substrate. (Item 26) 26. The optical system of claim 25, wherein the polymer material has a bulk refractive index less than the second refractive index and the inorganic material has a bulk refractive index greater than the second refractive index. (Item 27) 26. The optical system of claim 25, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. (Item 28) 26. The optical system of claim 25, wherein the diffraction angle is greater than 50 degrees. (Item 29) Item 26. The optical system of item 25, further comprising a light source configured to emit light of the wavelength into the pattern of the periodically repeating optical structures. (Item 30) Item 26. The optical system of item 25, further comprising a spatial light modulator configured to modulate light from the light source and output the modulated light in the pattern of the periodically repeating optical structures. (Item 31) Item 26. The optical system of item 25, wherein the periodically repeating optical structures are arranged to diffract light at a diffraction angle relative to a direction of incident light and cause the diffracted light to propagate within the substrate under total internal reflection. (Item 32) Item 26. The optical system of item 25, wherein the periodically repeating optical structures are arranged to diffract light guided in the substrate under total internal reflection at a diffraction angle relative to the direction of the light guided in the substrate. (Item 33) Item 33. The optical system of item 32, wherein the periodically repeating optical structures are arranged to diffract light guided within the substrate out of the substrate under total internal reflection. (Item 34) 1. A head-mounted display device configured to project light onto a user's eye and display augmented reality image content, the head-mounted display device comprising: a frame configured to be supported on the user's head; a display disposed on the frame, at least a portion of the display comprising: one or more waveguides, the one or more waveguides being transparent and positioned at locations in front of the user's eyes such that, when the user wears the head mounted display device, a transparent portion transmits light from a portion of the environment in front of the user to the user's eyes to provide a view of the portion of the environment in front of the user; one or more light sources; at least one diffraction grating configured to couple light from the light source into the one or more waveguides or to couple light out of the one or more waveguides, the diffraction grating comprising: a substrate having a first refractive index and transparency within the visible spectrum; a pattern of periodically repeating optical structures formed on the substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and comprising a polymeric material having an inorganic material incorporated therein; and At least one diffraction grating comprising: a display and A head-mounted display device comprising: (Item 35) Item 35. The device of item 34, wherein the one or more light sources comprise a fiber scanning projector. (Item 36) Item 35. The device of item 34, wherein the display is configured to project light into the user's eye to present image content to the user at multiple depth planes. (Item 37) 1. A method of fabricating an optical element, comprising: providing a substrate that is transparent within the visible spectrum; forming a periodically repeating polymer structure on the substrate, the periodically repeating polymer structure having a first refractive index; exposing the substrate to a metal precursor and then to an oxidizing precursor; Including, The method wherein the exposing is carried out at a pressure and temperature such that inorganic material comprising the metal of the metal precursor is incorporated into the periodically repeating polymer structure, thereby increasing the refractive index of the periodically repeating polymer structure and forming a pattern of periodically repeating optical structures configured to diffract visible light. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 illustrates a user's view of an augmented reality (AR) device.

[0015] [Figure 2] FIG. 2 illustrates an example of a wearable display system.

[0016] [Figure 3] FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user.

[0017] [Figure 4] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes.

[0018] [Figure 5] 5A-5C illustrate the relationship between the radius of curvature and the radius of focus.

[0019] [Figure 6] FIG. 6 illustrates an embodiment of a waveguide stack for outputting image information to a user.

[0020] [Figure 7] FIG. 7 illustrates an example of an output beam output by a waveguide.

[0021] [Figure 8] FIG. 8 illustrates an example of a stacked waveguide assembly where each depth plane contains an image formed using multiple different primary colors.

[0022] [Figure 9A] FIG. 9A illustrates a cross-sectional side view of an example of a set of stacked waveguides, each including an internal coupling optical element.

[0023] [Figure 9B] FIG. 9B illustrates a perspective view of the multiple stacked waveguide embodiment of FIG. 9A.

[0024] [Figure 9C] FIG. 9C illustrates a top-down plan view of the multiple stacked waveguide embodiment of FIGS. 9A and 9B.

[0025] [Figure 10] FIG. 10 schematically illustrates a cross-sectional view of an optical element comprising a periodically repeating polymer-based optical structure having inorganic materials incorporated therein.

[0026] [Figure 11] FIG. 11 illustrates diagrammatically a method of fabricating an optical element comprising a periodically repeating polymer-based optical structure having inorganic materials incorporated therein.

[0027] [Figure 12] 12A-12C are cross-sectional views of intermediate structures at various stages in providing a periodically repeating base polymer structure using a photolithographic process.

[0028] [Figure 13] 13A-13C are cross-sectional views of intermediate structures at various stages in the fabrication of a periodically repeating base polymer structure using a nanoimprint process.

[0029] [Figure 14] 14A-14B are cross-sectional views of intermediate structures at various stages in the fabrication of an optical element comprising a periodically repeating polymer-based optical structure having inorganic materials incorporated therein.

[0030] [Figure 15] 15A-15B are cross-sectional views of intermediate structures at various stages in the fabrication of an optical element comprising a periodically repeating polymer-based optical structure having inorganic materials incorporated therein.

[0031] [Figure 16] 16A-16B are cross-sectional views of intermediate structures at various stages in the fabrication of an optical element comprising a periodically repeating polymer-based optical structure having inorganic materials incorporated therein.

[0032] [Figure 17] 17A-17H illustrate an optical element comprising a plurality of waveplate elements, each comprising a pattern of periodically repeating polymer-based optical structures having inorganic material incorporated therein that respond to changes in the polarization vector of incident light corresponding to rotations of the fast axis of the waveplate element by angles θ of 0, π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4, respectively.

[0033] [Figure 18A]FIG. 18A illustrates a cross-sectional side view of a diffraction grating having a two-level geometric phase optical element formed from a polymer-based optical structure having inorganic materials incorporated therein.

[0034] [Figure 18B] FIG. 18B illustrates a top-down view of the diffraction grating of FIG. 18A.

[0035] [Figure 19] FIG. 19 illustrates a top-down view of a diffraction grating having a four-phase level geometric phase optical element formed from a polymer-based optical structure having inorganic materials incorporated therein. DETAILED DESCRIPTION OF THE INVENTION

[0036] Optical systems, such as display systems, often utilize optical elements to control the propagation of light. In some applications, due to the demand for compact optical systems, optical elements having reduced dimensions (e.g., thin structures) can be useful. Such optical elements can include, for example, diffractive optical elements.

[0037] An exemplary diffractive optical element is a diffraction grating for coupling light into an optical waveguide, e.g., a waveguide. The optical waveguide may have a diffraction grating configured, e.g., disposed on or within it, to couple light incident on the optical waveguide at normal incidence into the optical waveguide at an angle such that the diffracted light is guided within the optical waveguide by total internal reflection. A diffractive optical element, such as a diffraction grating, may be included within or on an optical waveguide to couple light guided within the optical waveguide out of the optical waveguide by total internal reflection. Diffractive optical elements may also be used to manipulate, e.g., redirect and / or modify a beam of light propagating within the optical waveguide by total internal reflection. Also, methods as described herein for fabricating such diffractive optical elements may be useful to provide increased confinement of light within an optical waveguide and / or increase diffraction efficiency.

[0038] Such diffractive optical elements may comprise a pattern of periodically repeating optical structures formed on a substrate and configured to diffract visible light, the optical structures having a refractive index greater than that of the substrate. The diffractive optical elements are formed from a polymer material having an inorganic material incorporated therein. The polymer material can, in some cases, act as a photoresist that remains in the final optical structure, significantly reducing processing complexity. The incorporation of inorganic materials into the optical structure potentially allows for versatile tuning of optical properties, such as refractive index, and mechanical properties, such as stiffness. The inorganic materials can be incorporated using atomic layer deposition, which can allow for precise control of the amount and depth of incorporation into the optical structure.

[0039] Another approach to providing compact optical elements involves the use of diffraction gratings based on thin films, e.g., metasurfaces formed from thin-film-based nanostructures. Metasurfaces, i.e., metamaterial surfaces, offer the opportunity to realize virtually flat, aberration-free optical systems at scales much smaller than geometric optics. Without being limited by theory, in some embodiments, metasurfaces comprise dense arrays of surface structures that function as resonant optical antennas. The resonant nature of the interaction between light and the surface structures provides the ability to manipulate optical wavefronts. In some cases, metasurfaces may enable the replacement of bulky or difficult-to-manufacture optical components with thin, relatively planar elements formed by simple patterning processes. However, fabrication of thin-film-based optical elements can involve patterning metals or high-index dielectric materials by lithography or nanoimprinting, both of which can be expensive and / or difficult to implement for structures with small dimensions and / or complex shapes.

[0040] Advantageously, polymer-based optical structures having inorganic materials incorporated therein can be configured as metasurfaces to form various optical elements, including diffraction gratings. The metasurfaces may take the form of gratings formed by a plurality of repeating unit cells. Each unit cell may comprise two or more sets of nanobeams elongated in intersection directions, i.e., one or more first nanobeams elongated in a first direction and a plurality of second nanobeams elongated in a second direction different from the first direction.

[0041] Some diffractive optical elements, including metasurfaces formed from polymer-based optical structures, may be utilized within wearable display systems to provide compact optical elements. Augmented reality systems can display virtual content to a user or viewer while still allowing the user to see the world around them. This content can be displayed on a head-mounted display, which may be mounted on the viewer's head. The head-mounted display may be part of eyewear, for example, and may project image information into the user's eyes. In addition, the display may also transmit light from the surrounding environment to the user's eyes, allowing a view of the surrounding environment.

[0042] Reference is now made to the drawings, wherein like reference numerals refer to like parts throughout.

[0043] Exemplary Display System FIG. 2 illustrates an example of a wearable display system 60. The display system 60 includes a display 70 and various mechanical and electronic modules and systems to support the functionality of the display 70. The display 70 may be coupled to a frame 80, which is wearable by a display system user or viewer 90 and configured to position the display 70 directly in front of the user's 90 eyes. The display 70 may, in some embodiments, be considered eyewear. In some embodiments, a speaker 100 is coupled to the frame 80 and configured to be positioned adjacent to the user's 90 ear canal (in some embodiments, another speaker, not shown, may optionally be positioned adjacent the user's other ear canal to provide stereo / shapeable sound control). The display system may also include one or more microphones 110 or other devices to detect sound. In some embodiments, the microphone may be configured to allow a user to provide input or commands (e.g., voice menu command selections, natural language questions, etc.) to system 60 and / or enable audio communication with other persons (e.g., other users of similar display systems). The microphone may also be configured as an ambient sensor to collect audio data (e.g., sounds from the user and / or the environment). In some embodiments, the display system may also include ambient sensor 120a, which may be separate from frame 80 and attached to the body of user 90 (e.g., the head, torso, on the limbs, etc. of user 90). Ambient sensor 120a, in some embodiments, may be configured to obtain data characterizing a physiological state of user 90. For example, sensor 120a may be an electrode.

[0044] 2, the display 70 is operably coupled by a communication link 130, such as wired or wireless connectivity, to a local data processing module 140, which may be mounted in a variety of configurations, such as fixedly attached to the frame 80, fixedly attached to a helmet or hat worn by the user, integrated into headphones, or otherwise removably attached to the user 90 (e.g., in a backpack-type configuration, in a belt-type configuration). Similarly, the sensor 120a may be operably coupled to the local data processing module 140 by a communication link 120b, such as wired or wireless connectivity. The local processing and data module 140 may include a hardware processor and digital memory, such as non-volatile memory (e.g., flash memory or a hard disk drive), both of which may be utilized to aid in processing, caching, and storing data. The data includes a) data captured from sensors (e.g., which may be operatively coupled to frame 80 or otherwise attached to user 90), such as image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, wireless devices, gyroscopes, and / or other sensors disclosed herein, and / or b) data obtained and / or processed using remote processing module 150 and / or remote data repository 160 (including data related to virtual content), possibly for processing or retrieval and then passage to display 70. Local processing and data module 140 may be operatively coupled to remote processing module 150 and remote data repository 160 by communication links 170, 180, such as via wired or wireless communication links, such that these remote modules 150, 160 are operatively coupled to each other and available as resources to local processing and data module 140. In some embodiments, the local processing and data module 140 may include one or more of an image capture device, a microphone, an inertial measurement unit, an accelerometer, a compass, a GPS unit, a wireless device, and / or a gyroscope.In some other embodiments, one or more of these sensors may be mounted on the frame 80 or may be freestanding structures that communicate with the local processing and data module 140 via wired or wireless communication paths.

[0045] 2 , in some embodiments, remote processing module 150 may comprise one or more processors configured to analyze and process data and / or image information. In some embodiments, remote data repository 160 may comprise a digital data storage facility that may be available through the Internet or other networking configuration in a “cloud” resource configuration. In some embodiments, remote data repository 160 may include one or more remote servers that provide information, for example, information for generating augmented reality content, to local processing and data module 140 and / or remote processing module 150. In some embodiments, all data is stored and all calculations are performed within the local processing and data module, allowing for fully autonomous use from the remote module.

[0046] Referring now to FIG. 3, the perception of an image as “three-dimensional” or “3-D” can be achieved by providing a slightly different presentation of the image to each eye of a viewer. FIG. 3 illustrates a conventional display system for simulating a three-dimensional image for a user. Two distinct images 190, 200, one for each eye 210, 220, are output to the user. The images 190, 200 are spaced from the eyes 210, 220 by a distance 230 along an optical axis, or z-axis, parallel to the viewer's line of sight. The images 190, 200 are flat, and the eyes 210, 220 can focus on the images by assuming a single accommodative state. Such a 3-D display system relies on the human visual system to combine the images 190, 200 and provide the perception of depth and / or scale of the combined image.

[0047] However, it should be appreciated that the human visual system is more complex and providing a realistic perception of depth is more difficult. For example, many viewers of conventional “3-D” display systems find such systems uncomfortable or may not perceive any sense of depth at all. Without being limited by theory, it is believed that viewers of objects may perceive the objects as “three-dimensional” due to a combination of vergence and accommodation. The vergence of two eyes relative to each other (i.e., the rolling of the eyes, in which the pupils move toward or away from each other to converge the gaze of the eyes and fixate on an object) is closely linked to the focusing (or “accommodation”) of the eye lenses and pupils. Under normal conditions, changing the focus of the eye's lens, or accommodating the eye and shifting focus from one object at a different distance to another, will automatically produce a matched change in convergence at the same distance, a relationship known as the "accommodation-vergence reflex" and pupil dilation or constriction. Similarly, changes in convergence will induce a matched change in accommodation in lens shape and pupil size under normal conditions. As described herein, many stereoscopic or "3-D" display systems display a scene using slightly different presentations (and therefore slightly different images) to each eye so that a three-dimensional perspective is perceived by the human visual system. However, such systems can be uncomfortable for many users, particularly because they simply provide different presentations of the scene, but the eyes view all image information in a single accommodated state, working against the "accommodation-vergence reflex." Display systems that provide better matching between accommodation and convergence may produce more realistic and comfortable simulations of three-dimensional images.

[0048] FIG. 4 illustrates aspects of an approach for simulating a three-dimensional image using multiple depth planes. With reference to FIG. 4 , objects at various distances from the eyes 210, 220 on the z-axis are accommodated by the eyes 210, 220 so that the objects are in focus. The eyes 210, 220 assume particular accommodated states, focusing objects at different distances along the z-axis. As a result, a particular accommodated state may be said to be associated with a particular one of the depth planes 240 having an associated focal length such that an object or portion of an object at a particular depth plane is in focus when the eye is in an accommodated state relative to that depth plane. In some embodiments, a three-dimensional image may be simulated by providing a different presentation of an image for each eye 210, 220 and by providing a different presentation of an image corresponding to each of the depth planes. While shown as separate for clarity of illustration, it should be understood that the fields of view of the eyes 210, 220 may overlap, for example, as the distance along the z-axis increases. Additionally, although shown as flat for ease of illustration, it should be understood that the contour of the depth plane may be curved in physical space so that all features within the depth plane are in focus with the eye in a particular accommodative state.

[0049] The distance between an object and the eye 210 or 220 can also change the amount of divergence of light from the object as viewed by that eye. Figures 5A-5C illustrate the relationship between distance and divergence of light rays. The distance between the object and the eye 210 is represented by decreasing distances R1, R2, and R3. As shown in Figures 5A-5C, light rays become more divergent as the distance to the object decreases. As the distance increases, the light rays become more collimated. In other words, the light field generated by a point (an object or part of an object) can be said to have a spherical wavefront curvature that is a function of the distance the point is from the user's eye. The curvature increases as the distance between the object and the eye 210 decreases. As a result, the divergence of light rays at different depth planes also differs, and the divergence increases as the distance between the depth plane and the viewer's eye 210 decreases. While only a single eye 210 is illustrated in FIGS. 5A-5C and various other figures herein for clarity of illustration, it should be understood that the discussion regarding eye 210 may apply to both eyes 210 and 220 of a viewer.

[0050] Without being limited by theory, it is believed that the human eye is typically capable of interpreting a finite number of depth planes to provide depth perception. As a result, a highly realistic simulation of perceived depth can be achieved by providing the eye with different representations of images corresponding to each of these limited number of depth planes. The different representations may be focused separately by the viewer's eyes, thereby serving to provide depth cues to the user based on the ocular accommodation required to focus on different image features for a scene located on the different depth planes and / or based on the observation of different image features on the different depth planes that are out of focus.

[0051] FIG. 6 illustrates an example of a waveguide stack for outputting image information to a user. Display system 250 includes a stack of waveguides or stacked waveguide assembly 260 that can be utilized to provide a three-dimensional perception to the eye / brain using multiple waveguides 270, 280, 290, 300, 310. In some embodiments, display system 250 is system 60 of FIG. 2 , and FIG. 6 diagrammatically illustrates some portions of system 60 in greater detail. For example, waveguide assembly 260 may be part of display 70 of FIG. 2 . It should be understood that display system 250 may, in some embodiments, be considered a light field display.

[0052] Continuing with reference to FIG. 6, the waveguide assembly 260 may also include multiple features 320, 330, 340, 350 between the waveguides. In some embodiments, the features 320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280, 290, 300, 310 and / or multiple lenses 320, 330, 340, 350 may be configured to transmit image information to the eye using various levels of wavefront curvature or ray divergence. Each waveguide level may be associated with a particular depth plane and configured to output image information corresponding to that depth plane. The image injection devices 360, 370, 380, 390, 400 may act as light sources for the waveguides and may be utilized to inject image information into the waveguides 270, 280, 290, 300, 310, each configured to disperse incident light across each individual waveguide for output toward the eye 210, as described herein. Light exits output surfaces 410, 420, 430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 and is injected into corresponding input surfaces 460, 470, 480, 490, 500 of the waveguides 270, 280, 290, 300, 310. In some embodiments, each input surface 460, 470, 480, 490, 500 may be an edge of the corresponding waveguide or may be a portion of a major surface of the corresponding waveguide (i.e., one of the waveguide surfaces that directly faces the world 510 or the viewer's eye 210). In some embodiments, a single beam of light (e.g., a collimated beam) may be launched into each waveguide, outputting a total field of cloned collimated beams that are directed toward the eye 210 at a particular angle (and divergence) corresponding to the depth plane associated with the particular waveguide. In some embodiments, a single one of the image launch devices 360, 370, 380, 390, 400 may be associated with and launch light into multiple (e.g., three) waveguides 270, 280, 290, 300, 310.

[0053] In some embodiments, each of the image input devices 360, 370, 380, 390, 400 is a discrete display that generates image information for input into a corresponding waveguide 270, 280, 290, 300, 310. In some other embodiments, the image input devices 360, 370, 380, 390, 400 are the output of a single multiplexed display that may, for example, send image information via one or more optical conduits (such as fiber optic cables) to each of the image input devices 360, 370, 380, 390, 400. It should be understood that the image information provided by the image input devices 360, 370, 380, 390, 400 may include light of different wavelengths or colors (e.g., different primary colors, as discussed herein).

[0054] In some embodiments, light injected into the waveguides 270, 280, 290, 300, 310 is provided by a light projector system 520, which includes a light module 530, which may include a light emitter such as a light emitting diode (LED). Light from the light module 530 may be directed to and modified by a light modulator 540, e.g., a spatial light modulator, via a beam splitter 550. The light modulator 540 may be configured to change the perceived intensity of the light injected into the waveguides 270, 280, 290, 300, 310. Examples of spatial light modulators include liquid crystal displays (LCDs), including liquid crystal on silicon (LCOS) displays.

[0055] In some embodiments, the display system 250 may be a scanning fiber display comprising one or more scanning fibers configured to project light in various patterns (e.g., raster scan, spiral scan, Lissajous pattern, etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimately to the viewer's eye 210. In some embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent a single scanning fiber or a bundle of scanning fibers configured to inject light into one or more waveguides 270, 280, 290, 300, 310. In some other embodiments, the illustrated image injection devices 360, 370, 380, 390, 400 may diagrammatically represent multiple scanning fibers or multiple bundles of scanning fibers, each configured to inject light into an associated one of the waveguides 270, 280, 290, 300, 310. It should be understood that one or more optical fibers may be configured to transmit light from the optical module 530 to one or more waveguides 270, 280, 290, 300, 310. It should be understood that one or more intervening optical structures may be provided between the scanning fiber or fibers and one or more waveguides 270, 280, 290, 300, 310, for example, to redirect light exiting the scanning fiber into one or more waveguides 270, 280, 290, 300, 310.

[0056] Controller 560 controls the operation of one or more of stacked waveguide assemblies 260, including the operation of image input devices 360, 370, 380, 390, 400, light source 530, and light module 540. In some embodiments, controller 560 is part of local data processing module 140. Controller 560 includes programming (e.g., instructions in a non-transitory medium) that coordinates the timing and provision of image information to waveguides 270, 280, 290, 300, 310, for example, according to any of the various schemes disclosed herein. In some embodiments, the controller may be a single integrated device or a distributed system connected by a wired or wireless communication channel. Controller 560 may, in some embodiments, be part of processing module 140 or 150 (FIG. 2).

[0057] Continuing with reference to FIG. 6 , the waveguides 270, 280, 290, 300, and 310 may be configured to propagate light within each individual waveguide by total internal reflection (TIR). Each of the waveguides 270, 280, 290, 300, and 310 may be planar or have another shape (e.g., curved) with major top and bottom surfaces and edges extending between the major top and bottom surfaces. In the illustrated configuration, the waveguides 270, 280, 290, 300, and 310 may each include outcoupling optical elements 570, 580, 590, 600, and 610 configured to extract light from the waveguide by redirecting light propagating within each individual waveguide and outputting image information from the waveguide to the eye 210. The extracted light may also be referred to as outcoupled light, and the optical element that outcouples light may also be referred to as a light extraction optical element. The extracted beam of light may be output by the waveguide at a location where light propagating within the waveguide strikes the light extraction optical element. The outcoupling optical element 570, 580, 590, 600, 610 may be a grating, for example, including diffractive optical features as discussed further herein. While shown disposed on the bottom major surface of the waveguides 270, 280, 290, 300, 310 for ease of explanation and clarity of the drawings, in some embodiments, the outcoupling optical element 570, 580, 590, 600, 610 may be disposed on the top and / or bottom major surfaces and / or directly within the volume of the waveguides 270, 280, 290, 300, 310, as discussed further herein. In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 may be formed within a layer of material attached to a transparent substrate and forming the waveguides 270, 280, 290, 300, 310. In some other embodiments, the waveguides 270, 280, 290, 300, 310 may be monolithic pieces of material, and the outcoupling optical elements 570, 580, 590, 600, 610 may be formed on and / or within the material pieces.

[0058] Continuing with reference to FIG. 6 , as discussed herein, each waveguide 270, 280, 290, 300, 310 is configured to output light and form an image corresponding to a particular depth plane. For example, the waveguide 270 closest to the eye may be configured to deliver collimated light (injected into such waveguide 270) to the eye 210. The collimated light may represent an optical infinity focal plane. The next upper waveguide 280 may be configured to send collimated light that passes through a first lens 350 (e.g., a negative lens) before reaching the eye 210. Such first lens 350 may be configured to generate a slight convex wavefront curvature so that the eye / brain interprets light emerging from the next upper waveguide 280 as emerging from a first focal plane closer inward from optical infinity toward the eye 210. Similarly, the third upper waveguide 290 passes its output light through both the first lens 350 and the second lens 340 before reaching the eye 210. The combined refractive power of the first lens 350 and the second lens 340 may be configured to produce another, increasing amount of wavefront curvature such that the eye / brain interprets the light emerging from the third waveguide 290 as originating from a second focal plane that is closer inward from optical infinity towards the person than was the light from the next upper waveguide 280.

[0059] The other waveguide layers 300, 310 and lenses 330, 320 are similarly configured, with the highest waveguide 310 in the stack sending its output through all of the lenses between it and the eye for a collective focal power representing the focal plane closest to the person. To compensate for the stack of lenses 320, 330, 340, 350 when viewing / interpreting light originating from the world 510 on the other side of the stacked waveguide assembly 260, a compensating lens layer 620 may be placed on top of the stack to compensate for the collective power of the lower lens stacks 320, 330, 340, 350. Such a configuration provides as many perceived focal planes as there are available waveguide / lens pairs. Both the outcoupling optical elements of the waveguides and the focusing sides of the lenses may be static (i.e., not dynamic or electro-active). In some alternative embodiments, one or both may be dynamic using electro-active features.

[0060] In some embodiments, two or more of the waveguides 270, 280, 290, 300, 310 may have the same associated depth plane. For example, multiple waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth plane, or multiple subsets of waveguides 270, 280, 290, 300, 310 may be configured to output images set at the same depth planes, with one set per depth plane. This may provide the advantage of forming tiled images to provide an extended field of view at those depth planes.

[0061] Continuing with reference to FIG. 6 , the outcoupling optical elements 570, 580, 590, 600, 610 may be configured to redirect light from its respective waveguide and output the light with an appropriate amount of divergence or collimation for a particular depth plane associated with that waveguide. As a result, waveguides with different associated depth planes may have different configurations of outcoupling optical elements 570, 580, 590, 600, 610, which output light with different amounts of divergence depending on the associated depth plane. In some embodiments, the light-extraction optical elements 570, 580, 590, 600, 610 may be volume or surface features, which may be configured to output light at specific angles. For example, the light-extraction optical elements 570, 580, 590, 600, 610 may be volume holograms, surface holograms, and / or diffraction gratings. In some embodiments, features 320, 330, 340, 350 may not be lenses. Rather, they may simply be spacers (e.g., cladding layers and / or structures for forming air gaps).

[0062] In some embodiments, the outcoupling optical elements 570, 580, 590, 600, 610 are diffractive features or "diffractive optical elements" (also referred to herein as "DOEs") that form a diffraction pattern. Preferably, the DOEs have a sufficiently low diffraction efficiency so that only a portion of the light in the beam is deflected toward the eye 210 at each intersection of the DOE, while the remainder continues traveling through the waveguide via TIR. The light carrying the image information is thus split into several related output beams that exit the waveguide at various locations, resulting in a fairly uniform pattern of output emission toward the eye 210 for this particular collimated beam bouncing within the waveguide.

[0063] In some embodiments, one or more DOEs may be switchable between an "on" state in which they actively diffract and an "off" state in which they do not significantly diffract. For example, a switchable DOE may comprise a layer of polymer-dispersed liquid crystal in which microdroplets comprise a diffractive pattern in a host medium, and the refractive index of the microdroplets may be switched to substantially match the refractive index of the host material (in which case the pattern does not significantly diffract incident light), or the microdroplets may be switched to a refractive index that does not match that of the host medium (in which case the pattern actively diffracts incident light).

[0064] In some embodiments, a camera assembly 630 (e.g., a digital camera, including visible and infrared light cameras) may be provided to capture images of the eye 210 and / or tissue surrounding the eye 210, for example, to detect user input and / or monitor the physiological state of the user. As used herein, a camera may be any image capture device. In some embodiments, the camera assembly 630 may include an image capture device and a light source that projects light (e.g., infrared light) onto the eye, which may then be reflected by the eye and detected by the image capture device. In some embodiments, the camera assembly 630 may be mounted on the frame 80 ( FIG. 2 ) and may be in electrical communication with processing modules 140 and / or 150, which may process image information from the camera assembly 630. In some embodiments, one camera assembly 630 may be utilized per eye, monitoring each eye separately.

[0065] 7, an example of an output beam output by a waveguide is shown. While one waveguide is illustrated, it should be understood that other waveguides in waveguide assembly 260 (FIG. 6) may function similarly, and that waveguide assembly 260 includes multiple waveguides. Light 640 is launched into waveguide 270 at input surface 460 of waveguide 270 and propagates within waveguide 270 by TIR. At the point where light 640 impinges on DOE 570, a portion of the light exits the waveguide as output beam 650. Output beam 650 is illustrated as being approximately parallel, but may be redirected to propagate to eye 210 at an angle (e.g., forming a diverging output beam), as discussed herein and depending on the depth plane associated with waveguide 270. It should be understood that a nearly collimated exit beam may refer to a waveguide with outcoupling optics that outcouples light to form an image that appears to be set at a depth plane at a large distance (e.g., optical infinity) from the eye 210. Other waveguides or other sets of outcoupling optics may output a more divergent exit beam pattern, which would require the eye 210 to accommodate to a closer distance and focus on the retina, and would be interpreted by the brain as light from a distance closer to the eye 210 than optical infinity.

[0066] In some embodiments, a full-color image may be formed at each depth plane by overlaying an image in each of the primary colors, for example, three or more primary colors. FIG. 8 illustrates an example of a stacked waveguide assembly, with each depth plane including an image formed using multiple different primary colors. The illustrated embodiment shows depth planes 240a-240f, but more or fewer depths are also contemplated. Each depth plane may have three or more primary color images associated with it, including a first image in a first color G, a second image in a second color R, and a third image in a third color B. Different depth planes are indicated in the diagram by different numbers for diopters (dpt) following the letters G, R, and B. By way of example only, the number following each of these letters indicates the diopter (1 / m), i.e., the inverse distance of the depth plane from the viewer, and each box in the diagram represents an individual primary color image. In some embodiments, the exact locations of the depth planes for different primary colors may be varied to account for differences in the eye's focusing of light of different wavelengths. For example, different primary color images for a given depth plane may be placed on depth planes corresponding to different distances from the user. Such an arrangement may increase visual acuity and user comfort and / or reduce chromatic aberrations.

[0067] In some embodiments, light for each primary color may be output by a single dedicated waveguide, such that each depth plane may have multiple waveguides associated with it. In such embodiments, each box in the diagram containing the letter G, R, or B may be understood to represent an individual waveguide, and three waveguides may be provided per depth plane, resulting in three primary color images per depth plane. While the waveguides associated with each depth plane are shown adjacent to each other in this drawing for ease of illustration, it should be understood that in a physical device, the waveguides may all be arranged in a stack with one waveguide per level. In some other embodiments, multiple primary colors may be output by the same waveguide, such that, for example, only a single waveguide may be provided per depth plane.

[0068] 8, in some embodiments, G is green, R is red, and B is blue. In some other embodiments, other colors associated with other wavelengths of light, including magenta and cyan, may be used in addition to or replace one or more of red, green, or blue.

[0069] It should be understood that references throughout this disclosure to a given color of light are understood to encompass light of one or more wavelengths within the range of wavelengths of light that are perceived by a viewer as that given color. For example, red light may include one or more wavelengths of light that are within the range of about 620-780 nm, green light may include one or more wavelengths of light that are within the range of about 492-577 nm, and blue light may include one or more wavelengths of light that are within the range of about 435-493 nm.

[0070] In some embodiments, light source 530 (FIG. 6) may be configured to emit light at one or more wavelengths outside the range of a viewer's visual perception, e.g., infrared and / or ultraviolet wavelengths. Additionally, the waveguide incoupling, outcoupling, and other light redirecting structures of display 250 may be configured to direct and emit this light from the display toward the user's eye 210, e.g., for imaging and / or user stimulation applications.

[0071] Referring now to FIG. 9A , in some embodiments, light impinging on a waveguide may need to be redirected to incoupling the light into the waveguide. An incoupling optical element may be used to redirect and incoupling the light into its corresponding waveguide. FIG. 9A illustrates a cross-sectional side view of an example of a plurality or set 660 of stacked waveguides, each including an incoupling optical element. The waveguides may each be configured to output light of one or more different wavelengths or one or more different wavelength ranges. While stack 660 may correspond to stack 260 ( FIG. 6 ), and the illustrated waveguides of stack 660 may correspond to a portion of multiple waveguides 270, 280, 290, 300, 310, it should be understood that light from one or more of image injection devices 360, 370, 380, 390, 400 is injected into the waveguide from a location requiring the light to be redirected for incoupling.

[0072] The illustrated set 660 of stacked waveguides includes waveguides 670, 680, and 690. Each waveguide includes an associated internal coupling optical element (which may also be referred to as the light input area on the waveguide), for example, internal coupling optical element 700 is disposed on a major surface (e.g., the top major surface) of waveguide 670, internal coupling optical element 710 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and internal coupling optical element 720 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some embodiments, one or more of internal coupling optical elements 700, 710, 720 may be disposed on the bottom major surface of an individual waveguide 670, 680, 690 (particularly, one or more internal coupling optical elements are reflective polarizing optical elements). As shown, the internal coupling optical elements 700, 710, 720 may be disposed on the upper major surfaces of their respective waveguides 670, 680, 690 (or on top of the next lower waveguide), and in particular, the internal coupling optical elements are transmissive turning optical elements. In some embodiments, the internal coupling optical elements 700, 710, 720 may be disposed within the body of the respective waveguides 670, 680, 690. In some embodiments, as discussed herein, the internal coupling optical elements 700, 710, 720 are wavelength selective, selectively redirecting one or more wavelengths of light while transmitting other wavelengths of light. While illustrated on one side or corner of the respective waveguides 670, 680, 690, it should be understood that the internal coupling optical elements 700, 710, 720 may be disposed within other areas of the respective waveguides 670, 680, 690 in some embodiments.

[0073] As shown, the in-coupling optical elements 700, 710, 720 may be laterally offset from one another. In some embodiments, each in-coupling optical element may be offset to receive light without that light passing through another in-coupling optical element. For example, each in-coupling optical element 700, 710, 720 may be configured to receive light from a different image input device 360, 370, 380, 390, and 400, as shown in FIG. 6 , and may be separated (e.g., laterally spaced) from the other in-coupling optical elements 700, 710, 720 so as to substantially not receive light from others of the in-coupling optical elements 700, 710, 720.

[0074] Each waveguide also includes an associated optically dispersive element, for example, optically dispersive element 730 is disposed on a major surface (e.g., the top major surface) of waveguide 670, optically dispersive element 740 is disposed on a major surface (e.g., the top major surface) of waveguide 680, and optically dispersive element 750 is disposed on a major surface (e.g., the top major surface) of waveguide 690. In some other embodiments, optically dispersive elements 730, 740, 750 may be disposed on the bottom major surfaces of the associated waveguides 670, 680, 690, respectively. In some other embodiments, the optically dispersive elements 730, 740, 750 may be disposed on both the top and bottom major surfaces of the associated waveguides 670, 680, 690, respectively, or the optically dispersive elements 730, 740, 750 may be disposed on different ones of the top and bottom major surfaces in different associated waveguides 670, 680, 690, respectively.

[0075] Waveguides 670, 680, 690 may be spaced apart and separated, for example, by gas, liquid, and / or solid layers of material. For example, as shown, layer 760a may separate waveguides 670 and 680, and layer 760b may separate waveguides 680 and 690. In some embodiments, layers 760a and 760b are formed from a low refractive index material (i.e., a material having a lower refractive index than the material forming immediately adjacent ones of waveguides 670, 680, 690). Preferably, the refractive index of the material forming layers 760a, 760b is 0.05 or greater, or 0.10 or less, relative to the refractive index of the material forming waveguides 670, 680, 690. Advantageously, the lower refractive index layers 760a, 760b may function as cladding layers that promote total internal reflection (TIR) of light through the waveguides 670, 680, 690 (e.g., TIR between the top and bottom major surfaces of each waveguide). In some embodiments, the layers 760a, 760b are formed from air. Although not shown, it should be understood that the top and bottom of the illustrated set of waveguides 660 may include immediate cladding layers.

[0076] Preferably, for ease of manufacturing and other considerations, the materials forming waveguides 670, 680, 690 are similar or the same, and the materials forming layers 760a, 760b are similar or the same. In some embodiments, the materials forming waveguides 670, 680, 690 may differ between one or more waveguides, and / or the materials forming layers 760a, 760b may differ while still maintaining the various refractive index relationships discussed above.

[0077] 9A, light rays 770, 780, 790 enter the set of waveguides 660. It should be understood that light rays 770, 780, 790 may be injected into the waveguides 670, 680, 690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG. 6).

[0078] In some embodiments, light rays 770, 780, 790 have different properties, e.g., different wavelengths or different wavelength ranges, which may correspond to different colors. Each of the incoupling optical elements 700, 710, 720 deflects incident light such that the light propagates through a respective one of the waveguides 670, 680, 690 by TIR. In some embodiments, each of the incoupling optical elements 700, 710, 720 selectively deflects one or more particular wavelengths of light while transmitting other wavelengths to the underlying waveguide and associated incoupling optical element.

[0079] For example, in-coupling optical element 700 may be configured to selectively deflect light ray 770 having a first wavelength or wavelength range while transmitting light rays 1242 and 1244 having different second and third wavelengths or wavelength ranges, respectively. Transmitted light ray 780 impinges on and is deflected by in-coupling optical element 710, which is configured to selectively deflect light of the second wavelength or wavelength range. Light ray 790 is deflected by in-coupling optical element 720, which is configured to selectively deflect light of the third wavelength or wavelength range.

[0080] 9A , the deflected light rays 770, 780, 790 are deflected to propagate through the corresponding waveguides 670, 680, 690. That is, the in-coupling optical element 700, 710, 720 of each waveguide deflects the light into its corresponding waveguide 670, 680, 690 and in-couples the light into its corresponding waveguide. The light rays 770, 780, 790 are deflected at an angle that causes the light to propagate through the respective waveguides 670, 680, 690 by TIR. The light rays 770, 780, 790 propagate through the respective waveguides 670, 680, 690 by TIR until they impinge on the waveguide's corresponding optical dispersive element 730, 740, 750.

[0081] 9B, a perspective view of the multiple stacked waveguide embodiment of FIG. 9A is illustrated. As previously described, in-coupled light rays 770, 780, 790 are deflected by in-coupling optical elements 700, 710, 720, respectively, and then propagate by TIR within waveguides 670, 680, 690, respectively. Light rays 770, 780, 790 then impinge on optically dispersive elements 730, 740, 750, respectively. Optically dispersive elements 730, 740, 750 deflect light rays 770, 780, 790 to propagate toward out-coupling optical elements 800, 810, 820, respectively.

[0082] In some embodiments, the optically dispersive elements 730, 740, 750 are orthogonal pupil expanders (OPEs). In some embodiments, the OPEs deflect or disperse light into the out-coupling optical elements 800, 810, 820, and in some embodiments, may also increase the beam or spot size of this light as it propagates into the out-coupling optical elements. In some embodiments, the optically dispersive elements 730, 740, 750 may be omitted, and the in-coupling optical elements 700, 710, 720 may be configured to deflect light directly into the out-coupling optical elements 800, 810, 820. For example, with reference to FIG. 9A , the optically dispersive elements 730, 740, 750 may be replaced with the out-coupling optical elements 800, 810, 820, respectively. In some embodiments, the outcoupling optical elements 800, 810, 820 are exit pupils (EPs) or exit pupil expanders (EPEs) that direct light toward the viewer's eye 210 ( FIG. 7 ). It should be understood that an OPE may be configured to increase the size of the eyebox in at least one axis, and that the EPE may increase the eyebox in an axis that intersects the axis of the OPE, e.g., orthogonal to the axis of the OPE. For example, each OPE may be configured to redirect a portion of the light striking the OPE to an EPE in the same waveguide, while allowing the remaining portion of the light to continue propagating down the waveguide. Again, upon striking the OPE, another portion of the remaining light is redirected to the EPE, and the remainder of that portion continues propagating further down the waveguide, etc. Similarly, in response to striking an EPE, a portion of the impinging light is directed out of the waveguide toward the user, and the remainder of that light continues to propagate through the waveguide until it again strikes an EPE, at which point another portion of the impinging light is directed out of the waveguide, and so on. As a result, a single beam of internally coupled light may be "replicated" each time a portion of that light is redirected by the OPE or EPE, thereby forming a cloned beam field of light, as shown in Figure 6. In some embodiments, the OPE and / or EPE may be configured to modify the size of the beam of light.

[0083] 9A and 9B, in some embodiments, a waveguide set 660 includes, for each primary color, waveguides 670, 680, 690, in-coupling optical elements 700, 710, 720, optically dispersive elements (e.g., OPEs) 730, 740, 750, and out-coupling optical elements (e.g., EPs) 800, 810, 820. The waveguides 670, 680, 690 may be stacked with an air gap / cladding layer between each one. The in-coupling optical elements 700, 710, 720 redirect or deflect incident light into that waveguide (with different in-coupling optical elements receiving different wavelengths of light). The light then propagates at an angle that will result in TIR within the individual waveguides 670, 680, 690. In the example shown, light ray 770 (e.g., blue light) is deflected by the first in-coupling optical element 700 in the manner described above, then continues bouncing back down the waveguide, interacting with the optically dispersive element (e.g., OPE) 730 and then the out-coupling optical element (e.g., EP) 800. Light rays 780 and 790 (e.g., green and red light, respectively) pass through the waveguide 670, where light ray 780 strikes the in-coupling optical element 710 and is deflected thereby. Light ray 780 will then bounce back down the waveguide 680, via TIR, to its optically dispersive element (e.g., OPE) 740 and then the out-coupling optical element (e.g., EP) 810. Finally, light ray 790 (e.g., red light) passes through the waveguide 690 and strikes the optically in-coupling optical element 720 of the waveguide 690. The light in-coupling optical element 720 deflects the light ray 790 so that it propagates by TIR to the light dispersive element (e.g., OPE) 750 and then by TIR to the out-coupling optical element (e.g., EP) 820. The out-coupling optical element 820 then finally out-couples the light ray 790 to a viewer, who also receives the out-coupled light from the other waveguides 670, 680.

[0084] FIG. 9C illustrates a top-down plan view of an example of the multiple stacked waveguides of FIGS. 9A and 9B. As shown, waveguides 670, 680, 690 may be vertically aligned, along with each waveguide's associated optically dispersive elements 730, 740, 750 and associated out-coupling optical elements 800, 810, 820. However, as discussed herein, the in-coupling optical elements 700, 710, 720 are not vertically aligned. Rather, the in-coupling optical elements are preferably non-overlapping (e.g., laterally spaced apart, as seen in the top-down view). As discussed further herein, this non-overlapping spatial arrangement facilitates the injection of light from different sources into different waveguides on a one-to-one basis, thereby allowing a specific light source to be uniquely coupled to a specific waveguide. In some embodiments, arrays including non-overlapping, spatially separated in-coupling optical elements may be referred to as shifted-pupil systems, and the in-coupling optical elements in these arrays may correspond to sub-pupils.

[0085] Optical elements formed from polymer-based optical structures incorporating inorganic materials Display systems may employ various optical elements to control the propagation of light. However, in some contexts, such as display systems, including head-mounted display devices (e.g., display system 80 described above with reference to FIG. 2), conventional optical elements may be undesirable or unsuitable due to their relatively heavy weight, large size, manufacturing challenges, and / or shortcomings in optical properties such as diffraction angle and diffraction efficiency.

[0086] For example, as described above with reference to Figures 9A-9C, a display system may include optical elements (e.g., in-coupling optical elements, light-dispersive elements, and out-coupling optical elements), which may include diffraction gratings. Furthermore, as further described above with reference to Figures 9A-9C, light coupled into a corresponding waveguide may propagate within the waveguide by total internal reflection (TIR). To achieve TIR, it may be desirable for the diffraction grating to have a relatively high diffraction angle relative to the surface normal. In addition, high diffraction efficiency may be desirable to increase light intensity and image brightness. However, providing a diffraction grating capable of achieving high diffraction angles and high diffraction efficiency for visible light may present challenges. To address these and other needs, embodiments of the optical elements, e.g., diffraction gratings, disclosed herein may utilize optical elements formed from periodically repeating polymer-based optical structures incorporating inorganic materials therein.

[0087] 10 illustrates a cross-sectional view of an optical element, e.g., a diffraction grating 1000, comprising a periodically repeating polymer-based optical structure having inorganic material incorporated therein, according to various implementations. The diffraction grating 1000 includes a substrate 1004 having a first refractive index (n1) and transparency within the visible spectrum. The diffraction grating 1000 additionally includes a pattern of periodically repeating optical structures 1008 formed on the substrate 1004 and configured to diffract visible light. The optical structures 1008 include a polymer material having a second refractive index (n2) greater than the first refractive index and having inorganic material incorporated therein.

[0088] According to embodiments, the substrate 1004 is transparent within the visible spectrum. As described herein and throughout this specification, a "transmissive" or "transparent" structure, e.g., a transparent substrate, may allow at least a portion of incident light, e.g., at least 20, 30, 50, 70, 90%, or 95%, to pass therethrough, but may transmit less than 99% or 100%. The percent transmittance may be within any range defined by any of these values, or may be outside these ranges. Thus, a transparent substrate may, in some embodiments, be a glass, sapphire, or polymer substrate. A "reflective" structure, e.g., a reflective substrate, may reflect at least a portion of incident light, e.g., at least 20, 30, 50, 70, 90%, or 95% or more, therefrom, but may reflect less than 99% or 100%. The percent reflectance may be within any range defined by any of these values, or may be outside these ranges.

[0089] According to an embodiment, the substrate 1004 has a first refractive index (n1) that is greater than that of air but less than the second refractive index n2 of the optical structure 1008. n1 can have a value, for example, about 1.5, 1.6, 1.7, 1.8, 1.9, or any value within or outside any range defined by these values. Examples of materials for forming the substrate 1004 include silica glass (e.g., doped silica glass), silicon oxynitride, transition metal oxides (e.g., hafnium oxide, tantalum oxide, zirconium oxide, niobium oxide, lithium niobate, aluminum oxide (e.g., sapphire)), plastic, polymer, or other optically transmissive material having a suitable refractive index, for example, as described herein.

[0090] The pattern of periodically repeating optical structures 1008 formed on the substrate 1004 is configured to diffract visible light due to its material, dimensions, and geometric configuration as described herein.

[0091] Still referring to FIG. 10 , according to various embodiments, optical structure 1008 includes a base polymer material having inorganic material incorporated therein. The base polymer material may include a polymer suitable for incorporation of the inorganic material and for serving as a lithographically patternable material, such as a photosensitive material that can be photolithographically patterned, such as a photoresist, or another material that can be easily patterned. For example, the base polymer material may be polyethylene (PE) (—(CH—CH), to name a few, among other polymers. n -), polypropylene (PP) (-[CH2-CH(CH3)] n -), poly(vinyl chloride) (PVC) (-[CH2-CH(CH3)] n -), poly(vinylidene chloride) (-(CH2-CCl2) n -), polystyrene (PS) (-[CH2-CH(C6H5)] n -), polyacrylonitrile (PAN) (-(CH2-CHCN) n -), polytetrafluoroethylene (PTFE) (-(CF2-CF2) n -), poly(methyl methacrylate) (PMMA) (-[CH2-C(CH3)CO2CH3] n -), poly(vinyl acetate) (PVAc) (-(CH2-CHOCOCH3) n -), cis-polyisoprene (-[CH2-CH=C(CH3)-CH2] n -), and polychloroprene (cis + trans) (-[CH2-CH=CCl-CH2] n In some embodiments, the base polymer chain may be configured as a homopolymer. In some other embodiments, the base polymer chain may be configured as a copolymer. When configured as a copolymer, the base polymer chain may be configured to have one of a variety of morphologies, including, but not limited to, statistical copolymers, alternating copolymers, block copolymers, and graft copolymers, incorporating monomer units of the various polymers described above.

[0092] A specific polymer may be selected based on, among other factors, the deposition chemistry for forming the inorganic material to be incorporated into the base polymer material. For example, in various embodiments, the polymer chain of the base polymer unit may include various functional groups, such as carbonyl, hydroxyl, and pyridine groups, adapted to react with metal precursors that can be used to form the inorganic material, as will be described in more detail below. To provide one example, when the deposition chemistry includes Al(CH)(TMA) as the metal precursor and HO as the oxidation precursor for the formation of AlO, PMMA may be included within the polymer material such that the carbonyl groups of PMMA can react with TMA to form Al-OH species, which in turn react with HO in a hydrolysis reaction to form AlO. Additional examples are described in more detail below.

[0093] In various embodiments, the base polymer can be photosensitive or photoreactive. The base polymer can include or act as a photoresist. In some embodiments, the photoresist can be a positive resist, where portions exposed to light become soluble in a photoresist developer, while portions unexposed remain insoluble in the photoresist developer. In some other embodiments, the photoresist can be a negative photoresist, where portions exposed to light become insoluble in a photoresist developer, while portions unexposed are dissolved by the photoresist developer.

[0094] When included, in some embodiments, the photoresist in the base polymer can be a photopolymer photoresist, which can include, for example, an allylic monomer configured to generate free radicals upon exposure to light, which in turn initiates photopolymerization of the monomers to produce a polymer. When configured as a negative resist, the photopolymer photoresist can include, for example, methyl methacrylate. When included, in some other embodiments, the photoresist in the base polymer can be a photodegradable photoresist configured to generate a hydrophilic product under light. When configured as a positive resist, the photodegradable photoresist can include, for example, an azidoquinone, e.g., diazonaphthoquinone (DQ). When included, in some other embodiments, the photoresist in the base polymer can be a photocrosslinkable photoresist configured to crosslink chain-by-chain upon exposure to light to generate an insoluble network.

[0095] 10 , inorganic materials incorporated into optical structure 1008, according to various embodiments, may include insulating materials, such as metal oxides or metal nitrides. In some embodiments, the inorganic materials include oxides, nitrides, or oxynitrides of one or more transition metals, including, but not limited to, Al, Zn, Zr, Hf, Ti, and Ta. For example, the inorganic materials may include aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, titanium oxide, tantalum oxide, and combinations thereof, to name a few.

[0096] As described herein, when an inorganic material comprises an oxide, it can be stoichiometric or substoichiometric. For example, aluminum oxide can be in the stoichiometric form of Al2O3 and in the substoichiometric form of AlO x where x is less than the stoichiometric value of 1.5. Additionally, as described herein, the oxide of a metal can include other metals. For example, aluminum oxide can be aluminum hafnate (AlHfO x) The material may therefore comprise two different metals.

[0097] According to embodiments, the inorganic material may be selected based on its bulk refractive index. The refractive index of the inorganic material may be higher than the refractive index of the substrate. The refractive index of the inorganic material may be, for example, greater than 1.7, 2.0, 2.3, 2.6, 3.0, or within a range defined by these values, or may be outside these ranges. In some embodiments, the inorganic material may be a stoichiometric material selected based on its bulk refractive index. For example, the inorganic material may be stoichiometric aluminum oxide having a refractive index of 1.66, stoichiometric zinc oxide having a refractive index of 1.95, stoichiometric zirconium oxide having a refractive index of 1.95, stoichiometric hafnium oxide having a refractive index of 2.09, stoichiometric titanium oxide having a refractive index of 2.35, or combinations thereof, to name a few. In some other embodiments, the inorganic material may be a substoichiometric inorganic material having a refractive index greater than that of the corresponding stoichiometric inorganic material. For example, the refractive index of a metal oxide can be increased by 2%, 5%, 10%, 20%, or 30%, or any percentage within any range defined by these values, by reducing the oxygen content. In some other embodiments, the inorganic material may be a mixture of inorganic materials having a refractive index between the refractive indices of the component inorganic materials. For example, the refractive index of a ternary metal oxide may be adjusted to be between the refractive indices of the component binary metal oxides by adjusting the relative proportions.

[0098] In some embodiments, the optical structure 1008 has a refractive index between that of the base polymer material and the inorganic material incorporated therein. In various embodiments, the second refractive index of the optical structure including the optical material is greater than 1.7, 1.8, 1.9, 2.0, or 2.1 and is at least 0.2, 0.4, 0.6, 0.8, or 1.0 greater than the first refractive index of the substrate. However, embodiments are not so limited, and the second refractive index can be the same as or lower than the first refractive index.

[0099] The base polymer material of the optical structures 1008 can have inorganic material incorporated therein in various configurations. In the illustrated embodiment, the optical structures 1008 comprise a base polymer region 1008a and an infiltrated region 1008b infiltrated with the inorganic material described above. In the illustrated embodiment, the inorganic material is incorporated into the surface regions of the optical structures 1008 such that each optical structure 1008 has a base polymer region 1008a comprising a core region substantially free of inorganic material incorporated therein, and an infiltrated region 1008b comprising a surface region having inorganic material infiltrated therein.

[0100] According to embodiments, the infiltrated region 1008b has a width, depth, or thickness greater than about 1 nm, 10 nm, 20 nm, 50 nm, 100 nm, 200 nm, 300 nm, or a thickness within a range defined by these values or possibly outside of these ranges.

[0101] In some embodiments, the base polymer region 1008a is substantially free of inorganic material. In some cases, the base polymer region 1008a has less than 40%, 30%, 20%, 10%, 5%, 1%, 0.5%, or 0.1% (or any range defined by these values) of inorganic material, based on the total volume of the base polymer region 1008a. In contrast, the infiltrated region 1008b is substantially infiltrated with inorganic material. In some cases, the infiltrated region 1008b has more than 40%, 50%, 60%, 70%, 80%, or 90% (or any range defined by these values) of inorganic material, based on the total volume of the infiltrated region 1008b.

[0102] The diffraction grating 1000 has optical structures 1008 arranged such that adjacent ones of the periodically repeating optical structures 1008 are separated by spaces 1012. In the illustrated embodiment, the surface of the substrate within the spaces 1012 does not have base polymer material or inorganic material formed thereon. This is because the base polymer material may be completely removed from between adjacent ones of the base polymer structures prior to incorporating the inorganic material, such that the surface of the substrate is exposed within the resulting spaces 1012 between adjacent ones of the periodically repeating base polymer structures. Subsequently, because the exposed surface of the substrate does not have functional groups formed thereon that are adapted to adsorb or chemisorb metal precursors to form the inorganic material, no inorganic material is formed thereon or incorporated into the substrate 1004. As a result, the surface of the substrate within the spaces 1012 does not have base polymer material or inorganic material formed thereon. This process is described in more detail below with respect to Figures 14A-14B.

[0103] However, other embodiments are also possible, as illustrated in detail below. In other embodiments, adjacent ones of the periodically repeating optical structures 1008 are separated by spaces 1012, and a surface of the substrate within the spaces has a layer of polymer material (FIGS. 15B, 16B) formed thereon having an inorganic material incorporated therein, as described in detail with respect to FIGS. 15A-15B and 16A-16B. In these embodiments, prior to incorporating the inorganic material, the base polymer material is incompletely or partially removed from between adjacent ones of the periodically repeating base polymer structures such that the surface of the substrate remains coated with a thin layer of base polymer within the spaces 1012 between adjacent ones of the protruding base polymer structures (FIGS. 15A, 16A). Subsequently, the surfaces of the protruding base polymer structures and the surface of the polymer layer between adjacent ones of the protruding base polymer structures are exposed to a precursor to incorporate the inorganic material. For example, the incorporation of inorganic material may result from the presence of functional groups in the base polymer structure that adsorb or chemisorb a metal precursor, and subsequent reaction between the metal precursor and an oxidized precursor to form the inorganic material within the optical structure 1008. In some embodiments, the layer of polymer material formed within the space can have its entire thickness or a partial thickness incorporated with the inorganic material. These processes are described in more detail below with respect to Figures 15A-15B and 16A-16B.

[0104] Method for fabricating optical elements formed from polymer-based optical structures incorporating inorganic materials therein - Patents.com Described below is a method of fabricating a polymer-based optical element, e.g., a diffraction grating 1000 (FIG. 10), comprising a polymer-based optical structure incorporating an inorganic material therein. Referring to FIG. 11, method 1100 includes providing 1104 a substrate having a first refractive index and transparency in the visible spectrum. The method additionally includes forming 1108 a periodically repeating base polymer structure on the substrate. The method further includes exposing 1112 the substrate to a metal precursor and then to an oxidizing precursor. Exposing the substrate is performed under pressure and temperature such that inorganic material including the metal is incorporated into the periodically repeating base polymer structure, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light, the optical structure having a second refractive index greater than the first refractive index.

[0105] 11, a substrate having a first refractive index and transparency in the visible spectrum is provided 1104. This may include, for example, providing substrate 1004 as described above with respect to FIG.

[0106] Still referring to FIG. 11 , a periodically repeating base polymer structure is formed on the substrate (1108). Forming the polymer structure can be accomplished using a suitable process, including, for example, a lithography process (FIGS. 12A-12C) or a nanoimprinting process (FIGS. 13A-13C), as described below. In some embodiments, as described with respect to FIGS. 12A-12C, forming the periodically repeating optical structure on the substrate 1108 may be performed by depositing a suitable polymer material, such as described above with respect to FIG. 10, followed by patterning using lithography and etching processes. In some other embodiments, as described with respect to FIGS. 13A-13C, forming the periodically repeating optical structure on the substrate 1108 may be performed by depositing a suitable polymer material, such as described above with respect to FIG. 10, followed by patterning using nanoimprinting techniques.

[0107] 12A-12C illustrate cross-sectional views of intermediate structures 1200A-1200C, respectively, at various stages of fabricating a periodically repeating base polymer structure using a lithographic process, according to an embodiment. Referring to intermediate structure 1200A of FIG. 12A, the method includes providing a substrate 1004. Substrate 1004 includes an optically transparent material having a first refractive index (n1) and possibly various other material attributes as described above with reference to FIG. 10. The method additionally includes providing a layer of a material having a refractive index n 2initial and possibly various other material attributes as described above with reference to Figure 10. The base polymer layer 1208 is suitable when patterned to form a periodically repeating base polymer structure as described above with reference to Figure 10.

[0108] In some embodiments, the base polymer layer 1208 is formed from a single layer that serves to provide functional groups for subsequent adsorption, chemisorption, or reaction with a metal precursor. The base polymer layer 1208 also serves as a photoresist that can be photolithographically patterned by exposure / development and subsequent etching. The base polymer layer 1208 can be a single layer that serves both of these functionalities. However, the design need not be so limited, and in some other embodiments, the base polymer layer 1208 may include multiple layers, including a photoresist layer formed on a separate activated polymer layer that has functional groups for adsorption, chemisorption, or reaction with a metal precursor. That is, the base polymer layer 1208 may comprise a multilayer structure, for example, when the single base polymer layer 1208 does not sufficiently serve as a photoresist and does not provide functional groups for adsorption, chemisorption, or reaction with a metal precursor.

[0109] Depending on the design, the base polymer layer 1208 may be deposited by spin coating, followed by a post-bake.

[0110] 12B , after deposition and post-deposition baking, the method includes patterning the base polymer layer 1208 by selectively exposing portions thereof to a pattern of light produced by a photomask 1216. As shown, the photomask 1216 can be a positive photomask adapted for a positive photoresist and can be configured to pass light in areas where the base polymer layer 1208 is to remain. When the photomask 1216 is a negative photomask adapted for a negative photoresist, the photomask can conversely be configured to pass light in areas where the base polymer layer 1208 is to be removed.

[0111] Exposure to light 1212, e.g., coherent UV light or an electron beam, causes a chemical change, e.g., polymer cross-linking, in the base polymer layer 1208, including photoresist, that allows the exposed portions of the base polymer layer 1208 to be selectively removed using a developer solution for the base polymer layer 1208 that includes or acts as a positive photoresist, or the unexposed portions of the photoresist to be selectively removed using a developer solution for the base polymer layer 1208 that includes or acts as a negative photoresist.

[0112] Referring to intermediate structure 1200C in FIG. 12C , upon selective removal, the resulting periodically repeating base polymer structures 1220a / 1220b remain on the substrate 1004, thereby serving as a template for subsequent infiltration of inorganic material. Base polymer structures 1220a may be a set of base polymer structures elongated in a first direction, e.g., the y-direction. Alternatively, base polymer structures 1220b may be a set of base polymer structures elongated in a second direction, e.g., the x-direction. Base polymer structures may also include base polymer structures elongated in a first direction and base polymer structures elongated in a second direction. Other configurations are also possible.

[0113] 13A-13C illustrate cross-sectional views of intermediate structures 1300A-1300C, respectively, at various stages in the fabrication of a periodically repeating base polymer structure using a nanoimprint process. In the illustrated embodiment, the method for forming intermediate structure 1300A is similar to the method for forming intermediate structure 1200A of FIG. 12A. However, the methods for forming intermediate structures 1300B and 1300C of FIG. 13B and 13C, respectively, differ from the methods for forming intermediate structures 1200B and 1200C of FIG. 12B and 12C, respectively, and the differences are explained below.

[0114] 12B , instead of patterning the base polymer layer 1208 by selectively exposing and removing portions thereof using light or an electron beam and a developer solution, in the illustrated embodiment, a nanoimprint template 1316 or nanoimprint mold having a predetermined topological pattern according to which periodically repeating base polymer structures are formed is brought into contact with the base polymer layer 1204. The template 1316 is then pressed into the base polymer layer 1208, which may comprise a thermoplastic polymer, at a temperature above the glass transition temperature of the base polymer layer 1208, thereby transferring the pattern of the template 1316 into the softened base polymer layer 1208. After cooling, the template 1316 is separated from the base polymer layer 1208, leaving the patterned periodically repeating base polymer structures 1220a / 1220b on the substrate 1004. In one other approach, after being pressed into the base polymer layer 1208, the base polymer layer 1208 is solidified by cross-linking under UV light.

[0115] 11 , the method of fabricating a polymer optical element incorporating an inorganic material further includes exposing 1112 the substrate to a metal precursor and then to an oxidizing precursor, where the exposing of the substrate is carried out under pressure and temperature such that the inorganic material, including the metal, is incorporated into the periodically repeating base polymer structure, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index. Below, with reference to Figures 14A-14B, 15A-15B, and 16A-16C, different methods of exposing a substrate to incorporate inorganic material into the periodically repeating base polymer structure are described.

[0116] 14A illustrates an intermediate structure 1400A comprising a periodically repeating base polymer structure 1204 fabricated using a method similar to that illustrated above with respect to, for example, FIGS. 12A-12C and 13A-13C. The periodically repeating base polymer structure 1204 formed on the substrate 1004 is thus similar to the periodically repeating base polymer structures 1220a / 1220b illustrated above with respect to FIGS. 12A-12C and 13A-13C. FIG. 14B illustrates an intermediate structure 1400B comprising a periodically repeating optical structure 1008 having an inorganic material incorporated therein as described above with respect to FIG. 10. Below, with reference to FIGS. 14A and 14B, methods for incorporating inorganic material into the periodically repeating base polymer structure 1204 ( FIG. 14A ) and forming the periodically repeating optical structure 1008 ( FIG. 14B ) are described in detail.

[0117] Incorporation of inorganic materials into the periodically repeating base polymer structure 1204 ( FIG. 12A ) to form the periodically repeating optical structure 1008 ( FIG. 12B ) can be carried out using some process features used in atomic layer deposition (ALD). In some aspects, ALD can be considered to include a type of chemical vapor deposition (CVD) process with self-limited growth controlled by the distribution of chemical reactions into two separate half-reactions contained within a growth cycle. A growth cycle for such an ALD process can include four stages: (1) exposure of a first precursor, e.g., a metal precursor; (2) purging of the reaction chamber; (3) exposure of a second precursor, e.g., an oxidizing precursor; and (4) further purging of the reaction chamber. In the first stage of the ALD process, the first precursor reacts with sites on the substrate to form a full or partial molecular layer of the first precursor. In the second stage, unreacted first precursor molecules can be purged and / or pumped out using an inert gas, such as argon or N2, to reduce, prevent, or minimize gas-phase reactions that may occur between the remaining first precursor and the subsequently introduced second precursor, which would disrupt growth at the molecular layer level. In the third stage, a second precursor is introduced into the purged chamber and reacts with the molecular layer of the first precursor, thereby resulting in a monomolecular or quasi-molecular layer of the target material. The fourth stage involves purging / pumping out the remainder of the second precursor in preparation for another growth cycle, which can be repeated until the desired thickness is achieved.

[0118] As described above with respect to FIG. 10 , inorganic materials incorporated into the optical structure 1008 may include metal compounds, such as metal-containing dielectrics. The inorganic materials may include, for example, metal oxides or metal nitrides, such as oxides, nitrides, or oxynitrides of one or more transition metals, including Al, Zn, Zr, Hf, Ti, and Ta. An ALD growth cycle may therefore include (1) exposure of the substrate to a metal precursor containing a transition metal, (2) purging of the reaction chamber, (3) exposure of an oxidizing precursor, and (4) further purging of the reaction chamber. The inorganic materials may be produced by an oxidation process, resulting in, for example, a metal oxide, metal nitride, or other inorganic material.

[0119] Advantageously, the use of ALD processes to incorporate inorganic materials offers several advantages. For example, because the adsorption, chemisorption, or reaction of precursors provides control over the amount of material deposited at the monolayer or submonolayer level, the film thickness or amount of material deposited can be precisely controlled based on the number of reaction cycles. In addition, because precursors in the gas phase can reach surfaces that are difficult or impossible to access using other deposition techniques, such as physical vapor deposition (PVD) or plasma-enhanced chemical vapor deposition (PECVD), which may be line-of-sight and / or aspect ratio dependent, ALD can be a suitable method for depositing conformal thin films on three-dimensional surfaces. Furthermore, because the adsorption, chemisorption, or reaction can occur at relatively low temperatures (e.g., below 100°C), ALD can be suitable for deposition on structures or surfaces with limited thermal budgets or thermal tolerances.

[0120] Thus, in a preferred embodiment, the incorporation of inorganic materials into the periodically repeating base polymer structure 1204 to form the periodically repeating optical structure 1008 can be carried out in a reactor configured for ALD and / or using some of the process features used in ALD as described above.

[0121] Certain combinations of pressure, temperature, and time may be particularly suitable for forming optical structure 1008, as described in more detail below. Thus, according to embodiments, exposing the substrate to one or both of the metal precursor and the oxidizing precursor includes exposure at a total and / or partial pressure, and for such duration, sufficient to saturate the exposed surface of the base polymer structure with one of both the metal precursor and the oxidizing precursor.

[0122] Referring back to FIG. 11 , according to an embodiment, exposing 1112 is performed under a pressure above atmospheric pressure. Without being bound by any theory, a higher pressure may improve the diffusion of the precursor prior to reaction to form the inorganic material and / or improve the diffusion of the inorganic material after formation. One or both of the total pressure and the partial pressure during exposure with the metal and / or oxidizing precursor can be adjusted or optimized. In different cases, the total pressure during exposure can be about 10 mTorr to about 100 Torr, about 50 mTorr to about 50 Torr, about 100 mTorr to about 10 Torr, or any pressure within or outside the ranges defined by these values, such as about 800 mTorr to about 5 Torr or 1 Torr to 5 Torr. Under the total pressure, the partial pressure of the precursor can be 2%, 5%, 10%, 20%, 50% of the total pressure, or any pressure within or outside the ranges defined by these values, such as about 25 to 50 mTorr. The remaining partial pressure can be provided by a gas other than the precursor, for example, an inert gas, such as argon and / or N2.

[0123] During the purge process, the total pressure can be maintained to be the same or different from the total pressure during exposure to the precursor as described above.

[0124] Depending on the approach, exposing 1112 may include exposing the periodically repeating base polymer structure 1204 to one or both of the metal precursor and the oxide precursor for a duration of 1 second, 5 seconds, 10 seconds, 30 seconds, 60 seconds, 100 seconds, 500 seconds, or more than 1000 seconds, e.g., between about 10 and 400 seconds, or any range defined by these values. Durations outside these ranges are also possible. Depending on the circumstances, the exposure time may exceed some conventional exposure times employed in conventional ALD sufficient to saturate the deposition surface with precursor. Such exposure times can be less than 1 second. Without being bound by any theory, longer exposure times may advantageously provide sufficient time for diffusion of precursors into the base polymer structure 1204 prior to forming the inorganic material and / or provide sufficient time for diffusion of inorganic material after the formation of one or more monolayers of inorganic material. In some cases, a percentage of the exposure time may be sufficient to saturate the surface with the precursor, while the remainder of the exposure time may be spent diffusing the precursor and / or inorganic material. In some cases, the duration of exposure exceeds the duration sufficient to saturate the surface with the precursor by 10, 20, 50, 100, or 1000 times, or any range defined by these values. Values outside these ranges are also possible.

[0125] During the purge process, the purge time can be the same as the exposure time for the precursor exposure described above, or can be, for example, 2 times, 5 times, or 10 times longer, or any multiple within the range defined by these values. The purge time can also be outside these ranges. Thus, the durations of subcycles t1, t2, t3, and t4, corresponding to the first exposure time for exposing the substrate to the metal precursor, the first purge time for purging the metal precursor, the second exposure time for exposing the substrate to the oxidizing precursor, and the second purge time for purging the oxidizing precursor, can have a combination of the above durations, for example, t1, t3 = 1-100 seconds or any range described above, and t2, t4 = 5-500 seconds or any range described above.

[0126] Depending on the configuration and / or processing method, exposing 1112 may involve exposing the periodically repeating base polymer structure to one or both of the metal precursor and the oxide precursor at temperatures below about 100 degrees Celsius. Relatively low temperatures may be employed to achieve the desired diffusion depth of the precursor and / or inorganic material, as increased pressure and longer exposure times may compensate for lower temperatures. According to embodiments, exposing may be performed at temperatures below 200°C, 150°C, 100°C, 80°C, 60°C, 40°C, or 20°C, or any temperature within a range defined by these values. Temperatures outside these ranges, including temperatures above 100°C, may also be used.

[0127] Exposing the substrate to a metal precursor can include exposing to a precursor containing a transition metal, such as a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. For example, to incorporate transition metal oxides, including aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, titanium oxide, tantalum oxide, and combinations thereof, metal precursors used for the first stage can include halides (i.e., metals bonded to F, Cl, Br, or I), alkyl compounds, and alkoxides having a transition metal.

[0128] Depending on the desired structure and / or process, the metal halide precursor can include aluminum chloride or iodide, zinc chloride or iodide, zirconium chloride or iodide, hafnium chloride or iodide, titanium chloride or iodide, or tantalum chloride or iodide.

[0129] Depending on the desired structure and / or method, metal precursors with oxygen bound to the metal can be alkoxides (M-(O-CR)n), such as hafnium tert-butoxide, Hf(OC4H9)4, where each alkoxo ligand is bound to the metal atom through one O atom, and β-diketonates (M=(OC3R3), such as Zr(thd)4, where each diketonato ligand is bound to the metal through two metal-oxygen bonds (ligands that "chelate" the metal center). n may include:

[0130] Depending on the desired structure and / or method, precursors with nitrogen bound to the metal may be metal alkylamides (M(NR)), such as hafnium dimethylamide Hf(N(CH)). n ) and metal amidinates (M(N2CR3) n ).

[0131] Organometallic precursors having a metal atom directly bonded to carbon can also be used. Such organometallic precursors include alkyl M(C), such as trimethylaluminum Al(CH).x H y ) n and dicyclopentadienyl dimethyl hafnium, Hf(C5H5)2(CH3)2 (mixed ligand precursor). Other precursors can also be used.

[0132] Depending on the desired structure and / or process, exposing the substrate to an oxidizing precursor can include, according to embodiments, exposing the substrate to a precursor including oxygen (O, O), ozone (O), water (HO), hydrogen peroxide (HO), nitrous oxide (NO, NO), ammonia (NH), or combinations thereof. Other precursors, such as other oxidizing precursors, can also be used.

[0133] Different precursor combinations can be used and may depend on the inorganic material being incorporated into the periodically repeating base polymer structure 1204. For example, aluminum oxide may be more easily deposited from trimethylaluminum and water or ozone, while aluminum nitride may be more easily made from aluminum dimethylamide, Al(N(CH)), and ammonia. For the ALD of hafnium oxide and hafnium oxynitride, hafnium ethylmethylamine, Hf(N(CH)(CH)), may be a suitable liquid precursor, combining high reactivity with water, ozone, and ammonia with sufficient volatility and stability.

[0134] 10, the polymer chains of the base polymer units may include various functional groups, such as carbonyl, hydroxyl, and pyridine groups, configured to react with certain metal precursors to form inorganic materials. To provide one illustrative example, when the deposition chemistry includes Al(CH3)3 (TMA) and HO for the formation of Al2O3, PMMA may be included within the polymer base material such that the carbonyl groups of PMMA react with TMA to form Al-OH species, which in turn may react with HO in a hydrolysis reaction to form Al2O3 that is incorporated within the base polymer structure 1204.

[0135] 14A and 14B, based on the foregoing, various parameters, including exposure time, purge time, total or partial pressure, and substrate temperature, can be selected to control the diffusion of precursor and / or inorganic material to form an optical structure 1008 comprising a base polymer region 1008a and an infiltrated region 1008b infiltrated with the inorganic material. In some embodiments, the inorganic material is incorporated into surface regions of the optical structure 1008 such that the optical structure has a base polymer region 1008a comprising a core region of the optical structure substantially free of inorganic material incorporated therein, and a infiltrated region 1008b comprising a surface region having inorganic material infiltrated therein, respectively.

[0136] Furthermore, the diffusion of precursors and / or inorganic materials occurs in the infiltrated region 1008b (H i -H f and / or W i -W f) can be controlled to be greater than about 1 nm, 10 nm, 20 nm, 50 nm, 100 nm, 200 nm, 300 nm, or a thickness within the ranges defined by these values. Thicknesses outside these ranges are also contemplated. Thus, base polymer region 1008a may be substantially free of inorganic material. The base polymer region may have less than 40%, 30%, 20%, 10%, 5%, or 1% of inorganic material, based on the total volume of base polymer region 1008a, or any percentage within any range defined by these values. Percentages outside these ranges are also contemplated. In contrast, infiltrated region 1008b is substantially infiltrated with inorganic material. The wetting region 1008b may have a percentage of inorganic material greater than 40%, 50%, 60%, 70%, 80%, 90%, 95%, or 99%, based on the total volume of the base polymer region 1008a, or any percentage within any range defined by these values. Percentages outside these ranges are also possible.

[0137] However, the configuration is not so limited, in certain other configurations, where substantially all of the volume of the periodically repeating base polymer structure 1204 is infiltrated with inorganic material such that after infiltration, the base polymer structure 1204 is substantially free of base polymer regions 1008a that are free of inorganic material.

[0138] As explained above, one or more exposure conditions affect the diffusion characteristics of the precursors and / or inorganic material. Without being bound by any theory, in some embodiments, at least some of the precursors are diffused into the base polymer structure 1204 prior to forming the inorganic material. For example, at least a portion of the monolayer of the metal precursor may be diffused into the polymer structure 1204 to a depth equal to or less than the depth of the infiltration region 1008b, e.g., reacting with functional groups of the base polymer material of the polymer structure 1204. Thereafter, at least a portion of the monolayer of the oxidized precursor may be diffused into the base polymer structure 1204 to a depth equal to or less than the depth of the infiltration region 1008b, e.g., reacting with the metal precursor, thereby forming at least a portion of the inorganic material within or below the surface of the periodically repeating base polymer structure 1204.

[0139] However, the configuration is not so limited. Without being bound by any theory, in some other embodiments, at least a portion of the inorganic material is formed and then diffused into the base polymer structure 1204. For example, at least a portion of a monolayer of inorganic material may be formed on the surface of the base polymer structure 1204 and then diffused into the polymer structure 1204 to a depth equal to or less than the depth of the infiltration region 1008b.

[0140] 14A and 14B, advantageously, the base polymer material forming the periodically repeating polymer structure 1204 has a composition, structure, and density such that, after incorporation of the inorganic material under various processing and material parameters as described above, the dimensions of the periodically repeating polymer structure 1204 prior to incorporation of the inorganic material and the dimensions of the periodically repeating optical structure 1008 after incorporation of the inorganic material differ within a relatively limited amount. For example, for designs such as the illustrated embodiment having a generally rectangular cross-sectional shape, one or both of the width and height may vary by less than 30%, 20%, 10%, 5%, or 1%, or percentages within ranges defined by these values, although percentage variations outside these ranges are also possible. Relatively small variations in lateral dimensions are advantageous because, at least, variability in the critical dimension resulting from processing is reduced.

[0141] According to some embodiments, inorganic materials are incorporated or infiltrated into the base polymer structure 1204 using a process sequence similar to thermal atomic layer deposition (ALD). A thermal ALD process is deposition performed without the use of plasma. In some other embodiments, inorganic materials are incorporated or infiltrated using plasma-enhanced atomic layer deposition (PE-ALD). Whether thermal or PE-ALD is employed may depend on the dimensions and aspect ratio of the periodically repeating base polymer structure 1204. For example, for base polymer structures 1204 having a relatively high aspect ratio and / or a relatively small spacing between adjacent polymer structures 1204, plasma may, under some circumstances, not reach into deeper regions of the high aspect ratio base polymer structure 1204. Under these circumstances, when PE-ALD is employed, different portions of the base polymer structure 1204 may be exposed to different amounts of plasma, leading to non-uniform deposition, e.g., thicker films being deposited near upper regions of the base polymer structure 1204 compared to deeper regions. Alternatively, thermal ALD may be more advantageous because thermal ALD may not rely on the ability of plasma to reach the portion of the surface being deposited on. However, under other circumstances, PE-ALD may be more desirable because the plasma may lower the activation energy of the ALD reaction, e.g., to allow for lower temperature deposition.

[0142] Above, exemplary methods and apparatuses have been described in which inorganic materials are incorporated into, or infiltrated into, the periodically repeating optical structure 1008 using processes related to ALD. However, the methods and apparatuses are not so limited. Under some circumstances, for example, when the inorganic materials are formed prior to diffusion into the base polymer structure 1204 and / or when the dimensions of and spacing between the base polymer structures 1204 are relatively large, other deposition techniques may be employed, for example, for faster throughput. For example, inorganic materials can be infiltrated using processes such as chemical vapor deposition (CVD), which in some cases includes plasma-based CVD processes such as plasma-enhanced chemical vapor deposition (PECVD) and thermal-based CVD processes such as low-pressure chemical vapor deposition (LPCVD). Inorganic materials can also be infiltrated using physical vapor deposition (PVD) and evaporation, among other techniques.

[0143] According to various embodiments, exposing the substrate to the metal precursor and the oxidizing precursor advantageously incorporates inorganic material through the exposed surface of the base polymer material selectively to the exposed surface of the substrate. This is because, unlike the surface of the periodically repeating base polymer structure 1204, the surface of the substrate 1004 does not have functional groups adapted to adsorb, chemisorb, or react with the metal precursor, as described above. Thus, based on the selectivity of the adsorption, chemisorption, or reaction of the metal precursor, variations within the periodically repeating optical structure can be formed, as described below with respect to Figures 14A / 14B, 15A / 15B, and 16A / 16B.

[0144] 14A and 14B, when the periodically repeating base polymer structures 1204 are formed, adjacent ones of the periodically repeating base polymer structures are separated by spaces 1012. Unlike the surfaces of the base polymer structures 1204, the surfaces of the substrate within the spaces 1012 do not have base polymer material formed thereon. That is, prior to exposing the inorganic material to a precursor to incorporate the inorganic material into the polymer structures 1204, the base polymer material is completely removed from between adjacent ones of the base polymer structures 1204 such that the surfaces of the substrate are exposed within the spaces 1012. Subsequently, because the exposed surfaces of the substrate do not have functional groups formed thereon that are adapted to adsorb, chemisorb, or react with the metal precursor, no inorganic material is formed thereon.

[0145] 15A and 16A, respectively, and intermediate structures 1500B and 1600B, respectively, of FIGS. 15B and 16B, methods of incorporating inorganic materials into the periodically repeating base polymer structure 1204 (FIGS. 15A and 16A) to form the periodically repeating optical structure 1008 (FIGS. 15B and 16A) are described according to alternative embodiments. The various fabrication processes that result in intermediate structures 1500A and 1600A and 1500B and 1600B, respectively, which are similar to the fabrication processes that result in intermediate structures 1400A (FIG. 14A) and 1400B (FIG. 14B), are omitted herein, while the differences are described herein. In the illustrated embodiment, unlike the embodiment illustrated with respect to Figures 14A / 14B, forming the periodically repeating base polymer structures 1204 includes forming adjacent periodically repeating base polymer structures 1204 separated by spaces 1012 having a substrate surface onto which layers 1504 (Figure 15A), 1604 (Figure 16A) of base polymer material are formed. That is, prior to incorporating the inorganic material into the base polymer structures 1204, the base polymer material is incompletely or partially removed from the substrate surface within the spaces 1012. As a result, within the spaces 1012 between adjacent protruding periodically repeating base polymer structures 1204, the surface of the substrate 1004 remains coated with a layer of base polymer material. Subsequently, the surfaces of the protruding periodically repeating base polymer structures 1204 and the surfaces of the polymer layers 1504 (Figure 15A), 1604 (Figure 16A) on the substrate within the spaces 1012 are exposed to a precursor to incorporate the inorganic material. As explained above, the incorporation of inorganic material can result from the presence of functional groups in the base polymer structure that adsorb or chemisorb the metal precursor and subsequent reaction between the metal precursor and the oxidized precursor. Alternatively, the incorporation can result from the formation of inorganic material on the surface of the polymer material, which then diffuses into the periodically repeating base polymer structure 1204 and forms the periodically repeating optical structure 1008. As a result, the entire exposed surface incorporates the inorganic material, including the surface regions of the protruding optical structures 1008 and the surfaces of the polymer layers 1508 ( FIG. 15A ), 1608 ( FIG. 16A ) on the substrate surface in the spaces 1012 between adjacent ones of the optical structures 1008.

[0146] In some embodiments, as illustrated in FIG. 15A, the layer 1504 of polymer material formed on the substrate surface within the space 1012 has a relatively thin thickness, e.g., the thickness of the wetting region 1008b (H i -H f and / or W i -W f ) In these embodiments, after infiltration with the inorganic material, substantially the entire thickness of the layer 1508 of polymeric material within the space 1012 may (or may not) incorporate the inorganic material, as illustrated in FIG.

[0147] In some other embodiments, as illustrated in FIG. 16A, the layer 1604 of polymer material formed on the substrate surface in the space 1012 has a relatively large thickness, for example, the thickness of the wetting region 1008b (H i -H f and / or W i -W f ) In these embodiments, after infiltration with the inorganic material, a portion of the thickness (less than the total thickness) of the layer of polymeric material 1608 within the space 1012 incorporates the inorganic material within the surface region, as illustrated in FIG. 16B.

[0148] Advantageously, the incorporation of inorganic material into the base polymer structure 1204 to form the optical structure 1008 results in an increase in the refractive index of the structure. According to embodiments, the substrate 1004 has a first refractive index greater than that of air but less than the second refractive index of the optical structure 1008, e.g., 1.5, 1.6, 1.7, 1.8, 1.9, or a value within a range defined by these values. Refractive indexes outside these ranges are also possible. After the incorporation of the inorganic material, in various embodiments, the second refractive index is greater than 1.7, 1.8, 1.9, 2.0, 2.1, or a value within a range defined by these values, and is greater than the first refractive index by at least 0.2, 0.4, 0.6, 0.8, 1.0, or a value within a range defined by these values. Refractive indexes and refractive index increases outside these ranges are also possible. Prior to the incorporation of the inorganic material, the periodically repeating base polymer structure 1204 may have a refractive index substantially lower than the final second refractive index of the optical structure 1008. For example, the refractive index of the base polymer structure 1204 prior to the incorporation of the inorganic material may be 1.3, 1.4, 1.5, 1.6, 1.7, or a value within a range defined by these values. For example, PMMA and polystyrene have refractive indices of approximately 1.49 and approximately 1.59 at approximately 588 nm, respectively. Upon incorporation of an inorganic material having a refractive index above 1.7, 2.0, 2.3, 2.6, 3.0, or a value within the range defined by these values, the refractive index of the base polymer structure 1204 can be increased to, for example, a value within the above range. Thus, the refractive index can be increased above approximately 0.1, 0.2, 0.3, 0.4, 0.5, or to a value within the range defined by these values. Indices of refraction and increases in refractive index outside these ranges are also possible.

[0149] Advantageously, the incorporation of inorganic materials into the base polymer structure 1204 to form the optical structure 1008 can result in an increase in mechanical robustness, as measured, for example, by Young's modulus (E). Prior to the incorporation of inorganic materials according to embodiments disclosed herein, the Young's modulus of the periodically repeating base polymer structure 1204 can be within about 1.0 GPa to about 5 GPa. For example, PMMA can have a Young's modulus of about 2.5 to 3.5 GPa, e.g., about 3.1 GPa, and polystyrene can have a Young's modulus of about 1.5 to 2.5 GPa, e.g., about 2.0 GPa. Depending on the incorporation of inorganic materials, in various embodiments, the Young's modulus of the periodically repeating base polymer structure 1204 can increase above 1 GPa, 2 GPa, 5 GPa, 10 GPa, or a value within a range defined by these values. The resulting Young's modulus of the optical structure 1008 incorporating the inorganic material can be from about 2.5 GPa to about 17.5 GPa, from about 2.5 GPa to about 7.5 GPa, from about 7.5 GPa to about 12.5 GPa, or from about 12.5 GPa to about 17.5 GPa. Young's modulus values outside these ranges are also contemplated.

[0150] Although specific oxides and nitrides are disclosed herein to constitute inorganic materials, other materials are also possible. Additional oxides and nitrides may be formed by oxidation processes such as those described herein or by other types of oxidation processes. Other materials may also be formed by oxidation processes. Still other types of processes may also be used.

[0151] Optical elements based on geometric phase metasurfaces with polymer-based optical structures incorporating inorganic materials Metasurfaces may include surface structures that can locally modify the polarization, phase, and / or amplitude of light in reflection or transmission. Metasurfaces may include arrays of subwavelength-sized and / or subwavelength-spaced phase-shifting elements whose patterns are configured to control the wavefront of light so that various optical functionalities can be derived therefrom, including beam shaping, lensing, beam bending, and polarization splitting. Factors that can be used to manipulate the wavefront of light include the material, size, geometry, and orientation of the surface structures. By arranging surface structures with distinct scattering properties on a surface, spatially varying metasurfaces can be created, throughout which the optical wavefront can be substantially manipulated.

[0152] In conventional optical elements such as lenses and waveplates, wavefronts are controlled via the propagation phase in media much thicker than the wavelength. Unlike conventional optical elements, metasurfaces instead use subwavelength-sized resonators as phase-shifting elements to induce phase changes in light. Because metasurfaces are formed from relatively thin, uniform-thickness features, they can be patterned across surfaces using thin-film processing techniques, such as semiconductor processing techniques, and direct printing techniques, such as nanoimprinting.

[0153] As explained above, polymer optical elements incorporating inorganic materials offer tunable refractive index and robustness while being relatively easy to process. As a result, polymer optical elements incorporating inorganic materials are excellent candidates for metasurface-based optical elements. In the following optical elements, for example, metasurface-based diffraction gratings formed from polymer-based optical structures incorporating inorganic materials are described.

[0154] Without being bound by any theory, when a light beam is traced along a closed cycle in the space of the polarization states of the light, the dynamic phase can be obtained from the cumulative path length and the geometric phase. The dynamic phase obtained from the geometric phase is due to local changes in polarization. Some optical elements that rely on geometric phase to form a desired phase front can be referred to as Pancharatnam Berry Phase Optical Elements (PBOEs). PBOEs can be constructed from waveplate elements whose fast axis orientation depends on the spatial position of the waveplate element.

[0155] Without being limited by theory, by forming a metasurface with a geometric phase optical element, e.g., a half-wave plate formed from PBOE, with their fast axis orientation according to a function θ(x,y), an incident circularly polarized beam can be oriented according to φ g It can be completely transformed into a beam of opposite helicity with a geometric phase equal to (x,y)=+ / -2θ(x,y). By controlling the local orientation of the fast axis of the waveplate element from 0 to π, phase pickup / delay can be achieved that covers the full 0 to 2π range while maintaining a relatively high and uniform transmission amplitude across the entire optical element, thereby providing the desired wavefront.

[0156] Referring now to Figures 17A-17H, a geometric PBOE structure 1700 based on a plurality of geometrically rotating waveplate elements according to an embodiment is described, with each waveplate element comprising a pattern of periodically repeating optical structures (1008 in Figures 10, 14B, 15B, and 16B) as described above. In particular, a PBOE configured as a half-waveplate with a phase retardation of π is described. In the illustrated embodiment, eight neighboring half-waveplate elements are arranged to be equally spaced and feature a constant orientation angle difference Δθ between neighboring waveplates. However, it should be understood that a fewer or greater number of waveplate elements may be employed with different orientation angle differences Δθ between neighboring waveplates. For illustrative purposes, the bottom row diagrammatically depicts the rotation of the polarization vector of an incident light beam with left-handed circular polarization, i.e., |LCP> state. The middle row illustrates a half-wave plate element constructed from multiple periodically repeating optical structures, similar to those described with reference to Figures 14B, 15B, and 16B, with their fast axes oriented at different angles θ relative to the normal axis. The top row diagrammatically illustrates the corresponding polarization vectors of light delayed and transmitted through the wave plate element. The circular polarization and counterclockwise orientation angle of the fast axis of the wave plate are defined from the perspective of the light source.

[0157] Still referring to Figures 17A-17H, the incident light beam can be described by polarization vectors 1704 and 1708, with equal amplitudes in the x and y directions, respectively, and a phase delay of π / 2 1712 between the polarization vectors. In operation, the half-wave plate acts by shifting the phase between the two perpendicular polarizations by a phase of π. The net result for this work is to reverse the electric field oriented along the slow axis and maintain the electric field along the fast axis. This action can also be viewed as the original polarization vector being flipped to its mirror image, with the fast axis acting as a mirror. Considering the helical incidence situation, where the polarization vector rotates in time, it can be seen that the action of the wave plate switches the helicity from |LCP> to |RCP> or vice versa.

[0158] Referring to the bottom row of Figure 17A, the electric field of the incident |LCP> beam is directed upward toward the positive y-axis at an initial time t = t0, as shown by vector 1704. After one-quarter of an optical cycle (i.e., π / 2), the light is directed along the negative y-direction, as shown by vector 1708. The effect of the waveplate in the middle row of Figure 17A is to reflect vectors 1704 and 1708 into a mirror placed in the plane of the fast axis and the direction of light propagation. The effect of this mirror is to flip vector 1704 to the positive x-direction and keep vector 1708 in its original direction. As a result, the |LCP> beam is converted into an |RCP> beam.

[0159] 17B-17H illustrate how the polarization vector of the |LCP> beam changes when the fast axis of the waveplate is rotated by angles θ of π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4, respectively. Independent of the rotation angle, an |RCP> output beam is produced. However, referring to FIG. 17A, the produced phase retardation of vectors 1704 and 1708 is φ g = 2θ. For example, as shown in Figure 17E, when θ = π / 2, the effect of the waveplate is to flip vector 1708 from the negative y-direction to the positive y-direction while keeping vector 1704 in the same direction. This results in a φ g = 2θ = π, producing a |RCP> beam. Thus, for the half-wave plate shown, it will have spent half an optical cycle well before reaching the state shown in Figure 17A.

[0160] Thus, as an illustrative example, after passing through eight half-wave plate elements that are equally spaced and characterized by a constant orientation angle difference between neighbors, e.g., Δθ=π / 8, the transmitted RCP wave will have a constant phase difference Δφ between neighboring wave plates. g=π / 4. By using eight waveplate elements with fast-axis orientations varying from 0 to π, phase delay / pickup covering the full 0 to 2π range can be achieved. However, fabricating half-waveplate elements with high diffraction angles for visible light can be difficult. This is because the diffraction angle depends, among other things, on the period length of the periodically repeated waveplate elements, and forming a relatively large number of half-waveplate elements within a relatively short period length can be difficult due to space constraints.

[0161] 17A-17H, for illustrative purposes, the half-wave plate shown includes eight equally spaced adjacent half-wave plate elements with a constant orientation angle difference Δθ between adjacent wave plate elements, each including a pattern of periodically repeating polymer-based optical structures with inorganic material incorporated therein. However, embodiments are not so limited, and below are diffraction grating embodiments in which phase retardation / pickup covering the full 0-2π range can be achieved with a smaller number of wave plate elements, at relatively high diffraction angles and diffraction efficiencies, and with uniformity of diffraction efficiency across a relatively wide angle of incidence.

[0162] Applications of metasurfaces comprising PBOEs include diffraction gratings, e.g., blazed gratings, focusing lenses, and axicons, among various other applications. As described herein, blazed gratings are capable of steering a light beam into several diffraction orders. Blazed gratings may be configured to achieve high grating efficiency in one or more diffraction orders, e.g., the +1 and / or −1 diffraction orders, thereby concentrating the refractive power in the desired diffraction orders while leaving low residual refractive power in other orders (e.g., the zeroth order). Various embodiments of metasurfaces comprising PBOEs configured as diffraction gratings are described in this disclosure. According to various embodiments, the diffraction gratings have a combination of desirable optical properties, including one or more of a high diffraction angle, high diffraction efficiency, a wide range of acceptance angles, and highly uniform diffraction efficiency within the acceptance angle range. These desirable optical properties may result from a combination of various aspects of the invention, including the materials, dimensions, and geometric configurations of the metasurface elements.

[0163] As described herein, visible light can include light having one or more wavelengths within various color ranges, including the red, green, or blue ranges. As described herein, red light can include one or more wavelengths within the range of about 620-780 nm, green light can include one or more wavelengths within the range of about 492-577 nm, and blue light can include one or more wavelengths within the range of about 435-493 nm. Thus, visible light can include one or more wavelengths within the range of about 435-780 nm.

[0164] As described herein, a feature, e.g., a nanobeam, line, line segment, or unit cell, that is parallel, nominally parallel, or nearly parallel refers to a feature having an elongation direction that differs from the elongation direction by less than about 10%, less than about 5%, or less than about 3%. Additionally, a feature that is perpendicular, nominally perpendicular, or nearly perpendicular refers to a feature having an elongation direction that deviates from 90 degrees from the elongation direction by less than about 10%, less than about 5%, or less than about 3%.

[0165] As described herein, a structure configured to diffract light, such as a diffraction grating, can diffract light in a transmission mode and / or a reflection mode. As described herein, a structure configured to diffract light in a transmission mode refers to a structure in which the intensity of diffracted light on the side opposite the light incident side of the structure is greater than the intensity of diffracted light on the same side of the structure, for example, by at least 10%, 20%, or 30%. Conversely, a structure configured to diffract light in a reflection mode refers to a structure in which the intensity of diffracted light on the same side of the structure is greater than the intensity of diffracted light on the same side of the structure, for example, by at least 10%, 20%, or 30%.

[0166] As described herein, a line, also referred to as a beam or nanobeam, is an elongated structure having a volume. The line or nanobeam is formed from a polymeric material having inorganic material incorporated therein, as described above. It should be understood that the line is not limited to any particular cross-sectional shape. In some embodiments, the cross-sectional shape is rectangular.

[0167] 18A and 18B illustrate cross-sectional side and top-down views, respectively, of a diffraction grating 1800 comprising a metasurface with geometric phase optical elements, according to some embodiments. The diffraction grating 1800 comprises a two-level geometric phase metasurface. The cross-sectional side view illustrated with reference to FIG. 18A is of section AA′ illustrated in FIG. 18B. The diffraction grating 1800 includes a substrate 1804 having a surface on which a metasurface 1808 configured to diffract light having wavelengths within the visible spectrum is formed. The metasurface 1808 includes one or more first lines or nanobeams 1812 having a first orientation and generally extending in a first lateral direction (e.g., the y-direction) and a plurality of second lines or nanobeams 1816 having a second orientation generally extending in a second direction (e.g., the x-direction). The one or more first lines or nanobeams 1812 and the plurality of second lines or nanobeams are formed from a polymeric material having an inorganic material incorporated therein, as described above. The first lines or nanobeams 1812 can be considered to form a first set of nanobeams, and the second lines or nanobeams 1816 can be considered to form a second set of nanobeams. The one or more first lines 1812 and second lines 1816 are arranged adjacent to each other in a second direction, and the first lines 1812 and second lines 1816 alternate in the second direction with a period that is less than the wavelength of light that the metasurface is configured to diffract.

[0168] Preferably, each of the first lines 1812 has the same width. In some embodiments, the second lines 1816 are stacked laterally in the y-direction between one or more of the first lines 1812 of an adjacent pair. Without being limited by theory, the one or more first lines 1812 and the second lines 1816 are oriented at an angle relative to each other, preferably to create a phase difference between the visible light diffracted by the one or more first lines 1812 and the visible light diffracted by the second line 1816, where the phase difference between the visible light diffracted by the one or more first lines 1812 and the visible light diffracted by the second line 1816 is twice the angle.

[0169] In some embodiments, similar to the waveplate combinations illustrated above with reference to Figures 17A-17H, phase pickup / delay covering the full 0-2π range can be achieved by using a phase difference caused by the relative orientation of one or more first lines 1812 with respect to the second lines 1816, which can vary from 0 to π. In some embodiments, when one of the one or more first lines 1812 and second lines 1816 is rotated by π with respect to the other, e.g., perpendicular to one another, a phase pickup / delay of 2π can be achieved between one or more first lines 1812 and second lines 1816. That is, unlike Figures 18A-18H, phase pickup / delay covering the full 0-2π range can be achieved, according to some embodiments, simply based on a two-level geometric phase metasurface with lines oriented in two different directions. Advantageously, unlike Figures 17A-17H, by using the wave plate combination illustrated with reference to Figures 17A-17H, the footprint occupied by the illustrated metasurface 1808 is more compact and has a period that is less than or equal to a wavelength in the visible spectrum, which in turn allows for a relatively high diffraction angle θ of the diffracted beams 1838, 1842.

[0170] The first line 1812 and the second line 1816 are formed from an optically transmissive material. As described herein and throughout this specification, a "transmissive" or "transparent" structure, e.g., a transmissive substrate, may allow at least a portion, e.g., at least 20, 30, 50, 70, or 90%, of incident light to pass therethrough. Thus, a transparent substrate may, in some embodiments, be a glass, sapphire, or polymer substrate. A "reflective" structure, e.g., a reflective substrate, may reflect and have reflected therefrom at least a portion, e.g., at least 20, 30, 50, 70, 90%, or more, of incident light.

[0171] One or more of the first lines 1812 and second lines 1816 may be described as protrusions, ridges, flutes, or nanowires that protrude from the plane of the page, extend along the plane of the page, and have a width. Additionally or alternatively, the regions of separation between adjacent first lines 1812 and / or adjacent second lines 1816 may be described as depressions, troughs, recesses, or trenches that are recessed into the plane of the page and have a spacing. In some embodiments, the first lines 1812 and second lines 1816 are elongated rectangular structures having a generally rectangular cross-sectional shape in the yz-plane. However, other embodiments are also possible in which the first lines 1812 and second lines 1816 have cross-sectional shapes that may be circular, elliptical, triangular, parallelogram, diamond, trapezoidal, pentagonal, or any suitable shape.

[0172] Below, various configurations are described, including the dimensions and geometric arrangement of one or more first lines 1812 and second lines 1816, the combined effect of which is to produce a grating based on a geometric phase optical element with the desirable optical properties described herein, including one or more of a relatively high diffraction angle, a relatively high diffraction efficiency, a relatively wide range of acceptance angles, and a relatively uniform efficiency within the range of acceptance angles.

[0173] 18A and 18B, in operation, when an incident light beam 1830, e.g., visible light, is incident on metasurface 1808 at an angle of incidence α, normal to surface 1804S and measured relative to a plane extending parallel to first line 1812, e.g., the yz-plane, grating 1800 partially transmits the incident light as a transmitted light beam 1834 and partially diffracts the incident light as a diffracted light beam of +1st order 1842 at a diffraction angle θ1 and a diffracted light beam of −1st order 1838 at a diffraction angle θ2, the diffraction angles being measured relative to the same plane, e.g., the yz-plane, to measure α. One or both of diffracted light beams 1838 and 1842 may be incident at a critical angle θ for the occurrence of total internal reflection within substrate 1804 configured as a waveguide. TIRUpon diffracting at a diffraction angle greater than , the diffracted light beams 1838 and 1842 propagate in their respective opposite directions along the x-axis under total internal reflection (TIR) until the light beams reach the OPE / EPE 1846, which may correspond to the optical dispersive elements 730, 740, 750 and the outcoupling optical elements 800, 810, 820 (FIG. 9B).

[0174] Without being bound by any theory, it has been found that when the first line 1812 and the second line 1816, having subwavelength feature sizes, support leaky mode resonance, they can confine light, thereby causing a phase delay in the scattered light waves produced under TE and TM illumination. The effectiveness of the light confinement within one or more of the first line 1812 and the second line 1816 can result from being configured as a waveguide that acts as a resonator, and the resulting diffraction efficiency can depend, among other factors, on the refractive index and subwavelength dimensions of the material of the first line 1812 and the second line 1816.

[0175] Thus, in some embodiments, the first lines 1812 and / or the second lines 1816 are formed from a material having a relatively high refractive index. Thus, as explained above, according to embodiments, the first lines 1812 and / or the second lines 1816, after incorporation of the inorganic material, have a second refractive index greater than 1.7, 1.8, 1.9, 2.0, or 2.1, and greater than the first refractive index by at least 0.2, 0.4, 0.6, 0.8, or 1.0.

[0176] Continuing to refer to Figures 18A and 18B, in addition to being formed from various materials as described above, one or more of the first lines 1812 and second lines 1816 have a particular combination of dimensions and act as sub-wavelength sized resonators that induce a phase shift in light.

[0177] In various embodiments, the W of the first line 1812 nano1 and the second line 1816 W nano2and W are each smaller than the wavelength of light, preferably smaller than wavelengths in the visible spectrum, that metasurface 1808 is configured to diffract. nano1 and W nano2 are each in the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example 30 nm. According to some embodiments, each of the one or more first lines 1812 has the same width W nano1 According to some embodiments, each of the second lines 1816 has the same width W nano2 According to some embodiments, one or more of the first lines 1812 and the second lines 1816 have the same width, i.e., W nano1 =W nano2 However, in some other embodiments, W nano1 and W nano2 Additionally, in some embodiments, different ones of the one or more first lines 1812 and different ones of the second lines 1816 may have different widths.

[0178] According to some embodiments, immediately adjacent ones of the one or more first lines 1812 in the second direction are separated by a regular interval s1. Additionally, one of the one or more first lines 1812 and one of the second lines 1816 that are immediately adjacent to each other in the second direction are separated by a regular interval s2. According to some embodiments, one or both of s1 and s2 are smaller than the wavelength at which the metasurface 1808 is configured to diffract. Additionally, the first lines 1812 and the second lines 1816 each have a height h nano1 and h nano2 The spacing s1, s2 and the height h nano1 and h nano2A particular combination of may be selected to obtain a desired range of incident angles α (Δα), sometimes referred to as the range of acceptance angles or field of view (FOV). As described herein, the desired range Δα may be described by a range of angles spanning negative and positive values of α, outside of which the diffraction efficiency drops by more than 10%, more than 25%, more than 50%, or more than 75% relative to the diffraction efficiency at α = 0. For example, if a uniform intensity of diffracted light is desired within Δα, it may be desirable to have a Δα over which the diffraction efficiency is relatively flat. Referring back to FIG. 18A , an incident light beam 1830 is incident on the surface of metasurface 1808 and waveguide 1804 at an angle α relative to the surface normal, e.g., the yz-plane. According to some embodiments, as explained above, Δα is related to the angular bandwidth for the metasurface 1808 such that a light beam 1830 within Δα is efficiently diffracted by the metasurface 1808 at a diffraction angle θ relative to the surface normal (e.g., the yz plane). In particular, when θ is less than θ, TIR At or above this, the diffracted light propagates within the substrate 1804 under total internal reflection (TIR).

[0179] It has been found that Δα may depend on the shadowing effect produced by neighbors of one or more first lines 1812 in the second direction and directly neighbors of second lines 1816 in the first direction. That is, when an incident light beam 1830 is incident at an incident angle α above a certain value, the incident light beam directed towards a feature may be blocked by directly neighboring features. For example, Δα may be calculated as s / h nano1 , s2 / h nano1 , and / or s2 / h nano1 In various embodiments, the ratio s1 / h nano1 , s2 / h nano1 , and / or s2 / h nano1 is selected such that Δα is greater than 20 degrees (e.g., + / - 10 degrees), 30 degrees (e.g., + / - 15 degrees), 40 degrees (e.g., + / - 20 degrees), or 50 degrees (e.g., + / - 25 degrees), or in a range of angles defined by any of these values.nano1 , s2 / h nano1 , and / or s2 / h nano1 can be achieved, for example, when s1 and s2 are each in the range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, e.g., 30 nm. Of course, relatively low values of s1 and s2 can be achieved by reducing h nano1 and h nano2 has a correspondingly relatively low value.

[0180] Advantageously, according to some embodiments, the relatively high refractive index (n2) of the material of one or more of the first lines 1812 and / or second lines 1816 allows for a relatively small thickness or height. Thus, in various embodiments, the first lines 1812 and second lines 1816 may have a thickness of, for example, 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, and 10 nm to 50 nm, depending on n1, according to some embodiments, h nano1 and h nano2 For example, h nano1 and h nano2 may be 10 nm to 450 nm where n2 is greater than 3.3, and 10 nm to 1 μm where n1 is 3.3 or less. As another example, the heights of first line 1812 and second line 1816 may be 10 nm to 450 nm.

[0181] According to various embodiments, s1 and W nano1 The combination of s1 and W nano1 the pitch (p nano1 ) is selected from the range of 10 nm to 1 μm, 10 nm to 500 nm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm. nano1 and a value obtained by adding s1 selected from the range of 10 nm to 1 μm, 10 nm to 300 nm, 10 nm to 100 nm, or 10 nm to 50 nm, for example, p nano1= 95.5 nm.

[0182] Of course, relatively small values of s1 and s2 can be realized, and h nano1 and h nano2 Advantageously, one or more of the first lines 1812 and / or the second lines 1816 may be formed using a material with a relatively high refractive index n1, thereby reducing the refractive indices s1, s2, and h nano1 , and h nano2 A relatively small value of h can be obtained, which, as we have found, nano1 and h nano2 may be inversely proportional to the bulk refractive index of the material forming the first line 1812 and the second line 1816. Thus, for a polymer-based optical structure having refractive indices as described above, h nano1 and h nano2 In various embodiments, the thicknesses s1, s2, h1, and s2 may be in the ranges of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. Thus, the thicknesses s1, s2, h2, and s3 of the first and second lines 1812 and 1816 may be in the ranges of 500 nm to 1 μm, 300 nm to 500 nm, 100 nm to 300 nm, and 10 nm to 100 nm, respectively. nano1 , and h nano2 The overall pitch Λ a is also correspondingly reduced, which in turn may increase the diffraction angle θ, as explained further below.

[0183] Preferably, h nano1 and h nano2 are substantially equal, which may be advantageous for processing. However, embodiments are not so limited, and h nano1 and h nano2 may be substantially different.

[0184] In various embodiments, the first line 1812 and / or the second line 1816 may have a bulk refractive index (n 2bulk ) is higher than the refractive index n1 of the substrate 1804, i.e., n 2bulkIn some embodiments, the substrate 1804 may be configured as a waveguide and may correspond to the waveguides 310, 300, 290, 280, 270 (FIG. 6) and / or the waveguides 670, 680, and 690 (FIG. 9A). In such applications, the substrate is preferably formed from a material such that n 1bulk is less than, for example, 1.5, 1.6, 1.7, 1.8, 1.9, or higher, but n 2bulk 1816, which may provide benefits for increasing the Δα of a display that forms an image by outputting light from the substrate 1816.

[0185] 18A and 18B, the Metasurface 1808 may be described as forming a plurality of Metasurface unit cells 1820 that repeat in at least the x-direction. As described herein, a Metasurface unit cell 1820 may be defined as a footprint having a smallest repeating dimension in the x-direction that includes one or more first lines 1812 and second lines 1816. By way of example, each unit cell 1820 spans a unit cell width 1820a measured from the left vertical side of the left one of the first lines 1812 of one unit cell 1820 to the left vertical side of the left one of the first lines 1812 of an immediately adjacent unit cell 1820, thereby, in the illustrated embodiment, including a pair of first lines 1812 and a row of second lines 1816 stacked in the y-direction.

[0186] As described herein, the lateral dimension of a Metasurface unit cell 1820 or the period of the repeating units of the unit cell 1820 is referred to herein as the unit cell pitch Λ a The pitch Λ a repeats at least twice at regular intervals in the x-direction across the waveguide 1804. In other words, the unit cell pitch Λ a may be the distance between the same points of the nearest neighboring unit cells 1820. In various embodiments, Λ aΛ can be smaller than the wavelength that grating 1800 is configured to diffract, and can be smaller than a wavelength in the range of about 435 nm to 780 nm, or any wavelength. In some embodiments, Λ is configured to diffract at least red light. a can be less than a wavelength (or any wavelength) in the range of about 620-780 nm. In some other embodiments configured to diffract at least green light, Λ a can be less than a wavelength (or any wavelength) in the range of about 492-577 nm. In some other embodiments configured to diffract at least blue light, Λ a can be less than a wavelength (or any wavelength) in the range of about 435-493 nm. Alternatively, according to various embodiments, Λ a may be in the range of 10 nm to 1 μm, including 10 nm to 500 nm or 300 nm to 500 nm. It should be understood that each of the metasurfaces disclosed herein may be utilized to diffract light and may be part of a display system 250 (FIG. 6), which may be configured to direct light having a narrow band of wavelengths to the metasurface. Preferably, Λ for a given metasurface a is less than the smallest wavelength of the band of wavelengths that a light source of the display system is configured to direct at the metasurface.

[0187] In some embodiments, Λ a It has been found that α can have a value that is less than the ratio mλ / (sinα+n2sinθ), where m is an integer (e.g., 1, 2, 3...), and α, n2, and θ each have values described elsewhere herein. For example, α can be in the range Δα over 40 degrees, n2 can be in the range of 1 to 2, and θ can be in the range of 40 to 80 degrees.

[0188] In some embodiments, Λ a may be substantially constant across the surface 1804S of the grating 1800 formed by the plurality of unit cells. However, embodiments are not so limited, and in some other embodiments, Λa may vary across surface 1804S.

[0189] Still referring to FIG. 18B , in some embodiments, each of the second lines 1816 is at least two, three, four, or more times shorter than each of the one or more first lines 1812. However, embodiments in which the second lines 1816 are longer than the one or more first lines 1812 are also possible. According to various embodiments, the one or more first lines 1812 may have a length L1 in the range of 200 μm to 5 mm, 200 μm to 1 mm, or 1 mm to 5 mm. According to various embodiments, the second lines 1816 may have a length L2 in the range of 100 nm to 500 nm, 100 nm to 300 nm, and 300 nm to 500 nm. In some embodiments, the one or more first lines 1812 may have a length L1 corresponding to the total lateral dimension of the optical element formed by the metasurface, e.g., corresponding to the length of an internal or external coupling optical element formed by the metasurface comprising the lines 1812. In some embodiments, the second lines have a unit cell pitch Λ a About 40% to about 60% of, for example, Λ a In some embodiments, L1 is such that the one or more first lines 1812 span a distance in the y-direction corresponding to five second lines 1816. However, it should be understood that the one or more first lines 1812 may span a distance in the y-direction corresponding to more than 1, e.g., more than 10, more than 20, more than 50, or more than 100 second lines 1816, or any suitable number of second lines 1816 in the range between any of 10, 20, and 100, according to various embodiments.

[0190] 18A and 18B, in some embodiments, each of the second lines 1816 has the same length, such that the second lines 1816 extend in the x-direction and co-terminate without crossing any of the one or more first lines 1812. However, embodiments in which the second lines 1816 have different lengths are also possible.

[0191] Still referring to the illustrated embodiment of FIG. 18A , the extension direction (y-direction) of the one or more first lines 1812 is approximately perpendicular to the extension direction (x-direction) of the second lines 1816. That is, the second lines 1816 are rotated relative to the one or more first lines 1812 by a rotation angle of π / 2 when viewed from the propagation direction of the incident light (i.e., into the page). However, the embodiment is not so limited, and the second lines 1816 may extend in any direction that is rotated counterclockwise by an angle less than π / 2 when viewed from the propagation direction of the incident light (i.e., into the page). For example, the second lines 1816 may be rotated relative to the one or more first lines 1812 in a similar manner to how the nanobeams of the waveplates illustrated in FIGS. 17B-17H are rotated relative to the waveplate illustrated in FIG. 17A . For example, the second lines 1816 may be rotated relative to one or more of the first lines 1812 by rotation angles θ of π / 4, π / 2, 3π / 4, π, 5π / 4, 3π / 2, and 7π / 4, respectively. Thus, when a |LCP> beam is incident on the metasurface 1808 having the first and second lines 1812 and 1816, a |RCP> output beam is produced, and the resulting phase delay of the polarization vectors corresponding to the TE and TM polarizations is φ g = 2θ, where θ is the change in rotation angle when the fast axis of the wave plate is rotated by the rotation angle θ. In particular, for the illustrated embodiment, a second line 1816, which is rotated by θ = π / 2 relative to the one or more first lines 1812, diffracts an incident light beam, e.g., an |LCP> beam, thereby generating a diffracted |RCP> beam, which is diffracted by the second line 1816 through φ gThus, after passing through a metasurface 1808 in which one or more first lines 1812 and second lines 1816 alternating in the x-direction have a constant orientation angle difference Δθ=π / 2, as in the illustrated embodiment, the transmitted RCP wave is delayed by a constant phase difference Δφ g = π is shown between adjacent ones of one or more first lines 1812 and second lines 1816. As a result, by varying the fast axis orientation from 0 to π, phase pickup / delay covering the full 0 to 2π range can be achieved, but with a much more compact unit cell pitch and higher diffraction angles compared to the illustrated examples in Figures 17A-17H.

[0192] Display devices having geometric phase metasurface-based gratings formed from polymer-based optical structures incorporating inorganic materials - Patent Application 20070122999 As disclosed herein, in various embodiments described above, a periodic polymer-based optical structure having inorganic materials incorporated therein, which may be configured as a metasurface, may be implemented as an in-coupling optical element (e.g., as one or more of in-coupling optical elements 700, 710, 720 (FIG. 9A)) to in-couple incident light such that the light propagates through substrate 1304 via total internal reflection. However, given that metasurface 1808 may also be configured to deflect light impinging thereon from within substrate 1804, in some embodiments, metasurfaces disclosed herein may be applied to form out-coupling optical elements, such as one or more of out-coupling optical elements 570, 580, 590, 600, 610 (FIG. 6) or 800, 810, 820 (FIG. 9B), instead of or in addition to forming in-coupling optical elements at different locations on surface 2000a. In some other embodiments, the metasurface 1808 may be utilized as an optical dispersive element (e.g., OPE) 730, 740, 750 (FIG. 9B). It should be understood that when different waveguides have different associated primary colors, the out-coupling optical element and / or in-coupling optical element associated with each waveguide may have a geometric size and / or periodicity specific to the wavelength or color of light that the waveguide is configured to propagate. Thus, different waveguides may have metasurfaces with different arrangements of one or more first lines 1812 and second lines 1816. In particular, the different arrangements may depend on the wavelength or color of the incident light beam. For example, depending on the color of the incident light beam, Λ a may be configured differently according to the wavelengths that grating 1800 is configured to diffract. For example, to diffract at least red, green, or blue light, metasurface 1808 may have Λ, which is less than wavelengths in the range of about 620-780 nm, less than wavelengths in the range of about 492-577 nm, and less than wavelengths in the range of about 435-493 nm, respectively. a Λ may be configured to have aTo scale Λ, parameters such as the refractive index, width, height, and spacing of one or more of the first lines 1312 and / or second lines 1316 may be adjusted proportionally. a may be kept relatively uniform for different wavelengths of incident light by compensating for one or more of sin α, n 2 , and sin θ, as explained above.

[0193] FIG. 19 illustrates a top-down view of a diffraction grating 2500 comprising a metasurface with geometric phase optical elements according to some other embodiments. It should be understood that some embodiments of metasurfaces disclosed herein can be formed from two to four sets of nanobeams, each extending in a different direction. FIGS. 18A-18B illustrate a metasurface with two sets of nanobeams, and FIG. 19 illustrates a metasurface with four sets of nanobeams. In particular, the diffraction grating 2500 of FIG. 19 comprises a four-level geometric phase metasurface. Similar to the diffraction grating 1800 described above with reference to FIGS. 18A and 18B, the diffraction grating 2500 includes a substrate, e.g., a waveguide, on which a metasurface configured to diffract light having wavelengths within the visible spectrum is formed. The metasurface includes one or more first lines 2512 extending in a first lateral direction (e.g., the y-direction) and a plurality of second lines 2516 extending in a second direction (e.g., the x-direction). The one or more first lines 2512 and second lines 2516 are disposed adjacent to one another in the second direction, and the first lines 2512 and second lines 2516 alternate in the second direction with a period that is less than the wavelength in the visible spectrum at which the metasurface is configured to diffract. In some embodiments, the second lines 2516 are stacked laterally in the y-direction between adjacent pairs of first lines 2512. Various features of the one or more first lines 1812 and second lines 1816 of the diffraction grating 2500 are similar to the corresponding features of the diffraction grating 1800 described above with reference to Figures 18A and 18B, except for the following differences.

[0194] 18A and 18B , the diffraction grating 2500 further includes a plurality of third lines 2514 each extending in a third direction and a plurality of fourth lines 2518 each extending in a fourth direction. The first, second, third, and fourth directions may be different from each other. The plurality of third lines 2514 may be considered to form a third set of nanobeams, and the plurality of fourth lines 2518 may be considered to form a fourth set of nanobeams. The third lines 2514 are disposed on a first side of the second lines 2516 and are interposed in a second direction (e.g., the x-axis direction) between one or more of the first lines 2512 and the second lines 2516. The fourth line 2518 is disposed on a second side of the second line 2516 opposite the first side and is interposed in a second direction (e.g., the x-direction) between another one or more first lines 2512 and the second line 2516.

[0195] Unlike the diffraction grating 1800 described above with reference to Figures 18A and 18B, the diffraction grating 2500 may have only one first line 2512. In some other embodiments, the diffraction grating 2500 may have multiple first lines 2512, for example, a pair of first lines such as the diffraction grating 1800 described above with reference to Figures 18A and 18B.

[0196] In some embodiments, the third lines 2514 have the same length and / or the fourth lines 2518 have the same length such that the third lines 2514 and / or the fourth lines 2518 co-terminate in the third and fourth directions, respectively. However, other embodiments are possible in which different ones of the third lines 2514 and / or different ones of the fourth lines 2518 do not co-terminate. Additionally, in some embodiments, the co-terminating third lines 2514 and the co-terminating fourth lines 2518 have the same length. However, in other embodiments, the co-terminating third lines 2514 and the co-terminating fourth lines 2518 have different lengths.

[0197] In some embodiments, adjacent ones of the third lines 2514 are separated by a regular interval in a first direction (e.g., the y-direction) and / or adjacent ones of the fourth lines 2518 are separated by a regular interval in the first direction. However, other embodiments are possible in which the third lines 2514 and / or the fourth lines 2518 are not separated by a regular interval. Additionally, in some embodiments, the regularly spaced third lines 2514 and the regularly spaced fourth lines 2518 have the same regular interval. However, in other embodiments, the regularly spaced third lines 2514 and the regularly spaced fourth lines 2518 have different intervals.

[0198] In some embodiments, the third lines 2514 have the same width and / or the fourth lines 2518 have the same width. However, in other embodiments, the third lines 2514 and / or the fourth lines 2518 have different widths. Additionally, in some embodiments, the widths of the third lines 2514 and the fourth lines 2518 having the same width are the same. However, in some other embodiments, the widths of the third lines 2514 and the fourth lines 2518 having the same width are different. Additionally, in some embodiments, the third lines 2514 and the fourth lines 2518 have the same width as one or both of the first lines 2512 and the second lines 2416.

[0199] In some embodiments, the third lines 2514 extend in a third direction that, when viewed from the propagation direction of the incident light (e.g., into the plane of the page), is rotated counterclockwise relative to the one or more first lines 2512 by an angle that is less than the minimum rotation angle of the second lines 2516 relative to the one or more first lines 2512. In some embodiments, the second lines 2516 are rotated 90 degrees or π / 2 relative to the one or more first lines 2512, and the third lines 2514 are rotated 45 degrees or π / 4 relative to the one or more first lines 2512. Additionally, the fourth lines 2518 extend in a fourth direction that, when viewed from the propagation direction of the incident light, is rotated counterclockwise relative to the one or more first lines 2512 by an angle that is greater than the minimum rotation angle of the second lines 2516 relative to the one or more first lines 2512. In some embodiments, the second line 2516 is rotated 90° or π / 2 relative to one or more of the first lines 2512, and the third line 2514 is rotated 135° or 3π / 4 relative to one or more of the first lines 2512.

[0200] In some embodiments, similar to the waveplate combinations illustrated above with reference to Figures 17A-17H, the phase difference caused by the relative orientation of one or more of first lines 2512, second lines 2516, third lines 2514, and fourth lines 2518 can vary from 0 to π. When third lines 2514, fourth lines 2518, and second lines 2516 are rotated by π / 4, 3π / 4, and π with respect to one or more of first lines 2512, phase pickup / delays of π / 2, 3π / 2, and 2π, respectively, can be achieved, according to some embodiments, such that phase pickup / delays covering the full 0 to 2π range can be achieved. As a result, by varying the fast axis orientation from 0 to π, phase pickup / delays covering the full 0 to 2π range can be achieved, but with a much more compact unit cell pitch and higher diffraction angles compared to the examples illustrated in Figures 12A-12H.

[0201] Display devices based on geometric phase metasurfaces with polymer-based optical structures incorporating inorganic materials In various embodiments of the display system (see, e.g., back to Figures 9A and 9B), the set of waveguides 1200 may include a periodic polymer-based optical structure having inorganic material incorporated therein, which may be configured as a metasurface grating, configured to operate in a transmissive mode. In various embodiments, the set of waveguides 1200 includes waveguides 670, 680, 690 corresponding to each primary color (R, G, B), which in turn form individual ones of the internal coupling optical elements 700, 710, 720, which may include or correspond to the gratings 1300, 2500 therein or thereon, as described above with reference to Figures 18A, 18B, and 19. Waveguides 670, 680, 690 may additionally have formed therein or thereon respective ones of optically dispersive elements (e.g., OPEs) 730, 740, 750 and / or outcoupling optical elements (e.g., EPEs) 800, 810, 820, including or corresponding to EPE / OPE 1846, described above with reference to Figures 18A and 18B. In operation, in some embodiments, when an incident light beam 1830, e.g., visible light, is incident on metasurface 1808 at an incident angle α, grating 1800, 2500 diffracts the incident light into diffracted light beams 1842, 1838 at a diffraction angle θ2. One or both of diffracted light beams 1838 and 1842 are diffracted at a critical angle θ2 due to the occurrence of total internal reflection for substrate 1804, which is configured as a waveguide having a refractive index n2. TIR When the light is diffracted at a diffraction angle greater than θ, the condition θ2>θ TIR and θ1>θ TIR are satisfied, one or both of the diffracted light beams 1838 and 1842 propagate in their respective opposite directions along the x-axis by total internal reflection (TIR). Subsequently, in some embodiments, the diffracted light beam 1846 is coupled into the substrate 1804 under TIR mode until it reaches an orthogonal pupil expander (OPE) 1846 or an exit pupil expander (EPE) 1846, described above with reference to Figures 9A and 9B.

[0202] It should be understood that substrate 1804 configured as a waveguide with a metasurface formed thereon, according to various embodiments, can be used to form a display system, such as system 250 (FIG. 6) disclosed herein. For example, the metasurface may be utilized as an incoupling, light dispersing, and / or outcoupling optical element, as described herein. In some embodiments, after metasurface fabrication, waveguide 2000 may be optically coupled to a light pipe, such as a light pipe, for injecting image information from a spatial light modulator into the waveguide. The light pipe may, in some embodiments, be an optical fiber. Examples of light pipes include image injection devices 360, 370, 380, 390, 400 (FIG. 6) and scanning optical fibers. In some embodiments, multiple waveguides, each having a metasurface 1808, may be provided, and each of these waveguides may be optically coupled to one or more image injection devices. Additional Examples 1. A method of fabricating an optical element, comprising: providing a substrate having a first refractive index and transparency within the visible spectrum; and forming a periodically repeating polymer structure on the substrate; exposing the substrate to a metal precursor and then to an oxidizing precursor; wherein the exposing is carried out under pressure and temperature such that an inorganic material, including a metal of the metal precursor, is incorporated into the periodically repeating polymer structure, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index. 2. The method of example 1, wherein the exposing is carried out under a pressure of about 100 mTorr to about 10 Torr. 3. The method of example 1 or example 2, wherein the exposing is carried out at a temperature below about 150 degrees Celsius. 4. The method of any one of the preceding examples, wherein forming the periodically repeating polymeric structures comprises patterning by nanoimprinting. 5. The method of any one of the preceding embodiments, wherein forming the periodically repeating polymeric structure comprises lithographic patterning. 6. The method of any one of the preceding examples, wherein the periodically repeating polymer structure is formed from a material whose bulk refractive index is less than a second refractive index, and the inorganic material has a bulk refractive index higher than the second refractive index. 7. The method of any one of the preceding embodiments, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. 8. The method of any one of the preceding embodiments, wherein the substrate has a refractive index greater than 1.5. 9. The method of any one of the preceding embodiments, wherein the periodically repeating polymer structure comprises a photoresist. 10. The method of any one of the preceding embodiments, wherein exposing the substrate to a metal precursor comprises exposing to a precursor comprising a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. 11. The method of any one of the preceding examples, wherein exposing the substrate to the metal precursor and the oxidizing precursor comprises exposing at a partial pressure of, and for such a duration of time as is sufficient to saturate the exposed surface of the periodically repeating polymer structure with at least a monolayer of inorganic material. 12. The method of any one of the preceding examples, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration greater than 1 second. 13. The method of any one of the preceding examples, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal oxide. 14. The method of example 13, wherein the metal oxide comprises a transition metal oxide. 15. The method of example 14, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 16. The method of any one of the preceding embodiments, wherein the exposing incorporates inorganic material selectively to the exposed surface of the substrate through the exposed surface of the periodically repeating polymer structure. 17. The method of Example 16, wherein forming the periodically repeating polymer structure includes separating by spaces, the spaces having a substrate surface on which no polymer layer is disposed, and wherein exposing does not result in deposition of inorganic material on or incorporation of inorganic material through the substrate surface in the spaces. 18. The method of example 16, wherein forming the periodically repeating polymer structures includes separating by spaces, the spaces having a substrate surface on which a polymer layer is disposed, the polymer layer having a thickness less than a height of the periodically repeating polymer structures, and wherein exposing incorporates the inorganic material into the polymer layer formed on the substrate surface within the spaces. 19. The method of example 18, wherein the polymer layer formed on the substrate surface in the space has a total thickness that incorporates an inorganic material. 20. The method of example 18, wherein the polymer layer formed on the substrate surface in the space has a partial thickness that incorporates inorganic material and a partial thickness that does not incorporate inorganic material. 21. An optical element comprising: a substrate having a first refractive index and transparency within the visible spectrum; a pattern of periodically repeating optical structures formed on a substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and including a polymeric material having inorganic material incorporated therein; An optical element comprising: 22. The optical element of example 21, wherein the polymeric material has a bulk refractive index less than the second refractive index, and the inorganic material has a bulk refractive index greater than the second refractive index. 23. The optical element of example 21 or example 22, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. 24. The optical element of any one of Examples 21-23, wherein the substrate has a refractive index greater than 1.5. 25. The optical element of any one of Examples 21-24, wherein the polymeric material comprises a photoresist. 26. The optical element of any one of Examples 21-25, wherein the inorganic material comprises a transition metal oxide. 27. The optical element of example 26, wherein the inorganic material comprises a metal oxide. 28. The optical element of example 27, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 29. The optical element of example 27, wherein the inorganic material is incorporated into a surface region of the optical structure and the core region of the optical structure does not have the inorganic material incorporated therein. 30. An optical element described in any one of Examples 21-29, wherein adjacent ones of the periodically repeating optical structures are separated by a space, and the surface of the substrate within the space does not have inorganic material disposed thereon. 31. An optical element described in any one of Examples 21-30, wherein adjacent ones of the periodically repeating optical structures are separated by a space, and a surface of the substrate within the space has a layer of polymer material formed thereon having inorganic material incorporated therein, the layer of polymer material having a thickness less than the height of the optical structures. 32. The optical element of example 31, wherein the layer of polymeric material formed within the space is incorporated with inorganic material throughout its thickness. 33. The optical element of example 31, wherein the layer of polymeric material formed within the space is partially incorporated with inorganic material in the surface region and partially not incorporated with inorganic material. 34. The optical element of any one of examples 21-33, wherein the substrate is configured such that visible light diffracted by the periodically repeating optical structure propagates under total internal reflection. 35. An optical system comprising: An optical element comprising: a substrate having a first refractive index and transparency within the visible spectrum; a pattern of periodically repeating optical structures formed on a substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and including a polymeric material having inorganic material incorporated therein; wherein the periodically repeating optical structure comprises nanobeams arranged as a metasurface, the metasurface comprising a plurality of repeating unit cells, each unit cell comprising: a first nanobeam set formed by one or more first nanobeams; a set of second nanobeams formed by one or more second nanobeams disposed adjacent to the one or more first nanobeams and separated from each other by a sub-wavelength spacing, wherein the one or more first nanobeams and the plurality of second nanobeams are elongated in different orientation directions; An optical system comprising an optical element. 36. The optical system of example 35, wherein the unit cells repeat with a period of about 10 nm to 1 μm or less. 37. The optical system of example 35 or example 36, wherein the one or more first nanobeams and the second nanobeam are oriented at an angle relative to each other that causes a phase difference between visible light diffracted by the one or more first nanobeams and visible light diffracted by the second nanobeam. 38. The optical system of any one of Examples 35-37, wherein the one or more first nanobeams and the second nanobeam are oriented in orientation directions that are rotated approximately 90 degrees relative to one another. 39. The optical system of any one of Examples 35-38, wherein the unit cells repeat with a period of less than a wavelength, and the wavelength is within the visible spectrum. 40. The optical system of any one of Examples 35-39, wherein the one or more first nanobeams and the second nanobeam have a height that is less than the wavelength. 41. An optical system comprising a waveguide configured to propagate visible light; a substrate having a first refractive index and transparency within the visible spectrum such that light may be guided therein by total internal reflection; a pattern of periodically repeating optical structures formed on a substrate and configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index and including a polymeric material having inorganic material incorporated therein; wherein the periodically repeating optical structures are arranged to diffract light at a diffraction angle relative to a direction of incident light and cause the diffracted light to propagate within the substrate under total internal reflection, or are arranged to diffract light guided within the substrate under total internal reflection at a diffraction angle relative to a direction of the light guided within the substrate. 42. The optical system of example 41, wherein the polymeric material has a bulk refractive index less than the second refractive index, and the inorganic material has a bulk refractive index greater than the second refractive index. 43. The optical system of example 41 or example 42, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. 44. The optical system of any one of Examples 41-43, wherein the diffraction angle is greater than 50 degrees. 45. The optical system of any one of Examples 41-44, further comprising a light source configured to emit light of wavelengths into the pattern of periodically repeating optical structures. 46. The optical system of any one of Examples 41-45, further comprising a spatial light modulator configured to modulate light from the light source and output the modulated light in a pattern of periodically repeating optical structures. 47. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; and a display disposed on the frame, wherein at least a portion of the display comprises: one or more waveguides, the one or more waveguides being transparent and positioned at locations in front of the user's eyes such that, when the user wears the head mounted display device, the transparent portions transmit light from a portion of the environment in front of the user to the user's eyes to provide a view of the portion of the environment in front of the user; one or more light sources; at least one diffraction grating configured to couple light from a light source into or out of one or more waveguides, the diffraction grating comprising an optical element, the optical element comprising: a substrate having a first refractive index and transparency within the visible spectrum; A pattern of periodically repeating optical structures formed on a substrate and configured to diffract visible light. a pattern of periodically repeating optical structures comprising a polymeric material having a second refractive index greater than the first refractive index and having inorganic material incorporated therein; a diffraction grating comprising: a display comprising: A head-mounted display device comprising: 48. The device of example 47, wherein the one or more light sources comprise a fiber scanning projector. 49. A device described in Example 47 or Example 48, wherein the display is configured to project light into the user's eye so as to present image content to the user at multiple depth planes. 50. The method of any one of Examples 1-20, wherein the exposing is carried out under a pressure of less than 10 atm (atmospheric pressure). 51. The method of any one of Examples 1-20 and 50, wherein the exposing is carried out at a temperature greater than 25 degrees Celsius. 52. The method of any one of Examples 1-20 and 50-51, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration of from about 1 second to about 1000 seconds. 53. The method of any one of Examples 1-20 and 50-52, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal nitride. 54. An optical element according to any one of Examples 21-34, wherein the periodically repeating optical structure comprises a metasurface. 55. The optical element of any one of Examples 21-34 and 54, wherein the substrate is configured such that visible light is guided therein under total internal reflection and diffracted out of the substrate by the periodically repeating optical structure. 56. An optical element described in any one of Examples 21-34 and 54-55, wherein the substrate is configured such that visible light is guided therein under total internal reflection, diffracted by the periodically repeating optical structure, and modifies the direction of the light beam propagating within the substrate by total internal reflection. 57. An optical system described in any one of Examples 41-46, wherein the periodically repeating optical structure is arranged to diffract light at a diffraction angle relative to the direction of the incident light and cause the diffracted light to propagate within the substrate under total internal reflection. 58. The optical system of any one of Examples 41-46 and 57, wherein the periodically repeating optical structures are arranged to diffract light guided within the substrate under total internal reflection at a diffraction angle relative to the direction of the light guided within the substrate. 59. The optical system of example 58, wherein the periodically repeating optical structures are arranged to diffract light guided within the substrate out of the substrate under total internal reflection. 60. A method for fabricating an optical element, comprising: providing a substrate that is transparent in the visible spectrum; forming a periodically repeating polymer structure on a substrate, the periodically repeating polymer structure having a first refractive index; exposing the substrate to a metal precursor and then to an oxidizing precursor; wherein the exposing is carried out at a pressure and temperature such that an inorganic material, including a metal of the metal precursor, is incorporated into the periodically repeating polymer structure, thereby increasing the refractive index of the periodically repeating polymer structure and forming a pattern of periodically repeating optical structures configured to diffract visible light. 61. The method of example 60, wherein the exposing is carried out under a pressure of about 100 mTorr to about 10 Torr. 62. The method of example 60 or example 61, wherein the exposing is carried out at a temperature below about 150 degrees Celsius. 63. The method of any one of Examples 60-62, wherein forming a periodically repeating polymer structure comprises patterning by nanoimprinting. 64. The method of any one of Examples 60-63, wherein forming the periodically repeating polymer structure comprises lithographic patterning. 65. The method of any one of Examples 60-64, wherein the periodically repeating polymer structure is formed from a material whose bulk refractive index is less than the refractive index of the periodically repeating optical structure, and the inorganic material has a bulk refractive index higher than the refractive index of the periodically repeating optical structure. 66. The method of any one of Examples 60-65, wherein the refractive index of the periodically repeating optical structure is greater than 1.7 and greater than the refractive index of the periodically repeating polymer structure by at least 0.2. 67. The method of any one of examples 60-66, wherein the substrate has a refractive index greater than 1.5. 68. The method of any one of Examples 60-67, wherein the periodically repeating polymer structure comprises a photoresist. 69. The method of any one of Examples 60-68, wherein exposing the substrate to a metal precursor comprises exposing to a precursor comprising a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. 70. The method of any one of Examples 60-69, wherein exposing the substrate to the metal precursor and the oxidizing precursor comprises exposing at a partial pressure of, and for such duration of time as is sufficient to saturate the exposed surface of the periodically repeating polymer structure with at least a monolayer of inorganic material. 71. The method of any one of Examples 60-70, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration greater than 1 second. 72. The method of any one of examples 60-71, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal oxide. 73. The method of example 72, wherein the metal oxide comprises a transition metal oxide. 74. The method of example 73, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 75. The method of any one of Examples 60-74, wherein the exposing incorporates inorganic material through the exposed surface of the periodically repeating polymer structure selectively to the exposed surface of the substrate. 76. The method of Example 75, wherein forming the periodically repeating polymer structure includes separating by spaces, the spaces having a substrate surface on which no polymer layer is disposed, and the exposing does not result in deposition of an inorganic material on or incorporation of an inorganic material through the substrate surface in the spaces. 77. The method of example 75, wherein forming the periodically repeating polymer structures includes separating by spaces, the spaces having a substrate surface on which a polymer layer is disposed, the polymer layer having a thickness less than a height of the periodically repeating polymer structures, and wherein exposing incorporates the inorganic material into the polymer layer formed on the substrate surface within the spaces. 78. The method of example 77, wherein the polymer layer formed on the substrate surface in the space has a total thickness that incorporates an inorganic material. 79. The method of example 77, wherein the polymer layer formed on the substrate surface in the space has a partial thickness that incorporates inorganic material and a partial thickness that does not incorporate inorganic material. 80. A method for fabricating an optical element, comprising: providing a substrate having a first refractive index and transparency within the visible spectrum, the substrate having a periodically repeating polymer structure formed thereon; exposing the substrate to a metal precursor and then to an oxidizing precursor; wherein the exposing is carried out under pressure and temperature such that an inorganic material, including a metal of the metal precursor, is incorporated into the periodically repeating polymer structure, thereby forming a pattern of periodically repeating optical structures configured to diffract visible light, the optical structures having a second refractive index greater than the first refractive index. 81. The method of example 80, wherein the exposing is carried out under a pressure of about 100 mTorr to about 10 Torr. 82. The method of example 80 or example 81, wherein the exposing is carried out at a temperature below about 150 degrees Celsius. 83. The method of any one of examples 80-82, wherein forming a periodically repeating polymer structure comprises patterning by nanoimprinting. 84. The method of any one of examples 80-83, wherein forming the periodically repeating polymer structure comprises lithographic patterning. 85. The method of any one of examples 80-84, wherein the periodically repeating polymer structure is formed from a material whose bulk refractive index is less than a second refractive index, and the inorganic material has a bulk refractive index higher than the second refractive index. 86. The method of any one of examples 80-85, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. 87. The method of any one of examples 80-86, wherein the substrate has a refractive index greater than 1.5. 88. The method of any one of Examples 80-87, wherein the periodically repeating polymer structure comprises a photoresist. 89. The method of any one of Examples 80-88, wherein exposing the substrate to a metal precursor comprises exposing to a precursor comprising a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. 90. The method of any one of Examples 80-89, wherein exposing the substrate to the metal precursor and the oxidizing precursor comprises exposing at a partial pressure of, and for such duration of time as is sufficient to saturate the exposed surface of the periodically repeating polymer structure with at least a monolayer of inorganic material. 91. The method of any one of Examples 80-90, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration greater than 1 second. 92. The method of any one of examples 80-91, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal oxide. 93. The method of example 92, wherein the metal oxide comprises a transition metal oxide. 94. The method of example 93, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 95. The method of any one of Examples 80-94, wherein the exposing incorporates inorganic material through the exposed surface of the periodically repeating polymer structure selectively to the exposed surface of the substrate. 96. The method of Example 95, wherein forming the periodically repeating polymer structure includes separating by spaces, the spaces having a substrate surface on which no polymer layer is disposed, and the exposing does not result in deposition of an inorganic material on or incorporation of an inorganic material through the substrate surface in the spaces. 97. The method of Example 95, wherein forming the periodically repeating polymer structures includes separating by spaces, the spaces having a substrate surface on which a polymer layer is disposed, the polymer layer having a thickness less than a height of the periodically repeating polymer structures, and wherein exposing incorporates the inorganic material into the polymer layer formed on the substrate surface within the spaces. 98. The method of Example 97, wherein the polymer layer formed on the substrate surface in the space has a total thickness that incorporates an inorganic material. 99. The method of Example 97, wherein the polymer layer formed on the substrate surface in the space has a partial thickness that incorporates inorganic material and a partial thickness that does not incorporate inorganic material. 100. The method of any one of Examples 80-99, wherein the exposing is carried out under a pressure of less than 10 atm (atmospheric pressure). 101. The method of any one of Examples 80-100, wherein the exposing is carried out at a temperature greater than 25 degrees Celsius. 102. The method of any one of Examples 80-101, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration of from about 1 second to about 1000 seconds. 103. The method of any one of examples 80-102, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal nitride. 104. The method of example 1, wherein the exposing is carried out under a pressure of about 100 mTorr to about 10 Torr. 105. The method of example 2, wherein the exposing is carried out at a temperature below about 150 degrees Celsius. 106. The method of example 1, wherein forming the periodically repeating polymer structure comprises patterning by nanoimprinting. 107. The method of example 1, wherein forming the periodically repeating polymer structure comprises lithographic patterning. 108. The method of example 1, wherein the periodically repeating polymer structure is formed from a material whose bulk refractive index is less than a second refractive index, and the inorganic material has a bulk refractive index higher than the second refractive index. 109. The method of example 1, wherein the second refractive index is greater than 1.7 and greater than the first refractive index by at least 0.2. 110. The method of example 1, wherein the substrate has a refractive index greater than 1.5. 111. The method of example 1, wherein the periodically repeating polymer structure comprises a photoresist. 112. The method of example 1, wherein exposing the substrate to a metal precursor comprises exposing to a precursor comprising a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. 113. The method of Example 1, wherein exposing the substrate to the metal precursor and the oxidizing precursor comprises exposing at a partial pressure of, and for such duration of time as is sufficient to saturate the exposed surface of the periodically repeating polymer structure with at least a monolayer of inorganic material. 114. The method of example 1, wherein exposing the substrate to one or both of the metal precursor and the oxidizing precursor comprises exposing for a duration greater than 1 second. 115. The method of example 1, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal oxide. 116. The method of example 13, wherein the metal oxide comprises a transition metal oxide. 117. The method of example 14, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 118. The method of example 1, wherein the exposing incorporates inorganic material through the exposed surface of the periodically repeating polymer structure selectively to the exposed surface of the substrate. 119. The method of Example 16, wherein forming the periodically repeating polymer structure includes separating by spaces, the spaces having a substrate surface on which no polymer layer is disposed, and the exposing does not result in deposition of an inorganic material on or incorporation of an inorganic material through the substrate surface in the spaces. 120. The method of Example 16, wherein forming the periodically repeating polymer structures includes separating by spaces, the spaces having a substrate surface on which a polymer layer is disposed, the polymer layer having a thickness less than a height of the periodically repeating polymer structures, and wherein exposing incorporates inorganic material into the polymer layer formed on the substrate surface within the spaces. 121. The method of Example 18, wherein the polymer layer formed on the substrate surface in the space has a total thickness that incorporates an inorganic material. 122. The method of Example 18, wherein the polymer layer formed on the substrate surface in the space has a partial thickness that incorporates inorganic material and a partial thickness that does not incorporate inorganic material. 123. The method of example 80, wherein the exposing is carried out under a pressure of about 100 mTorr to about 10 Torr. 124. The method of example 80, wherein the exposing is carried out at a temperature below about 150 degrees Celsius. 125. The method of example 80, wherein forming a periodically repeating polymer structure comprises patterning by nanoimprinting. 126. The method of example 80, wherein forming the periodically repeating polymer structure comprises lithographic patterning. 127. The method of example 80, wherein the periodically repeating polymer structure is formed from a material whose bulk refractive index is less than the refractive index of the periodically repeating optical structure, and the inorganic material has a bulk refractive index higher than the refractive index of the periodically repeating optical structure. 128. The method of example 80, wherein the refractive index of the periodically repeating optical structure is greater than 1.7 and greater than the refractive index of the periodically repeating polymer structure by at least 0.2. 129. The method of example 80, wherein the substrate has a refractive index greater than 1.5. 130. The method of example 80, wherein the periodically repeating polymer structure comprises a photoresist. 131. The method of example 80, wherein exposing the substrate to a metal precursor comprises exposing to a precursor comprising a transition metal selected from the group consisting of aluminum, zinc, zirconium, hafnium, and titanium. 132. The method of example 80, wherein exposing the substrate to the metal precursor and the oxidizing precursor comprises exposing at a partial pressure of, and for such duration of time as is sufficient to saturate the exposed surface of the periodically repeating polymer structure with at least a monolayer of inorganic material. 133. The method of example 80, wherein exposing the substrate to one or both of the metal precursor and the oxidation precursor comprises exposing for a duration greater than 1 second. 134. The method of example 80, wherein the inorganic material incorporated into the periodically repeating polymer structure comprises a metal oxide. 135. The method of example 134, wherein the metal oxide comprises a transition metal oxide. 136. The method of example 135, wherein the metal oxide comprises an oxide selected from the group consisting of aluminum oxide, zinc oxide, zirconium oxide, hafnium oxide, and titanium oxide. 137. The method of example 80, wherein the exposing incorporates inorganic material through the exposed surface of the periodically repeating polymer structure selectively to the exposed surface of the substrate. 138. The method of Example 137, wherein forming the periodically repeating polymer structure includes separating by spaces, the spaces having a substrate surface on which no polymer layer is disposed, and the exposing does not result in deposition of an inorganic material on or incorporation of an inorganic material through the substrate surface in the spaces. 139. The method of example 137, wherein forming the periodically repeating polymer structures includes separating by spaces, the spaces having a substrate surface on which a polymer layer is disposed, the polymer layer having a thickness less than a height of the periodically repeating polymer structures, and wherein exposing incorporates the inorganic material into the polymer layer formed on the substrate surface within the spaces. 140. The method of example 139, wherein the layer of polymer formed on the substrate surface in the space has a total thickness that incorporates inorganic material. 141. The method of example 139, wherein the layer of the polymer layer formed on the substrate surface in the space has a partial thickness that incorporates inorganic material and a partial thickness that does not incorporate inorganic material. 142. A method of fabricating an optical element according to any one of Examples 1-20 and 50-53, further comprising integrating the optical element as part of head-mounted augmented reality eyewear. 143. A method of fabricating an optical element according to any one of Examples 60-79, further comprising integrating the optical element as part of head-mounted augmented reality eyewear. 144. A method of fabricating an optical element according to any one of Examples 80-103, further comprising integrating the optical element as part of head-mounted augmented reality eyewear. 145. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; and a display disposed on the frame, wherein at least a portion of the display comprises: one or more waveguides, the one or more waveguides being transparent and positioned at locations in front of the user's eyes such that, when the user wears the head mounted display device, the transparent portions transmit light from a portion of the environment in front of the user to the user's eyes to provide a view of the portion of the environment in front of the user; one or more light sources; The optical element of any one of Examples 21-34 and 54-56, wherein one or more waveguides of the display form a substrate of the optical element, and the optical element is configured to couple light from one or more light sources into or out of the one or more waveguides; and a display comprising: A head-mounted display device comprising: 146. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; and a display disposed on the frame; one or more light sources; The optical element of any one of Examples 21-34 and 54-56, configured to direct light from one or more light sources into an eye of a user; A head-mounted display device comprising: 147. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; and a display disposed on the frame; one or more light sources; 41. The optical system of any one of Examples 35-40, comprising: an optical element configured to direct light generated from one or more light sources into an eye of a user; A head-mounted display device comprising: 148. A head-mounted display device configured to project light into a user's eye and display augmented reality image content, comprising: a frame configured to be supported on a user's head; and a display disposed on the frame; one or more light sources; The optical element of any one of Examples 41-46 and 57-59, wherein the optical element is configured to direct light generated from one or more light sources into an eye of a user; A head-mounted display device comprising:

[0203] Various exemplary embodiments of the present invention are described herein. Reference is made to these examples in a non-limiting sense. They are provided to illustrate the more broadly applicable aspects of the invention. Various modifications may be made to the invention described, and equivalents may be substituted without departing from the true spirit and scope of the invention.

[0204] For example, while advantageously utilized with AR displays that provide images across multiple depth planes, the augmented reality content disclosed herein may also be displayed by systems that provide images on a single depth plane and / or with virtual reality displays. In some embodiments where multiplexed image information (e.g., light of different colors) is directed into the waveguide, multiple optical elements or metasurfaces may be provided on the waveguide, e.g., one optical element or metasurface active for each color of light. In some embodiments, the pitch or periodicity and / or geometric size of the protrusions forming the optical element or metasurface may vary across its surface. Such meta-optical elements or surfaces may be active in redirecting light of different wavelengths depending on the geometry and pitch at which the light impinges on the optical element or metasurface. In some other embodiments, the geometry and pitch of the optical element or metasurface features are configured to vary so that deflected light rays, even those of similar wavelengths, propagate away from the optical element or metasurface at different angles. It should also be understood that multiple separated optical elements or metasurfaces may be arranged across the substrate surface, with each optical element or metasurface having the same geometry and pitch in some embodiments, or at least some of the optical elements or metasurfaces having a different geometry and / or pitch than the other optical elements or metasurfaces in some other embodiments.

[0205] Although advantageously applied to displays such as wearable displays, optical elements or metasurfaces may also be applied to a variety of other devices where a compact, low-profile light redirecting element is desired. For example, optical elements or metasurfaces may be applied to form the light redirecting portions of optical plates (e.g., glass plates), optical fibers, microscopes, sensors, watches, cameras, and image projection devices in general.

[0206] In addition, many modifications may be made to adapt a particular situation, material, composition of matter, process, process acts or steps, to the objective, spirit, or scope of the present invention. Moreover, as will be understood by those skilled in the art, each of the individual variations described and illustrated herein has discrete components and features that can be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present invention. All such modifications are intended to be within the scope of the claims associated with this disclosure.

[0207] The present invention includes methods that may be implemented using the present device. The method may include the act of providing such a suitable device. Such provisioning may be performed by a user. In other words, the act of "providing" merely requires the user to obtain, access, approach, locate, configure, activate, power on, or otherwise act to provide the required device in the present method. The methods described herein may be carried out in any order of the recited events, and in the recited order of events, that is logically possible.

[0208] Exemplary aspects of the invention, along with details regarding material selection and manufacturing, have been described above. As for other details of the invention, these may be understood in conjunction with the above-referenced patents and publications and may generally be understood or understood by those skilled in the art. The same may be true with respect to method-based aspects of the invention in terms of additional acts as generally or theoretically employed.

[0209] For ease of description, various words are used herein to indicate the relative location of features. For example, various features may be described as being "on top of," "over," "to the side of," "higher than," or "lower than" other features. Other words of relative location may also be used. All such words of relative location assume that the aggregate structure or system formed by the features as a whole is in a certain orientation as a reference point for purposes of description, but it should be understood that when used, the structures may be positioned parallel, inverted, or in any number of other orientations.

[0210] Additionally, while the present invention has been described with reference to several embodiments that optionally incorporate various features, the present invention is not limited to what has been described or indicated as being considered with respect to each variation of the invention. Various modifications may be made to the invention as described, and equivalents may be substituted (whether described herein or not included for purposes of brevity) without departing from the true spirit and scope of the invention. Additionally, when a range of values is provided, it is understood that all intervening values between the upper and lower limits of that range, and any other stated or intervening value within that stated range, are encompassed within the invention.

[0211] It is also contemplated that any optional features of the described inventive variations may be set forth and claimed independently or in combination with any one or more of the features described herein. Reference to a singular item includes the possibility that there are plural of the same items. More specifically, as used herein and in the claims associated therewith, the singular forms "a," "an," "said," and "the" include plural referents unless specifically stated otherwise. In other words, the use of articles in the above description and in the claims associated with this disclosure allows for "at least one" of the subject item. Furthermore, it should be noted that such claims may be drafted to exclude any optional element. Accordingly, this statement is intended to serve as a predicate for the use of such exclusive terminology, such as "only," "only," and the like, in connection with the recitation of claim elements, or the use of a "negative" limitation.

[0212] Without using such exclusive language, the term "comprising" in the claims associated with this disclosure shall permit the inclusion of any additional elements, regardless of whether a given number of elements are recited in such claims or whether the addition of features can be considered to change the nature of the elements recited in such claims. Except as specifically defined herein, all technical and scientific terms used herein shall be given the broadest possible commonly understood meaning while maintaining the validity of the claims.

[0213] The scope of the present invention is not limited to the examples provided and / or this specification, but rather is limited only by the scope of the terms of the claims associated with this disclosure. Indeed, the novel apparatus, methods, and systems described herein may be embodied in a variety of other forms. Furthermore, various omissions, substitutions, and changes in the form of the systems and methods described herein may be made without departing from the spirit of the disclosure. For example, while blocks are presented in a given arrangement, alternative embodiments may perform similar functionality with different components and / or circuit topologies, and some blocks may be deleted, moved, added, subdivided, combined, and / or modified. Each of these blocks may be implemented in a variety of different ways. Any suitable combination of elements and acts of the various embodiments described above can be combined to provide further embodiments. The various features and processes described above may be implemented independently of each other or combined in various ways. All suitable combinations and subcombinations of features of the present disclosure are intended to be within the scope of the present disclosure.

Claims

1. 1. A method of fabricating an optical element, comprising: providing a substrate having a first refractive index, said substrate having transparency within the visible spectrum; forming a periodically repeating polymer structure on the substrate, the polymer structure having an initial refractive index; performing a first atomic layer deposition step to form a molecular layer of a first precursor on the periodically repeating polymer structure; performing a second atomic layer deposition step using a second precursor different from the first precursor to form a layer of target material on the periodically repeating polymer structure, wherein the periodically repeating polymer structure comprising the layer of target material is configured to diffract visible light and has a second refractive index greater than the first refractive index and greater than the initial refractive index; Including, performing the first atomic layer deposition step occurs in a reaction chamber, the method including purging the first precursor from the reaction chamber after performing the first atomic layer deposition step; performing the second atomic layer deposition step occurs within the reaction chamber, the method including purging the second precursor from the reaction chamber after performing the second atomic layer deposition step; performing the first atomic layer deposition step, purging the first precursor, performing the second atomic layer deposition step, and purging the second precursor constitute a growth cycle, and the method includes repeatedly performing the growth cycle until a predetermined thickness of the layer of the target material is achieved; The method includes controlling the diffusion of the first precursor and the second precursor into the periodically repeating polymer structure during the growth cycle by controlling purge time, total pressure, partial pressure, and / or substrate temperature.

2. The method of claim 1 , wherein the first precursor comprises a metal precursor.

3. The method of claim 2 , wherein the metal precursor comprises a transition metal.

4. The method of claim 3 , wherein the transition metal comprises Al, Zn, Zr, Hf, Ti, or Ta.

5. The method of claim 2 , wherein the metal precursor comprises an alkoxide or a β-diketonate.

6. The method of claim 2 , wherein the metal precursor comprises a halide compound.

7. The method of claim 2 , wherein the metal precursor comprises an alkyl compound.

8. The method of claim 2 , wherein the metal precursor comprises an alkoxide compound.

9. The method of claim 1 , wherein the second precursor comprises an oxidation precursor.

10. 10. The method of claim 9, wherein the oxidation precursor comprises molecular oxygen, ozone, water, hydrogen peroxide, nitrous oxide, ammonia, or a combination thereof.

11. The method of claim 1 , wherein the periodically repeating polymer structure comprises a plurality of functional groups configured to react with the first precursor to form an inorganic material.

12. The method of claim 11 , wherein the plurality of functional groups comprises a carbonyl group, a hydroxyl group, or a pyridine group.

13. The method of claim 1 , wherein at least a portion of the first precursor diffuses into the periodically repeating polymer structure and reacts with functional groups of the periodically repeating polymer structure.

14. 14. The method of claim 13, wherein at least a portion of the second precursor diffuses into the periodically repeating polymer structure and reacts with the first precursor to form the target material.

15. The method of claim 14 , wherein the target material is an inorganic material.

16. The method of claim 1 , wherein at least a portion of the target material diffuses into the periodically repeating polymer structure after it is formed.

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