Methods for improving the display efficiency and uniformity of AR waveguides.

Abstract

The disclosed embodiments generally relate to a method for modifying and engineering the effective thickness of an optical device substrate, which provides for depositing an index-matched material on the substrate to alter the thickness profile of the optical device. By adjusting the thickness profile, the optical path of the light is modulated to direct the light to an output coupling grating.

Description

[Technical field]

[0001] FIELD OF THE DISCLOSURE Embodiments of the present disclosure relate generally to optical devices. More particularly, embodiments described herein provide a method for modifying and engineering the effective thickness of an optical device substrate. [Background technology]

[0002] Virtual reality is generally considered to be a computer-generated simulated environment in which a user has an apparent physical presence. Virtual reality experiences are generated in 3D and may be viewed using a head-mounted display (HMD), such as glasses or other wearable display devices, that have a near-eye display panel as an optical device for displaying the virtual reality environment that replaces the real environment.

[0003] However, augmented reality allows for an experience where a user can still look through the optics of the glasses or other HMD device to view the surrounding environment, and can also see images of virtual objects that are generated for display and appear as part of that environment. Augmented reality can include any type of input, such as audio and haptic input, as well as virtual images, graphics, and video, that enhances or augments the environment the user experiences. As an emerging technology, there are many challenges and design constraints for augmented reality.

[0004] In particular, it can be difficult to maintain color uniformity and high coupling efficiency of an optical device, which are related to optical interference between different light paths within the optical device. Therefore, what is needed in the art is an improved method for modulating the optical interference to improve light coupling efficiency to an output coupler and optimize efficiency over a field of view. Summary of the Invention

[0005] In one embodiment, an optical device is provided. The optical device includes a substrate having a substrate thickness distribution defined by a top surface of the substrate and a bottom surface of the substrate. The substrate thickness distribution varies along a first length parallel to the top surface and a second length perpendicular to the first length. The optical device further includes an index-matched layer disposed on the bottom surface of the substrate, the index-matched layer having an engineered thickness distribution defined by an outer surface of the index-matching layer and the bottom surface of the substrate. The engineered thickness distribution varies along the first length and a second length perpendicular to the first length. The optical device further includes a plurality of optical device structures formed on the top surface of the substrate, a low index layer disposed on the plurality of optical device structures, and an anti-reflective layer disposed on the outer surface of the index-matching layer.

[0006] In another embodiment, a method for forming a design thickness distribution in an optical device is provided. The method includes measuring a substrate thickness distribution of a substrate defined by a distance between a top surface and a bottom surface of the substrate along a first length parallel to the top surface of the substrate and a second length perpendicular to the first length, disposing an index matching layer over the bottom surface of the substrate, and etching the index matching layer to have a design thickness distribution to form the design thickness distribution. The design thickness distribution is defined by the design thickness distribution and the substrate thickness distribution, and the design thickness distribution varies along the first length and the second length.

[0007] In yet another embodiment, a method for forming an engineered thickness distribution in an optical device is provided. The method includes measuring a substrate thickness distribution of a substrate defined by a distance between a top surface and a bottom surface of the substrate along a first length parallel to the top surface of the substrate and a second length perpendicular to the first length, generating a phase map from the substrate thickness distribution across the bottom surface of the substrate, measuring a pitch non-uniformity between adjacent optical device structures of a plurality of optical device structures disposed on the top surface of the substrate, generating an engineered phase profile by subtracting the phase map and the pitch non-uniformity from an engineered phase map corresponding to a phase to be formed at each location of the optical device, and converting the engineered phase profile to an engineered thickness distribution. The method further includes disposing an index matching layer on the bottom surface of the substrate to have an engineered thickness distribution to form the engineered thickness distribution. The engineered thickness distribution is defined by the engineered thickness distribution and the substrate thickness distribution, and the engineered thickness distribution varies along the first length and the second length.

[0008] So that the above recited features of the present disclosure may be understood in detail, a more particular description of the present disclosure, briefly summarized above, may be made by reference to embodiments, some of which are illustrated in the accompanying drawings, It should be noted, however, that since the present disclosure may admit of other equally effective embodiments, the accompanying drawings merely illustrate exemplary embodiments and therefore should not be considered limiting in scope. [Brief description of the drawings]

[0009] [Figure 1] 1 is a perspective front view of an optical device according to an embodiment described herein. [Diagram 2] 4 is a flow diagram of a method for modifying a thickness of an optical device according to embodiments described herein. [Figure 3A-3B] 1 is a schematic side view of an optical device during the method according to an embodiment described herein. [Figure 3C-3D] 1 is a schematic side view of an optical device during the method according to an embodiment described herein. [Figure 4] 4 is a flow diagram of a method for modifying a thickness of an optical device according to embodiments described herein. [Figure 5A-5B] 1 is a schematic side view of an optical device during the method according to an embodiment described herein. [Fig. 5C-5D] 1 is a schematic side view of an optical device during the method according to an embodiment described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] For ease of understanding, wherever possible, like reference numbers have been used to designate like elements that are common to the figures. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.

[0011] FIELD OF THE DISCLOSURE The embodiments of the present disclosure generally relate to optical devices. More specifically, the embodiments described herein provide a method for modifying and engineering the effective thickness of an optical device substrate. The methods described herein for modulating the optical interference of an optical device improve the waveguide efficiency, color uniformity, and eyebox uniformity. The methods include removing or covering an excess dielectric layer on the optical device substrate. The thickness of the dielectric layer varies in a two-dimensional plane parallel to the optical device substrate.

[0012] FIG. 1 is a perspective front view of an optical device 100. It should be understood that the optical device 100 described below is an exemplary optical device. In one embodiment, which may be combined with other embodiments described herein, the optical device 100 is a waveguide combiner, such as an augmented reality waveguide combiner. The optical device 100 includes a plurality of optical device structures 102 disposed on a top surface 103 of a substrate 101. The optical device structures 102 may be nanostructures having submicron dimensions, e.g., nano-sized dimensions. In one embodiment, which may be combined with other embodiments described herein, regions of the optical device structures 102 correspond to one or more gratings 104, such as a first grating 104a, a second grating 104b, and a third grating 104c. In another embodiment, which may be combined with other embodiments described herein, the optical device 100 is a waveguide combiner including at least a first grating 104a corresponding to an input coupling grating and a third grating 104c corresponding to an output coupling grating. The waveguide combiner according to an embodiment, which may be combined with other embodiments described herein, includes a second grating 104b corresponding to an intermediate grating.

[0013] 1 shows the optical device structure 102 as having a square or rectangular shaped cross section, the cross section of the optical device structure 102 may have other shapes, including, but not limited to, circular, triangular, elliptical, regular polygonal, irregular polygonal, and / or irregular shaped cross sections. In some embodiments that may be combined with other embodiments described herein, the cross sections of the optical device structure 102 have cross sections of different shapes. In other embodiments that may be combined with other embodiments described herein, the cross sections of the optical device structure 102 have cross sections with substantially the same shape. The optical device structure 102 may also be angled with respect to the top surface 103 of the substrate 101.

[0014] A light engine 110 is configured to direct light beams 112 to the optical device 100. In one example, the light engine 110 includes a microdisplay that provides a pattern to the optical device 100 via the light beams 112. The light beams 112 undergo total internal reflection through the optical device 100. The optical device 100 directs the light beams 112 to a human eye of a user of the optical device 100. To improve the coupling efficiency and color uniformity of the optical device 100, the optical device 100 can be modulated to direct more of the light beams 112 in a first direction 114 compared to a second direction 116. The first direction 114 corresponds to a direction toward the third grating 104c, and the second direction 116 corresponds to a direction away from the third grating 104c. When the local substrate thickness variations are small (e.g., variations less than 500 nm), the first direction 114 has a high probability of destructive interference and the second direction 116 has a high probability of constructive interference. The constructive interference along the second direction 116 and the destructive interference along the first direction 114 will reduce the coupling efficiency of the optical device 100.

[0015] Methods 200 and 400 described below involve removing or covering an excess dielectric layer on an optical device substrate. The thickness of the dielectric layer varies in a two-dimensional plane parallel to the substrate 101. Methods 200 and 400 described herein allow for tuning the optical path of optical device 100 after fabrication to improve one or more characteristics of optical device 100. For example, optical device 100 that does not meet a predetermined threshold of optical efficiency can be retroactively tuned to achieve the threshold using embodiments described herein.

[0016] FIG. 2 is a flow diagram of a method 200 for modifying the thickness of the optical device 100. FIGS. 3A-3D are schematic side views of the optical device 100 during the method 200. The method 200 improves the display efficiency and display uniformity of the optical device 100 without compromising and / or reducing the display resolution. The method 200 will also help the optical device 100 with a low efficiency or display uniformity below a certain threshold. The optical device 100 may already be formed but have a lower efficiency due to the thickness of the optical device or the pitch uniformity of the optical device structure. Adjusting the thickness variation will allow the light to enter the correct optical path towards the output coupling grating, e.g., the third grating 104c. The phase profile is adjusted by changing the thickness of the optical device 100.

[0017] As shown in Figures 3A-3D, the optical device 100 includes a plurality of optical device structures 102 formed on a substrate 101. The method 200 is applied to the optical device structures 102 with well-controlled pitch and angle uniformity (e.g., high uniformity). The pitch (see Figure 5A) of the optical device structures 102 is defined as the distance between the rising or falling edges of adjacent optical device structures 102. The optical device structures 102 have a ratio of the standard deviation of the pitch to the nominal pitch of about 10 -4 If it is smaller than , it is well controlled.

[0018] Substrate 101 includes a bottom surface 105 and a top surface 103. Regions of optical device structure 102 correspond to one or more gratings 104, such as first grating 104a, second grating 104b, and third grating 104c. Prior to method 200, optical device 100 is inspected. For example, a metrology process inspects optical device 100 to determine whether optical device 100 meets predetermined thresholds for display efficiency and display uniformity.

[0019] In operation 201, as shown in FIG. 3A, a substrate thickness distribution 302 of the substrate 101 is measured. The substrate thickness distribution 302 is measured using a laser interferometer. The substrate thickness distribution 302 is defined by the distance between the top surface 103 and the bottom surface 105 of the substrate along a first length 107 of the substrate 101. The first length 107 is parallel to the top surface 103 of the substrate 101. The substrate thickness distribution 302 can also vary along a second length 109 that is perpendicular to the first length 107. The substrate thickness distribution 302 is collected as data and sent to a controller or computer.

[0020] In operation 202, a design thickness distribution 304 is determined. The design thickness distribution 304 is a target thickness distribution that is to be formed from the substrate thickness distribution 302. The design thickness distribution 304 can vary across the first length 107 of the substrate with a linear or non-linear distribution. The design thickness distribution 304 can also vary along a direction perpendicular to the first length 107, for example, the design thickness distribution 304 can vary along the second length 109.

[0021] In operation 203, a tooling thickness distribution 306 is determined. The tooling thickness distribution 306 is determined by subtracting the design thickness distribution 304 at each position along the first length 107 from the substrate thickness distribution 302 at each position along the first length 107. The tooling thickness distribution may also be determined to vary along a direction perpendicular to the first length 107, for example, the design thickness distribution 304 may vary along the second length 109. The tooling thickness distribution 306 is calculated with a physical optics and ray tracing optical model using the complete optical device 100 design information, for example, the critical dimensions of the optical device structure 102, the height, pitch, and angle of the optical device structure 102, and the optical material properties of the optical device 100.

[0022] In operation 204, as shown in FIG. 3B, an index matching layer 308 having an engineered thickness distribution 306 is disposed to form a designed thickness distribution 304. The designed thickness distribution 304 is different from the substrate thickness distribution 302. The index matching layer 308 is disposed on the bottom surface 105 of the substrate 101. The index matching layer 308 has a first refractive index that matches or substantially matches a second refractive index of the substrate 101. For example, the first refractive index and the second refractive index are within about 5% of each other. The refractive indexes of the substrate 101 and the index matching layer 308 are between about 1.7 and about 2.9. The difference between the refractive index of the substrate 101 and the refractive index matching layer 308 is between about 0 and about 0.1.

[0023] The substrate 101 and the index matching layer 308 may be formed from any suitable material, provided that the substrate 101 can adequately transmit light at the target wavelength or range of wavelengths and can act as a sufficient support for the optical device 100. The substrate 101 may be materials including, but not limited to, amorphous dielectrics, non-amorphous dielectrics, crystalline dielectrics, silicon oxides, polymers, and combinations thereof. In some embodiments, which may be combined with other embodiments described herein, the substrate 101 comprises a transparent material. In one example, the substrate 101 is made of a high refractive index glass, silicon dioxide (SiO 2 ), fused silica, quartz, silicon carbide (SiC), LiNbO 3 , diamond (C), gallium nitride (GaN), sapphire, or combinations thereof. The index matching layer 308 is a deposited thin film comprising silicon nitride (SiN), titanium oxide (TiOx), tantalum oxide (TaOx), niobium oxide (NbOx), zirconium oxide (ZrOx), or a synthetic nanoparticle material. For example, the index matching layer 308 may be a titanium oxide (TiO 2 ) or zirconium oxide (ZrO 2 ) materials. In one example, the substrate 101 and the index matching layer 308 are different materials. In another example, the substrate 101 and the index matching layer 308 are the same material.

[0024] The substrate 101 and the index matching layer 308 combine to form a designed thickness distribution 304. The designed thickness distribution 304 is defined by the distance between the top surface 103 of the substrate 101 and an outer surface 310 of the index matching layer 308 along a first length 107 and a second length 109 perpendicular to the first length 107. The outer surface 310 faces away from the substrate 101. The designed thickness distribution 304 and the engineered thickness distribution 306 are not limited by Figures 3A-3D and may be distributed as determined to improve optical device performance.

[0025] In a first embodiment, which may be combined with other embodiments described herein, the index matching layer 308 is disposed on the bottom surface 105 of the substrate 101. The index matching layer 308 is selectively etched to form the engineered thickness distribution 306. The selective etching includes at least one of ion implantation, ion beam etching (IBE), reactive ion etching (RIE), directional RIE, plasma etching, and thermal atomic layer etching. The engineered thickness distribution 306 combines with the substrate thickness distribution 302 to form the designed thickness distribution 304. In a second embodiment, which may be combined with other embodiments described herein, the index matching layer 308 is selectively deposited. For example, the index matching layer 308 is selectively deposited using an inkjet printing process to form the engineered thickness distribution 306. The engineered thickness distribution 306 combines with the substrate thickness distribution 302 to form the designed thickness distribution 304.

[0026] In optional operation 205, as shown in FIG. 3C, an anti-reflective layer 312 is disposed on the outer surface 310 of the index matching layer 308. The anti-reflective layer 312 is conformal to the index matching layer 308. In one embodiment, the anti-reflective layer 312 includes multiple stacked layers of material. For example, the layers of anti-reflective material include one or more of SiOx, ZrOx, and TiOx. The anti-reflective layer 312 may include alternating low and high refractive index layers. The low refractive index layers have a refractive index between about 1.4 and about 1.7. The high refractive index layers have a refractive index greater than about 2. The low refractive index layers are SiOx materials. The high refractive index layers are metal oxide materials. The anti-reflective layer 312 is configured to increase the efficiency of the optical device by reducing light lost due to reflection. The anti-reflective layer 312 is disposed via an ALD process.

[0027] In optional operation 206, as shown in FIG. 3D, a low refractive index layer 314 is disposed on the plurality of optical device structures 102. The low refractive index layer 314 is a SiOx material. The low refractive index layer is utilized to improve anti-reflective properties. The low refractive index layer 314 has a refractive index of about 1.4 to about 1.7.

[0028] By forming the design thickness distribution 304, the phase change of the optical device 100 is tailored to modulate the optical interference between the different light paths. Forming the design thickness distribution 304 will improve the light coupling efficiency into the output coupling grating, e.g., the third grating 104c, optimizing the efficiency across the optical device 100. The method 200 may be utilized to enable an already manufactured optical device 100 that does not meet a predetermined efficiency threshold to meet the predetermined efficiency threshold.

[0029] FIG. 4 is a flow diagram of a method 400 for modifying the thickness of the optical device 100. FIGS. 5A-5D are schematic side views of the optical device 100 during the method 400. The method 400 improves the display efficiency and display uniformity of the optical device 100 without compromising and / or reducing the display resolution. The method 400 will also help the optical device 100 with a low efficiency or display uniformity below a certain threshold. The optical device 100 may already be formed but have a lower efficiency due to the thickness of the optical device or the pitch uniformity of the optical device structure. Adjusting the thickness variation will allow the light to enter the correct optical path towards the output coupling grating, e.g., the third grating 104c. The phase profile is adjusted by changing the thickness of the optical device 100.

[0030] 5A, the optical device 100 includes a plurality of optical device structures 102 formed on a substrate 101. The method 400 is applied to the optical device structures 102 that have uncontrolled pitch and angle uniformity (e.g., low uniformity). The optical device structures 102 have a ratio of the standard deviation of the pitch 516 to the nominal pitch 516 of about 10. -4 is considered to be well controlled.

[0031] The substrate 101 includes a bottom surface 105 and a top surface 103. Areas of the optical device structures 102 correspond to one or more gratings 104, such as a first grating 104a, a second grating 104b, and a third grating 104c. An anti-reflection layer 512 is disposed on the bottom surface 105 of the substrate 101. A low refractive index layer 514 is disposed on the plurality of optical device structures 102.

[0032] Prior to method 400, optical device 100 is inspected. For example, a metrology process inspects optical device 100 to determine whether it meets predetermined thresholds for display efficiency and display uniformity. If optical device 100 does not meet the predetermined thresholds, method 400 may be performed. Method 400 may be performed to restore optical device 100 to meet the predetermined thresholds.

[0033] In operation 401, as shown in FIG. 5A, a substrate thickness distribution 502 of the substrate 101 is measured and a phase map is generated. The substrate thickness distribution 502 is measured using a laser interferometer. The substrate thickness distribution 502 is defined by the distance between the top surface 103 and the bottom surface 105 of the substrate 101 along a first length 107 of the substrate 101 and perpendicular to the first length 107, for example, along a second length 109 perpendicular to the first length 107. The substrate thickness distribution 502 is collected as data and sent to a controller or computer. A phase map is generated based on the substrate thickness distribution 502. The phase map specifies the phase at each location on the substrate 101 across the bottom surface 105 of the substrate 101. The phase map is generated by determining the phase change at each location. The phase change is determined by taking the thickness variation at each location and dividing by the wavelength of the light transmitted×2π.

[0034] In operation 402, a design thickness distribution 504 is determined and a design phase map is generated. The design thickness distribution 504 is a target thickness distribution that is to be formed from the substrate thickness distribution 502. The design thickness distribution 504 can vary over a first length 107 of the substrate 101 and along a second length 109 perpendicular to the first length 107 with a linear or non-linear distribution. The design phase map is generated from the design thickness distribution 504. The design phase map specifies the phase that will be formed at each location on the substrate 101 in the final optical device 100. The design phase map is generated by a waveguide design software application.

[0035] In operation 403, the non-uniformity of the pitch 516 of the multiple optical device structures 102 is measured. The pitch 516 is defined as the distance between the rising or falling edges of adjacent optical device structures 102. The pitch 516 of each of the adjacent optical device structures 102 is measured to determine the degree of non-uniformity of the pitch 516 across the substrate 101. The pitch 516 at each location across the substrate 101 is mapped. The uniformity of the optical device structures 102 is defined by the ratio of the standard deviation of the pitch 516 to the nominal value of the pitch 516.

[0036] In operation 404, a tooling phase profile is generated. The tooling phase profile is the change in phase of the phase map to form the design phase map. The tooling phase profile is generated by subtracting the phase map and the pitch 516 non-uniformity from the design phase map at each location across the optical apparatus 100. The tooling phase profile may be generated of the tooling phase at each location along the first length 107 and a direction perpendicular to the first length 107, for example, along the second length 109.

[0037] In operation 405, the workpiece phase profile is converted to a workpiece thickness distribution 506. The workpiece phase profile is converted to a workpiece thickness distribution 506 by dividing the phase change at each location by the wavelength of the transmitted light times 2π.

[0038] The tooling thickness distribution 506 is determined by subtracting the design thickness distribution 504 at each location along the first length 107 from the substrate thickness distribution 502 at each location along the first length 107 and perpendicular to the first length 107, e.g., along a second length 109. The tooling thickness distribution 506 is calculated with a physical optics and ray tracing optical model using the complete optical device 100 design information (e.g., critical dimensions of the optical device structure 102, height, pitch, and angle of the optical device structure 102, optical material properties of the optical device 100).

[0039] In operation 406, the anti-reflective layer 512 is removed, as shown in Figure 5B. The anti-reflective layer 512 is removed via an etch process. In operation 407, an index matching layer 508 is disposed, as shown in Figures 5B and 5C. The index matching layer 508 is disposed on the bottom surface 105 of the substrate 101. The index matching layer 508 has a first refractive index that matches or substantially matches a second refractive index of the substrate 101.

[0040] In a first embodiment shown in Figures 5B and 5C, which may be combined with other embodiments described herein, an index matching layer 508 is disposed on the bottom surface 105 of the substrate 101 (see Figure 5B). The index matching layer 508 is selectively etched to form an engineered thickness distribution 506. The selective etching includes at least one of ion implantation, ion beam etching (IBE), reactive ion etching (RIE), directional RIE, plasma etching, and thermal atomic layer etching. The engineered thickness distribution 506 combines with the substrate thickness distribution 502 to form a design thickness distribution 504.

[0041] In a second embodiment shown in FIG. 5C, which may be combined with other embodiments described herein, the index matching layer 508 is selectively deposited. For example, the index matching layer 508 is selectively deposited using an inkjet printing process to form an engineered thickness distribution 506. In other words, the index matching layer 508 is deposited to have an engineered thickness distribution 506 without an etching process. Therefore, the operation shown in FIG. 5B is optional. The engineered thickness distribution 506 combines with the substrate thickness distribution 502 to form the designed thickness distribution 504.

[0042] The substrate 101 and the index matching layer 508 combine to form a design thickness distribution 504. The design thickness distribution 504 is defined by the distance between the top surface 103 of the substrate 101 and the outer surface 510 of the index matching layer 508 along the first length 107 and perpendicular to the first length 107, for example, along the second length 109. The design thickness distribution 504 differs from the substrate thickness distribution 502. The outer surface 510 faces away from the substrate 101. The design thickness distribution 504 and the engineered thickness distribution 506 are not limited by Figures 5A-5D and can be distributed as determined to improve optical device performance.

[0043] In optional operation 408, as shown in FIG. 5D, an antireflective layer 512 is disposed on the outer surface 510 of the index matching layer 508. The antireflective layer 512 is conformal to the index matching layer 508. In one embodiment, the antireflective layer 512 includes multiple stacked layers of material. The antireflective material may include alternating low and high refractive index layers. The antireflective layer 512 is configured to increase the efficiency of the optical device by reducing light lost due to reflection. The antireflective layer 512 is disposed via an ALD process.

[0044] By forming the design thickness distribution 504, the phase change of the optical device 100 is tailored to modulate the optical interference between the different light paths. Forming the design thickness distribution 504 will improve the light coupling efficiency into the output coupling grating, e.g., the third grating 104c, optimizing the efficiency across the optical device 100. The method 400 may be utilized to enable an already manufactured optical device 100 that does not meet a predetermined efficiency threshold to meet the predetermined efficiency threshold.

[0045] In summary, a method is provided for modifying and engineering the effective thickness of an optical device substrate. The method provides for depositing an index-matched material onto the substrate to modify the thickness distribution of the optical device. By adjusting the thickness distribution, the optical path of the light is modulated to direct the light to the output coupling grating. The method improves display efficiency and uniformity without compromising display resolution. The method is also used to modify optical devices that do not meet a predetermined efficiency threshold such that the optical device will meet the predetermined threshold.

[0046] While the forgoing is directed to embodiments of the present disclosure, other and further embodiments of the present disclosure may be devised without departing from the basic scope thereof, which is determined by the following claims.

Claims

1. a substrate having a substrate thickness distribution defined by a top surface of the substrate and a bottom surface of the substrate, the substrate thickness distribution varying along a first length parallel to the top surface and a second length perpendicular to the first length; an index matching layer disposed over the bottom surface of the substrate, the index matching layer having a machined thickness profile defined by an outer surface of the index matching layer and the bottom surface of the substrate, the machined thickness profile varying along the first length and along the second length perpendicular to the first length; a plurality of optical device structures formed on the top surface of the substrate; a low refractive index layer disposed on the plurality of optical device structures; an anti-reflective layer disposed on the outer surface of the index matching layer; An optical device comprising:

2. 10. The optical device of claim 1, wherein the substrate has a first refractive index and the index-matching layer has a second refractive index, the second refractive index being substantially matched to the first refractive index.

3. The optical apparatus of claim 1 , wherein the machined thickness distribution varies in a first direction parallel to the top surface and in a second direction perpendicular to the first direction.

4. The optical device of claim 1 , wherein the anti-reflective layer comprises two or more stacked layers of material.

5. 5. The optical device of claim 4, wherein the antireflective layer comprises alternating low and high refractive index layers, the low refractive index layers having a refractive index between about 1.4 and about 1.7, and the high refractive index layers having a refractive index greater than about 2.

0.

6. The optical device of claim 1 , wherein the low refractive index layer has a refractive index of about 1.4 to about 1.

7.

7. The optical device of claim 1 , wherein the low refractive index layer is a silicon oxide material.

8. The optical device of claim 1 , wherein the plurality of optical device structures are angled with respect to the bottom surface of the substrate.

9. The optical device of claim 1 , wherein the index matching layer is a polymeric material or a nanoparticle-based material.

10. 1. A method for forming a designed thickness distribution in an optical device, comprising: measuring a substrate thickness distribution of the substrate defined by a distance between a top surface of the substrate and a bottom surface of the substrate along a first length parallel to the top surface of the substrate and a second length perpendicular to the first length; disposing an index matching layer on the bottom surface of the substrate; etching the index matching layer to have a design thickness profile to form a design thickness profile, the design thickness profile being defined by the design thickness profile and the substrate thickness profile, the design thickness profile varying along the first length and the second length; A method comprising:

11. 11. The method of claim 10, wherein the etching comprises at least one of ion implantation, ion beam etching (IBE), reactive ion etching (RIE), directional RIE, plasma etching, and thermal atomic layer etching.

12. The method of claim 10 further comprising disposing an anti-reflective layer on the index-matching layer.

13. The method of claim 10 , further comprising disposing a low index layer on a plurality of optical devices disposed on the top surface of the substrate.

14. 1. A method for forming a designed thickness distribution in an optical device, comprising: measuring a substrate thickness distribution of the substrate defined by a distance between a top surface of the substrate and a bottom surface of the substrate along a first length parallel to the top surface of the substrate and a second length perpendicular to the first length; generating a phase map from the substrate thickness distribution across the bottom surface of the substrate; measuring a pitch non-uniformity between adjacent optical device structures among a plurality of optical device structures disposed on the top surface of the substrate; generating a design phase profile by subtracting the phase map and the non-uniformity in pitch from a design phase map corresponding to a phase to be formed at each location of the optical device; converting the machining phase profile into a machining thickness distribution; disposing an index matching layer over the bottom surface of the substrate to have the engineered thickness distribution to form a designed thickness distribution, the designed thickness distribution being defined by the engineered thickness distribution and the substrate thickness distribution, the designed thickness distribution varying along the first length and the second length; A method comprising:

15. The method of claim 14 , wherein the index-matching layer is disposed to have the engineered thickness profile via an inkjet printing process.

16. 15. The method of claim 14, wherein the substrate has a first refractive index and the index matching layer has a second refractive index, the second refractive index being substantially matched to the first refractive index.

17. The method of claim 14 , further comprising removing an anti-reflective layer from the bottom surface of the substrate prior to providing the index-matching layer.

18. 20. The method of claim 17, further comprising disposing the anti-reflective layer on an outer surface of the index matching layer via an ALD process.

19. The method of claim 17 , wherein the antireflective layer comprises two or more stacked layers of material.

20. 20. The method of claim 17, wherein the antireflective layer comprises alternating low and high refractive index layers, the low refractive index layers having a refractive index between about 1.4 and about 1.7, and the high refractive index layers having a refractive index greater than about 2.0.

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