Waveguide for augmented reality with expanded field of view

Abstract

Optical elements and waveguides for augmented reality devices are described. The optical element includes a waveguide, an in-coupling element, and an out-coupling element. The waveguide includes reflective coatings on opposing surfaces to expand the range of incidence angles (field of view) capable of being transmitted within the waveguide from the in-coupling element to the out-coupling element. The in-coupling and out-coupling elements may be interfaced with or formed on a surface of the waveguide or a reflective coating. Imaging light over a range of incidence angles is directed into the in-coupling element and coupled into the waveguide. The coupled light propagates within the waveguide by total internal reflection or specular reflection to the out-coupling element and is directed from the out-coupling element to form a virtual image in the viewing field of a user of the device.

Description

SP24-164WAVEGUIDE FOR AUGMENTED REALITY WITH EXPANDED FIELD OF VIEW

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Application Serial No. 63 / 665,057 filed on June 27, 2024, the content of which is relied upon and incorporated herein by reference in its entirety.FIELD

[0002] This description relates to optical elements for use in augmented reality devices. More particularly, this description relates to waveguides for optical elements for augmented reality devices. Most particularly, this description relates to waveguides with reflective coatings on opposing surfaces that act to expand the field of view of the waveguide.BACKGROUND

[0003] Augmented reality devices are gaining in consumer acceptance as the dimensions decrease and more socially acceptable form factors are developed. An augmented reality device generates a virtual image and superimposes it on the viewing field of an observer. The virtual image includes information that supplements, enhances, or interprets objects in the viewing field. A common design for augmented reality devices is based on a combination of optical elements that include imaging optics, a waveguide, and light-coupling elements. The imaging optics generate a virtual image and direct it to an in-coupling element. The in-coupling element couples the imaging light into the waveguide whereupon it is transmitted within the waveguide to an out-coupling element. The out-coupling element directs the imaging light to form a virtual image at a specified location in the observer’s field of vision.

[0004] The in-coupling and out-coupling elements are refractive or diffractive light-coupling optical elements designed, respectively, to couple light into and out of the waveguide. Refractive light-coupling optical elements include prisms and mirrors. A diffractive light-coupling optical element typically includes a surface relief grating with diffractive features formed by nanoimprinting, a holographic grating with volumetric diffractive features formed by single or multiple beam holographic recording, polarization volume gratings, and metasurfaces. Diffractive light-coupling optical elements typically consist of a single layer of a base material with the diffractive features formed thereon or therein.SP24-164

[0005] Light provided by the imaging optics is typically collimated and approaches the incoupling element as a series of components that span a range of incidence angles. Upon coupling into the waveguide by the in-coupling element, the range of incidence angles produces components of light in the waveguide that transmit over a range of propagation angles to the out- coupling element. The mechanism of propagation within the waveguide is total internal reflection.

[0006] The conditions needed to support total internal reflection limit the range of propagation angles guided by the waveguide, which in turn limits the range of incidence angles of imaging light available for forming the virtual image. To enrich the virtual experience, it is desirable to increase the range of incidence angles of imaging light capable of transmission within the waveguide from the in-coupling element to the out-coupling element. One strategy for increasing the range of incidence angles is to increase the refractive index of the waveguide. Waveguides with high refractive index support total internal reflection over a wider range of incidence angles (larger field of view (FOV)). High-index waveguides, however, require material compositions with high density, which increases the weight of augmented reality devices and leads to user fatigue. It is desirable to develop waveguides for augmented reality that can be formed from materials with low refractive index that support an expanded range of incidence angles.

[0007] In addition to limits imposed by the conditions of total internal reflection, the range of incidence angles is also limited by the wavelength of imaging light. Imaging light commonly includes red, green, and blue wavelengths and each of these wavelengths is diffracted with different efficiency into the waveguide by an in-coupling element. Diffractive in-coupling elements include diffraction gratings with a fixed grating spacing. The diffraction efficiency varies with wavelength and can be optimized for a particular wavelength by adjusting the grating spacing. Optimizing the diffraction efficiency for one wavelength, however, compromises diffraction efficiency for other wavelengths, which leads to wavelength-dependent variations and limitations on the range of incidence angles capable of being diffracted into the waveguide. For this reason, it is common for augmented reality devices to incorporate separate waveguides with in-coupling elements differing in grating spacing for each color of imaging light used to form the virtual image. In particular, it is common to employ separate waveguides for red, green, and blue wavelengths, each optimized to maximize the diffraction efficiency and range of incidence angles for its respective wavelength. The need to include separate waveguides dedicated toSP24-164 specific wavelengths increases the weight, cost, and complexity of augmented reality devices. It would be desirable to develop waveguides for augmented reality devices capable of supporting multiple wavelengths of imaging light over a wide range of incidence angles for each wavelength.SUMMARY

[0008] The present disclosure provides optical elements and waveguides that can be used in augmented reality and other devices. The optical element includes a waveguide, an in-coupling element, and an out-coupling element. The waveguide includes reflective coatings on opposing surfaces to expand the range of incidence angles capable of being transmitted within the waveguide from the in-coupling element to the out-coupling element. The in-coupling and out- coupling elements may be interfaced with or formed on a surface of the waveguide or a reflective coating. Imaging light over a range of incidence angles (field of view) is directed into the incoupling element and coupled into the waveguide. The coupled light propagates within the waveguide by total internal reflection or specular reflection to the out-coupling element and is directed from the out-coupling element to the vision field of a user of the device.

[0009] The present disclosure extends to:An optical element comprising: a waveguide configured for transmission of light over a range of propagation angles from an in-coupling grating to an out-coupling grating, the transmission occurring within the waveguide between a first surface and a second surface, the range of propagation angles including a first interval of propagation angles over which the transmission occurs by total internal reflection and a second interval of propagation angles over which the transmission occurs by specular reflection, the first interval of propagation angles extending from a minimum angle of total internal reflection 0PTIR to a maximum angle of total internal reflection 0PMAX, the second interval of propagation angles extending from a minimum angle of specular reflection 0Rmin to a maximum angle of specular reflection 0Rmax, the second interval of propagation angles comprising propagation angles not included in the first interval of propagation angles; a first coating on the first surface, the first coating reflecting the light of the second interval of propagation angles with a reflectivity greater than or equal to 95%; andSP24-164 a second coating on the second surface, the second coating reflecting the light of the second interval of propagation angles with a reflectivity greater than or equal to 95%.

[0010] Additional features and advantages will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the appended drawings.

[0011] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understand the nature and character of the claims.

[0012] The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings are illustrative of selected aspects of the present description, and together with the specification serve to explain principles and operation of methods, products, and compositions embraced by the present description. Features shown in the drawing are illustrative of selected embodiments of the present description and are not necessarily depicted in proper scale.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter of the written description, it is believed that the specification will be better understood from the following written description when taken in conjunction with the accompanying drawings, wherein:

[0014] FIG. 1 A depicts an optical element that includes a waveguide, an in-coupling element, and an out-coupling element.

[0015] FIG. IB depicts the convention used to define the incidence angle a of imaging light into the in-coupling element of the optical element of FIG. 1A.

[0016] FIG. 2A depicts an angle of diffraction 0 of imaging light diffracted into a waveguide through a diffractive in-coupling element.

[0017] FIG. 2B depicts the convention used to define the incidence angle a of imaging light into the in-coupling element of the optical element of FIG. 1A.

[0018] FIG. 3A depicts a correspondence between a range of incidence angles and a range of propagation angles for a waveguide operating by the mechanism of total internal reflection.SP24-164

[0019] FIG. 3B depicts a component of light with an incidence angle outside of the range of incidence angles associated with total internal reflection and a corresponding component of diffracted light.

[0020] FIG. 4 depicts the mechanism of specular reflection in a waveguide having reflective coatings on opposing surfaces.

[0021] FIG. 5 depicts a correspondence between a range of incidence angles and a range of propagation angles for a waveguide operating by the mechanism of specular reflection.

[0022] FIG. 6 illustrates an expansion in the field of view (FOV) of a waveguide with reflective coatings on opposing surfaces relative to a waveguide lacking reflective coatings on opposing surfaces.

[0023] FIG. 7 illustrates an expansion in the field of view (FOV) of a waveguide with reflective coatings on opposing surfaces relative to a waveguide lacking reflective coatings on opposing surfaces for an embodiment in which multiple wavelengths of light are transmitted in the waveguide.

[0024] FIG. 8A depicts the transmittance and reflectance of an exemplary reflective coating.

[0025] FIG. 8B is an enlargement of FIG. 8A in the region of high reflectance.

[0026] The embodiments set forth in the drawings are illustrative in nature and not intended to be limiting of the scope of the detailed description or claims. Whenever possible, the same reference numeral will be used throughout the drawings to refer to the same or like feature.DETAILED DESCRIPTION

[0027] The present disclosure is provided as an enabling teaching and can be understood more readily by reference to the following description, drawings, examples, and claims. Those skilled in the relevant art will recognize and appreciate that many changes can be made to the various aspects of the embodiments described herein, while still obtaining the beneficial results. It will also be apparent that some of the desired benefits of the present embodiments can be obtained by selecting some of the features without utilizing other features. Accordingly, those who work in the art will recognize that many modifications and adaptations are possible and can even be desirable in certain circumstances and are a part of the present disclosure. Therefore, it is to be understood that this disclosure is not limited to the specific compositions, articles, devices, and methods disclosed unless otherwise specified. It is also to be understood that the terminologySP24-164 used herein is for the purpose of describing particular aspects only and is not intended to be limiting.

[0028] The present disclosure describes optical elements and waveguides that can be used in augmented reality and other devices. The optical elements include light-coupling elements; in particular, an in-coupling element and an out-coupling element. Light-coupling elements include diffractive optical elements (DOE). Diffractive optical elements include diffractive in-coupling elements, which diffract imaging light into the waveguide, and diffractive out-coupling elements, which diffract imaging light that propagates within the waveguide out of the waveguide. The optical elements may also include an expanding element, such as an exit pupil expander, which may also be a diffractive element. The expanding element may be integrated with or separate from a light-coupling element. Gratings for light-coupling and expanding elements include ID gratings, 2D gratings, holographic gratings, and polarization volume gratings. Diffractive incoupling and out-coupling elements may be interfaced with or formed on a surface of the waveguide. Diffractive in-coupling and out-coupling elements may be integrated into or onto a surface of the waveguide. Imaging light is directed to an in-coupling grating is diffracted into the waveguide. The diffracted light propagates within the waveguide to the out-coupling grating and is diffracted by the outcoupling grating to the vision field of a user of the device.

[0029] The waveguide includes reflective coatings on opposing sides. The reflective coatings act to expand the range of incidence angles of the imaging light that can transmitted from the incoupling grating to the out-coupling grating by providing a mechanism of transmission in addition to total internal reflection. In particular, the reflective coatings enable transmission of light by specular reflection from opposing reflective coatings and expand the range of incidence angles beyond the range that satisfies the conditions of total internal reflection. The critical angle defines the minimum angle of total internal reflection and sets a limit on the range of incidence angles capable of transmission within the waveguide upon diffraction from the incoupling grating. Introduction of specular reflection as a mechanism of transmission within the waveguide enables transmission of components of imaging light diffracted into the waveguide at propagation angles that fail to satisfy the conditions of total internal reflection. The net result is transmission of imaging light over an expanded range of incidence angles and production of virtual images from an expanded field of view.SP24-164

[0030] Disclosed are components (including materials, compounds, compositions, and method steps) that can be used for, in conjunction with, in preparation for, or as embodiments of the disclosed reflecting optical elements and methods for making reflecting optical elements. It is understood that when combinations or subsets, interactions of the components are disclosed, each component individually and each combination of two or more components is also contemplated and disclosed herein even if not explicitly stated. If, for example, if a combination of components A, B, and C is disclosed, then each of A, B, and C is individually disclosed as is each of the combinations A-B, B-C, A-C, and A-B-C. Similarly, if components D, E, and F are individually disclosed, then each combination D-E, E-F, D-F, and D-E-F is also disclosed. This concept applies to all aspects of this disclosure including, but not limited to, components corresponding to materials, compounds, compositions, and steps in methods.

[0031] In this specification and in the claims which follow, reference will be made to a number of terms which shall be defined to have the following meanings:

[0032] ‘ ‘Include,” “includes,” or like terms means encompassing but not limited to, that is, inclusive and not exclusive.

[0033] As used herein, the term “and / or,” when used in a list of two or more items, means that any one of the listed items can be employed by itself, or any combination of two or more of the listed items can be employed. For example, if a composition is described as containing components A, B, and / or C, the composition can contain A alone; B alone; C alone; A and B in combination; A and C in combination; B and C in combination; or A, B, and C in combination.

[0034] In this document, relational terms, such as first and second, top and bottom, and the like, are used solely to distinguish one entity or action from another entity or action, without necessarily requiring or implying any actual such relationship or order between such entities or actions.

[0035] As used herein, contact refers to direct contact or indirect contact. Direct contact refers to contact in the absence of an intervening material and indirect contact refers to contact through one or more intervening materials. Elements in direct contact touch each other. Elements in indirect contact do not touch each other, but are otherwise joined to each other through one or more intervening materials. Elements in contact may be rigidly or non-rigidly joined.Contacting refers to placing two elements in direct or indirect contact. Elements in direct (indirect) contact may be said to directly (indirectly) contact each other.SP24-164

[0036] The construction and arrangement of the elements of the present disclosure, as shown in the exemplary embodiments, is illustrative only. Although only a few embodiments of the present innovations have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel and nonobvious teachings and advantages of the subject matter recited. For example, elements shown as integrally formed may be constructed of multiple parts, or elements shown as multiple parts may be integrally formed, the operation of the interfaces may be reversed or otherwise varied, the length or width of the structures, and / or members, or connectors, or other elements of the system, may be varied, and the nature or number of adjustment positions provided between the elements may be varied. It should be noted that the elements and / or assemblies of the system may be constructed from any of a wide variety of materials that provide sufficient strength or durability, in any of a wide variety of colors, textures, and combinations. Accordingly, all such modifications are intended to be included within the scope of the present innovations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the desired and other exemplary embodiments without departing from the spirit of the present innovations.

[0037] The indefinite article “a” or “an” and its corresponding definite article “the” as used herein means at least one, or one or more, unless specified otherwise.

[0038] The term “na” refers to refractive index at a wavelength of 587.56 nm.

[0039] The claims as set forth below are incorporated into and constitute part of this Detailed Description.

[0040] Reference will now be made in detail to illustrative embodiments of the present description.

[0041] FIG. 1A illustrates an optical element 100 in cross-section. Optical element 100 includes waveguide 105, in-coupling grating 110, and out-coupling grating 115. In-coupling grating 110 and out-coupling grating 115 are diffractive light-coupling elements disposed on or within incidence surface 102 of waveguide 105. Waveguide 105 includes an incidence surface 102 and a back surface 104. Incidence surface 102 is the surface of waveguide 105 upon which imaging light 120 is incident and back surface 104 opposes incidence surface 102. WaveguideSP24-164105 has a thickness d and a thickness direction z. Thickness refers to the smallest linear dimension describing the shape of waveguide 105 (e.g., the smallest of length, width, and height for a planar waveguide, or the smaller of diameter and height for a cylindrical or disk-shaped waveguide). The coordinate z defining the thickness direction has a value of zero at the incidence surface 102 and increases in the direction toward back surface 104. In standard designs, waveguide 105 has a uniform refractive index na and is uncoated.

[0042] In operation, waveguide 105 receives imaging light 120 at in-coupling grating 110. Incoupling grating 110 diffracts the imaging light 120 into waveguide 105 as diffracted light 130. Diffracted light 130 propagates within waveguide 105 to out-coupling grating 115, which diffracts diffracted light 130 out of waveguide 105 to form a virtual image. The spacing between the midpoint of the in-coupling grating and the midpoint of the out-coupling grating is greater than 5 mm, or greater than 10 mm, or greater than 15 mm, or greater than 20 mm, or greater than 25 mm, or greater than 30 mm, or greater than 40 mm, or in the range from 5 mm to 50 mm, or in the range from 10 mm to 40 mm, or in the range from 15 mm to 35 mm. Shown in FIG. 1 A is a component of imaging light 120 that approaches incidence surface 102 at an angle of incidence a (depicted at 150) relative to normal 145 to incidence surface 102. For purposes of the present disclosure, the incidence angle a is defined relative to normal 145 such that imaging light 120 incident to in-coupling grating 110 in the direction of normal 145 has incidence angle a = 0° and the range of incidence angles a extends from -90° (direction parallel to incidence surface 102 that extends from in-coupling grating 110 toward out-coupling grating 115) to 90° (direction parallel to incidence surface 102 that extends from in-coupling grating 110 away from out- coupling grating 115). FIG. IB shows the distinction between positive (0° < oc < 90°) and negative (-90° < oc < 0°) incidence angles a. By way of example, the incidence angle a shown in FIG. 1A is positive. The depicted component of imaging light 120 is diffracted by incoupling grating 110 to form a component of diffracted light 130 having an angle of propagation 0 (depicted at 155 in FIG. 2A) in waveguide 105. The propagation angle 0 is defined relative to normal 145. FIG. 2B shows the distinction between positive (0° < 0 < 90°) and negative (-90° < 0 < 0°) propagation angles 0. Positive angles of propagation 0 correspond to angles at which diffracted light 130 is diffracted toward out-coupling grating 115 and negative angles ofSP24-164 propagation 0 correspond to angles at which diffracted light 130 is diffracted away from out- coupling grating 115.

[0043] Imaging light 120 representing a virtual image is provided by an imager (typically consisting of a microdisplay and optics) (not shown). Imaging light 120 is monochromatic or polychromatic. Imaging light 120 preferably includes one or more wavelengths between 400 nm and 700 nm, such as, for example, red, green, and / or blue light. The imaging light 120 is directed to an in-coupling grating 110, which diffracts the imaging light 120 into waveguide 105. Diffracted light 130 is monochromatic or polychromatic. Diffracted light 130 transmits internally within waveguide 105 and reaches out-coupling grating 115. Out-coupling grating 115 diffracts the transmitted light out of waveguide 105 as output light 135 at output angle 5 (depicted at 152), which is directed to a viewer. Output light 135 is monochromatic or polychromatic.

[0044] Although not depicted explicitly in the schematic of FIGS. 1A and IB, it is understood in the art that imaging light 120 includes multiple components that approach incidence surface 102 over a range of incidence angles a. The range of incidence angles a extends from a minimum incidence angle a.min to a maximum incidence angle otmax. The multiple components of imaging light 120 are diffracted by in-coupling grating 110 to form multiple components of diffracted light 130 that are transmitted over a range of propagation angles 0. The range of propagation angles 0 extends from a minimum propagation angle 0 min to a maximum propagation angle 0 max-

[0045] Selection of the imager and its operation to provide a desired virtual image controls the distribution of incidence angle a for the components of imaging light 120. In principle, the incidence angle a can range from -90° to 90°. Factors influencing the range of incidence angles a include the index and thickness of waveguide 105, and the dimensions of in-coupling grating 110. In various embodiments, the absolute value of the incidence angle a ranges from 0° to 90°, or from 0° to 70°, or from 0° to 50°, or from 0° to 40°, or from 0° to 30°, or from 0° to 20°, or from 5° to 85°, or from 5° to 70°, or from 5° to 55°, or from 5° to 40°, or from 5° to 30°, or from 5° to 20°, or from 10° to 80°, or from 10° to 70°, or from 10° to 55°, or from 10° to 40°, or from 10° to 30°, or from 10° to 20°, or from 15° to 75°, or from 15° to 70°, or from 15° to 55°, or from 15° to 40°, or from 15° to 30°, or from 15° to 25°, or from 20° to 70°, or from 25° to 65°,SP24-164 or from 30° to 60°, or from 35° to 55°. The minimum absolute value of the incidenceis greater than or equal to 0°, or greater than or equal to 1°, or greater than or equal to 5°, or greater than or equal to 10°, or greater than or equal to 15°, or greater than or equal to 20°, or greater than or equal to 25°, or greater than or equal to 30°, or greater than or equal to 35°, or less than or equal to 50°, or less than or equal to 45°, or less than or equal to 40°, or in the range from 5° to 50°, or in the range from 10° to 45°, or in the range from 15° to 40°, or in the range from 20° to 35°. The maximum absolute value of the incidence angle otmax is greater than or equal to 50°, or greater than or equal to 55°, or greater than or equal to 60°, or greater than or equal to 65°, or greater than or equal to 70°, or greater than or equal to 75°, or greater than or equal to 80°, or less than or equal to 90°, or less than or equal to 70°, or less than or equal to 60°, or less than or equal to 50°, or less than or equal to 30°, or less than or equal to 20°, or in the range from 10° to 50°, or in the range from 10° to 40°, or in the range from 10° to 30°, or in the range from 50° to 90°, or in the range from 55° to 85°, or in the range from 60° to 80°.

[0046] The in-coupling grating 110 provides diffracted light 130 with a correspondence of propagation angle 0 to incidence angle a. That is, components of imaging light 120 at each incidence angle a within a range of incidence angles a are diffracted by incoupling grating 110 into components of diffracted light 130 over a range of propagation angles 0, where the components of diffracted light 130 at each propagation angle 0 originate from a distinct component of imaging light 120 at a distinct angle of incidence a such that a correlation exists between each incidence angle a and one of the propagation angles 0. The nature of the correlation depends on characteristics of incoupling grating 110 (e.g., grating spacing).

[0047] Implementation of optical element 100 in augmented reality applications requires transmission of diffracted light 130 from in-coupling grating 110 to out-coupling grating 115. In the standard design, the mechanism of transmission is total internal reflection. Conditions required to sustain total internal transmission within waveguide 105 are known in the art and define a range of propagation angles 0 over which components of diffracted light 130 are transmitted by total internal reflection. FIG. 3 A depicts the range of propagation angles 0 over which total internal reflection occurs. The minimum propagation angle for total internal reflection, 0PTIR, corresponds to the critical angle of total internal reflection. The maximum propagation angle for total internal reflection, 0PMAX, depends on the thickness d of theSP24-164 waveguide and the dimensions of in-coupling grating 110. The range of propagation angles over which total internal reflection occurs extends from 0PTIR to 0PMAX. The corresponding range of incidence angles a extends from amR to OCIMAX. A component of imaging light 120 incident to in-coupling grating 110 at incidence angle amR is diffracted to form a component of diffracted light 130 with propagation angle 0PTIR. A component of imaging light 120 incident to incoupling grating 110 at incidence angle otiMAx is diffracted to form a component of diffracted light 130 with propagation angle 0PMAX. The range of incidence angles that provides diffracted light 130 capable of transmitting in waveguide 105 by total internal reflection extends from amR to otiMAx. This range of incidence angles defines the field of view for the standard waveguide design.

[0048] Diffracted light 130, however, includes components that fall outside of the range from 0PTIR to 0PMAX over which total internal reflection occurs. FIG. 3B, for example, illustrates a component 120a of imaging light 120 incident to in-coupling grating 110 at an incidence angle a outside of the range that extends from otiTiR to otiMAx. More specifically, the incidence angle a of component 120a of imaging light 120 is less than amR. Component 120a of imaging light 120 is diffracted to form component 130a of diffracted light 130. Component 130a of diffracted light 130 has a propagation angle 0 that is outside of the range from mR to aiMAx. More specifically, the propagation angle 0 of component 130a of diffracted light 130 is less than 0PTIR. Because the propagation angle 0 of component 130a of diffracted light 130 is outside of the range from amR to aiMAx, component 130a is unable to transmit by total internal reflection in waveguide 105 according to the standard design and as a result, component 120a of imaging light 120 is outside of the field of view of light that contributes to the virtual image produced by out-coupling grating 115.

[0049] The present disclosure describes an improved waveguide capable of expanding the field of view of imaging light 120 that forms the virtual image produced by out-coupling grating 115. The waveguide provides a mechanism of transmission of diffracted light 130 in the waveguide that supplements total internal reflection. In particular, the waveguide enables transmission of diffracted light 130 by specular reflection and total internal reflection. At least some components of imaging light 120 with incidence angles a outside the range from amR to aiMAx are transmitted from in-coupling grating 110 to out-coupling grating 115 by specular reflectionSP24-164 in the present waveguide. By enabling transmission of components of imaging light 120 that are not capable of transmission by total internal reflection, specular reflection expands the field of view of imaging light 120 that forms the virtual image.

[0050] To enable specular reflection, the waveguide includes reflective coatings on opposing surfaces 102 and 104 of waveguide 105. The reflective coatings are in direct contact with surfaces 102 and 104 of waveguide 105. An embodiment is depicted in FIG. 4. Optical element 100 includes waveguide 105 with reflective coatings 160 and 165. Reflective coatings 160 and 165 are disposed on and in direct contact with waveguide 105. Reflective coatings 160 and 165 have thicknesses dl and d2, respectively, which may be the same or different. In-coupling grating 110 and out-coupling grating 115 are formed on or in reflective coating 160.

[0051] Also depicted in FIG. 4 are component 120a of imaging light 120 and component 130a of diffracted light 130 as described above in connection with FIG. 3B. As noted above, component 130a of diffracted light 130 is diffracted at a propagation angle 0 that is outside of the range from 0PTIR to 0PMAX over which total internal reflection occurs. Inclusion of reflective coatings 160 and 165 enables propagation of component 130a of diffracted light 130 from incoupling grating 110 to out-coupling 115 by specular reflection to produce component 135a of output light 135 that becomes included in the virtual image produced by optical element 170. It is noted that in the absence of reflective coatings 160 and 165, component 135a of output light 135 would be absent from the virtual image produced by optical element 170 and the field of view of the virtual image would be accordingly limited.

[0052] The virtual image produced by optical element 170 includes component 135a and other components of diffracted light 130 transmitted by specular reflection having propagation angles that are not transmitted by total internal reflection. The range of propagation angles 0 of optical element 170 that contribute to the virtual image includes a a first interval of propagation angles over which the transmission occurs by total internal reflection and a second interval of propagation angles over which the transmission occurs by specular reflection. The first interval of propagation angles extends from a minimum angle of total internal reflection 0PTIR to a maximum angle of total internal reflection 0PMAX. The second interval of propagation angles extends from a minimum angle of specular reflection 0Rminto a maximum angle of specular reflection 0Rmaxand the second interval of propagation angles includes propagation angles not transmitted by total internal reflection.SP24-164

[0053] Associated with each of the first and second intervals of propagation angles 0 is an interval of incidence angles a. FIG. 3A, described above, shows a correspondence between incidence angle a and propagation angle 0 for diffracted light 130 transmitted by total internal reflection in waveguide 105. FIG. 5 shows a similar correspondence between incidence angle a and propagation angle 0 for diffracted light 130 transmitted by specular reflection in waveguide 105. Components of imaging light 120 having incidence angles in the interval extending from ocRmin to ap,maxare diffracted into components of diffracted light 130 having propagation angles in the interval of propagation angles extending from 0Rminto 0Rmax.

[0054] In some embodiments, the interval of propagation angles 0 over which total internal reflection occurs and the interval of propagation angles 0 over which specular reflection occurs overlap. In other embodiments, the interval of propagation angles 0 over which total internal reflection occurs and the interval of propagation angles 0 over which specular reflection occurs are non-overlapping. In one embodiment, 0Rmin< 0PTIR, in another embodiment 0Rmax< 0PTIR, and in a further embodiment, 0Rmax> 0PMAX.

[0055] In some embodiments, the interval of incidence angles a over which total internal reflection occurs and the interval of incidence angles a over which specular reflection occurs overlap. In other embodiments, the interval of incidence angles a over which total internal reflection occurs and the interval of incidence angles a over which specular reflection occurs are non-overlapping. In one embodiment, o Rmin < OCITIR and in another embodiment,

[0056] Of particular interest for the present disclosure is the non- overlapping portions of the intervals of incidence angles a and propagation angles 0 associated with transmission of diffracted light 130 by total internal reflection and specular reflection in waveguide 105.Incidence angles a and propagation angles 0 for which specular reflection occurs that are outside the interval over total internal reflection occurs provide new components of output light 135 and an expanded field of view of imaging light 120 at in-coupling grating 110. For reference purposes, FIG. 5 shows the minimum propagation angle 0PTIR for total internal reflection (corresponding to the critical angle for total internal reflection). The embodiment of FIG. 5 shows a minimum propagation angle 0Rminfor specular reflection that is less than the minimum propagation angle 0PTIR for total internal reflection. Propagation angles 0 between 0RminandSP24-164QpTiR transmit by specular reflection, but not total internal reflection and act to expand the field of view of imaging light 120.

[0057] The larger the difference (0PTIR - 0Rmin), the greater the expansion of field of view. In various embodiments, the difference (0PTIR - 0Rmin) is greater than or equal to 1 °, or greater than or equal to 5°, or greater than or equal to 10°, or greater than or equal to 15°, or greater than or equal to 20°, or greater than or equal to 25°, or in the range from 1° to 30°, or in the range from 3° to 25°, or in the range from 5° to 20°.

[0058] Associated with an expanded range of propagation angles 0 is an expanded range of incidence angles a. Components of diffracted light 130 having a propagation angle 0 less than the minimum propagation angle 0PTIR for total internal reflection are produced by components of imaging light 120 having an incidence angle a less than the minimum incidence angle ocmR for total internal reflection. To expand the field of view of imaging light 120, it is desirable to have a large difference (otiTiR - aRmin). In various embodiments, the difference (amR - otRmin) is greater than or equal to 1°, or greater than or equal to 5°, or greater than or equal to 10°, or greater than or equal to 15°, or greater than or equal to 20°, or greater than or equal to 25°, or in the range from 1° to 30°, or in the range from 3° to 25°, or in the range from 5° to 20°.

[0059] The expanded ranges of input angles a and output angles 0 arising from specular reflection as a mechanism of transmission within the waveguide lead to an expanded range of output angles 5. Differences in the ranges of input angle a and propagation angles 0 for specular reflection and total internal reflection lead to different ranges for the output angle 5. In particular, the range of output angles 5 for a waveguide having reflective coatings on opposing sides of the waveguide is greater than the range of output angles 5 when the waveguide lacks reflective coatings on opposing sides of the waveguide.

[0060] While not wishing to be bound by theory, the following model illustrates the scope of expansion of the field of view available from inclusion of reflective coatings on the waveguide. For convenience, the model assumes symmetry in the field of view of incident light; that is, equality of the absolute value of the minimum and maximum incidence angles a capable of propagating (irrespective of mechanism) from in-coupling grating 110 to out-coupling grating 115 to produce a component of output light 135 for the virtual image. As is known in the art, the symmetry or asymmetry of the field of view can be controlled through configuration of theSP24-164 grating and in particular the grating spacing as defined in the well-known grating equation applicable to diffractive gratings.

[0061] According to the model, the field of view (FOV) is given by Eq. (1):where it is assumed that the incident light enters the waveguide from air, n is the refractive index of waveguide 105, oci is the maximum angle of incidence of imaging light 120 capable, upon diffraction, of propagating (irrespective of mechanism) in waveguide 105 to produce a component of output light 135, -oci is the minimum angle of incidence of imaging light 120 capable, upon diffraction, of propagating (irrespective of mechanism) in waveguide 105 to produce a component of output light 135, 0PMAX is as described above and can be determined from Eq. (2):where A is the illuminated width of in-coupling grating 110 and d is the thickness of waveguide 105. The angle 02 is the minimum propagation angle of diffracted light 130 capable of propagating (irrespective of mechanism) in waveguide 105 to produce a component of output light 135.

[0062] In the standard design lacking reflective coatings depicted in FIG. 1 A, the angle 02 =0pTiR and Eq. (1) becomesFOV = 2 sin-1[Q (sinwhich, when recognizing that 0PTIR corresponds to the critical angle for total internal reflection given by Eq. (4),simplifies t

[0063] The minimum propagation angle 02 can be expressed by first rewriting Eq. (1) as shown in Eq. (6)SP24-164 (sin(0pAMX) - sin(02)) (6)and further simplifying through Snell’s Law, Eq. (7), sin tT = n sin(02) (7) to obtain Eq. (8): (sin(0pAMX) - sin(02)) (8)Rearrangement of Eq. (8) provides the following expression for 62:1 sin(02) = -sin(0pMAX) (9) which, when substituted into Eq. (1) gives Eq. (10):

[0064] FIG. 6 shows a comparison of model predictions of the field of view as a function of waveguide refractive index for waveguides with expanded (“FOV enhanced”) and conventional (“FOV conventional”) fields of view. The model prediction assumes 0PMAX = 72° (arrived at by setting A = 5 mm and d = 0.8 mm in Eq. (2)) and a refractive index n of the waveguide that is independent of wavelength. The result for the waveguide with the conventional field of view assumes transmission only by total internal reflection and was computed using Eq. (5). The result for the waveguide with the expanded field of view includes transmission by specular reflection and total internal reflection, and was computed using Eq. (10). FIG. 6 indicates that a significant expansion in field of view occurs when the waveguide is configured to enable transmission of light from an in-coupling grating to an out-coupling grating by specular reflection to supplement conventional transmission by total internal reflection.

[0065] A further advantage associated with the reflective coating is an increase in the FOV when multiple wavelengths of light are transmitted in waveguide 105. Most commonly, it is desirable to transmit a red wavelength (X ), a green wavelength ( G), and a blue wavelength (XB) in waveguide 105. Because of the wavelength dependence in the grating equation and the fixed configurations of the in-coupling and out-coupling gratings in a particular waveguide, the field of view for all three colors in a single waveguide operating solely by the mechanism of total internal reflection is limited. Configuring the grating to maximize the field of view for one wavelength leads to reductions in the field of view for other wavelengths.SP24-164

[0066] The optimal grating period A for maximizing the field of view (FOV) of a waveguide transmitting a red wavelength (XR), a green wavelength (AG), and a blue wavelength (XB) is given in Eq. (11):(11).and leads to the following expression for the field of view (FOV)

[0067] For a standard waveguide operating by total internal reflection without reflective coatings on opposing surfaces, the propagation angle 02 in Eq. (12) is equal to 0PTIR (given in Eq. (4)). When reflective coatings on opposing surfaces are included, the propagation angle 02 in Eq. (12) is given by Eq. (9) above. FIG. 7 shows model predictions of the field of view as a function of waveguide refractive index based on Eq. (12) for waveguides with expanded (“RGB, FOV enhanced” with 02 given by Eq. (9)) and conventional (“RGB, FOV conventional”, with 02 = 0PTIR) fields of view. The model prediction assumes 0PMAX = 72° (arrived at by setting A = 5 mm and d = 0.8 mm in Eq. (2)), AR = 650 nm, and AB = 450 nm. FIG. 7 shows that inclusion of opposing reflective coatings leads to a significant expansion in the field of view for a waveguide supporting transmission of red, green, and blue wavelengths.

[0068] To function most effectively in expanding the field of view, reflective coatings 160 and 165 of optical element 170 must satisfy certain conditions. Reflective coating 160 is disposed on and in direct contact with incidence surface 102 of waveguide. In-coupling grating 110 and out- coupling grating 115 are formed on or within reflective coating 160. In order for imaging light to diffract into waveguide 105 at in-coupling grating 110 and diffract out of waveguide 105 at out-coupling grating 115, reflective coating 160 must have low absorption. Absorption by reflective coating 160 attenuates the intensity of diffracted light 130 and output light 135. The absorption of reflective coating 165 must also be low. Absorption by either of reflective coatings 160 or 165 reduces the intensity of diffracted light 130 as it propagates by specular reflection in waveguide 105. Reflective coatings 160 and 165 must also have high reflectivity to efficiently transmit light by specular reflection from in-coupling grating 110 to out-coupling grating 115.SP24-164

[0069] The condition of high transmittance of reflective coating 160 applies to components of imaging light 120 that, upon diffraction, are transmitted in waveguide 105 by either total internal reflection or specular reflection. That is, reflective coating 160 preferably has high transmittance for components of imaging light 120 that extend over the full field of view, including the interval of incidence angles extending from otRmin to otRmax over which, upon diffraction, transmission by specular reflection occurs and / or the interval of incidence angles extending from ocmR to OCIMAX over which, upon diffraction, transmission by specular reflection occurs.

[0070] The transmittance of reflective coating 160 in the interval of incidence angles extending from ctRmin to otRmax, expressed in units of percent transmittance (%), is greater than or equal to 70%, or greater than or equal to 75%, or greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%.

[0071] The transmittance of reflective coating 160 for components of light in the interval of incidence angles extending from ocmR to OCIMAX, expressed in units of percent transmittance per micron of thickness (%), is greater than or equal to 70%, or greater than or equal to 75%, or greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90% / pm, or greater than or equal to 95%.

[0072] The transmittance of reflective coating 160 for components of light in the interval of propagation angles extending from ORmin to ORmax, expressed in units of percent transmittance (%), is greater than or equal to 70%, or greater than or equal to 75%, or greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%.

[0073] The transmittance of reflective coating 160 for components of light in the interval of propagation angles extending from 0PTIR to 0PMAX, expressed in units of percent transmittance (%), is greater than or equal to 70%, or greater than or equal to 75%, or greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%.

[0074] The condition of high reflectivity applies at least to components of diffracted light 130 that are transmitted in waveguide 105 by specular reflection. That is, reflective coatings 160 and 165 preferably have high reflectivity for components of diffracted light 130 in the interval of propagation angles extending from ORmin to ORmax. Since components of diffracted light 130 having a propagation angle in the interval extending from 0PTIR to 0PMAX transmits by totalSP24-164 internal reflection, the condition of high reflectivity is especially important for propagation angles outside of this range (e.g., propagation angles in the interval extending from 0Rminto 0PTIR (when 0Rmin 0pTIR).

[0075] The reflectivity of reflective coatings 160 and 165 for components of light in the interval of propagation angles extending from 0Rminto 0Rmaxis greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%, or greater than or equal to 97%, or greater than or equal to 99%.

[0076] The reflectivity of reflective coatings 160 and 165 for components of light in the interval of propagation angles extending from 0Rminto 0PTIR is greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%, or greater than or equal to 97%, or greater than or equal to 99%.

[0077] The reflectivity of reflective coatings 160 and 165 for components of light in the interval of propagation angles extending from 0PMAX to 0Rmaxis greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%, or greater than or equal to 97%, or greater than or equal to 99%.

[0078] The reflectivity of reflective coatings 160 and 165 for components of light in the interval of propagation angles over which transmission occurs by specular reflection, but not total internal reflection, is greater than or equal to 80%, or greater than or equal to 85%, or greater than or equal to 90%, or greater than or equal to 95%, or greater than or equal to 97%, or greater than or equal to 99%.

[0079] Reflective coatings 160 and 165 may have the same or different composition, and may have the same or different thickness. Reflective coatings 160 and 165 preferably consist of a series of layers that differ in refractive index. In one embodiment, reflective coatings 160 and 165 include a sequence of alternating high-index and low-index materials. In one embodiment, the sequence includes a periodic series of repeat units, where each repeat unit includes two layers, a high-index layer and a low-index layer, that differ in refractive index. Materials for the layers in the repeat unit include SiCh and metal oxides. Representative metal oxides include TiCh, Ta2Os, ISfeOs, HfCh, ZrCh, ZnO, and Y2O3.

[0080] The difference in refractive index na between the high-index layer of the repeat unit and the low- index layer of the repeat unit is greater than or equal to 0.2, or greater than or equal to 0.4, or greater than or equal to 0.6, or greater than or equal to 0.8, or greater than or equal to 1.0,SP24-164 or in the range from 0.2 to 1.4, or in the range from 0.3 to 1.2, or in the range from 0.4 to 1.0, or in the range from 0.5 to 0.9.

[0081] The thickness of each of the layers of reflective coatings 160 and 165 is greater than or equal to 20 nm, or greater than or equal to 40 nm, or greater than or equal to 60 nm, or greater than or equal to 80 nm, or greater than or equal to 100 nm, or greater than or equal to 120 nm, or greater than or equal to 140 nm, or greater than or equal to 160 nm, or in the range from 20 nm to 200 nm, or in the range from 40 nm to 180 nm, or in the range from 60 nm to 160 nm, or in the range from 80 nm to 140 nm.

[0082] The thickness of each of the higher index and lower index layers in embodiments of reflective coatings 160 and 165 with repeat units is greater than or equal to 20 nm, or greater than or equal to 40 nm, or greater than or equal to 60 nm, or greater than or equal to 80 nm, or greater than or equal to 100 nm, or greater than or equal to 120 nm, or greater than or equal to 140 nm, or greater than or equal to 160 nm, or in the range from 20 nm to 200 nm, or in the range from 40 nm to 180 nm, or in the range from 60 nm to 160 nm, or in the range from 80 nm to 140 nm.

[0083] The combined thickness of all layers in reflective coatings 160 (corresponding to dl) and 165 (corresponding to d2) is greater than or equal to 0.5 pm, or greater than or equal to 1.0 pm, or greater than or equal to 1.5 pm, or greater than or equal to 2.0 pm, or greater than or equal to 2.5 pm, or greater than or equal to 3.0 pm, or greater than or equal to 3.5 pm, or greater than or equal to 4.0 pm, or in the range from 0.5 pm to 5.0 pm, or in the range from 1.0 pm to 4.5 pm, or in the range from 1.5 pm to 4.0 pm, or in the range from 2.0 pm to 3.5 pm.

[0084] EXAMPLE

[0085] A representative reflective coating is given in Table 1. The reflective coating includes a repeat unit consisting of a layer of SiCh (low-index layer) and a layer of Ta2Os (high-index layer) with the refractive indices (na) and thicknesses listed. The total thickness of the reflective coating (combined thicknesses of all layers) is 1617.28 nm. Air references the surroundings exterior to the top layer of the reflective coating and the reflective coating is disposed on a glass substrate, which functions as a waveguide.Table 1 - Embodiment of a Reflective CoatingSP24-164

[0086] The transmitance and reflectivity of the reflective coating described in Table 1 were computed and the result is given in FIG. 8A. Trace 205 shows the transmitance of the reflective coating as a function of incidence angle a for a wavelength of 550 nm. Trace 210 shows the reflectance of the reflective coating as a function of propagation angle 0 for a wavelength of 550 nm. The angle 0PTIR for the glass waveguide (when lacking the reflective coating and interfaced to air) is 41° and is depicted in FIG. 8 A by a dashed line. The range of propagation angles 0 < OpTiR is also shown. Trace 210 indicates that the reflective coating provides high reflectance over a wide range of propagation angles below the minimum angle (0PTIR) required for total internal reflection. This range of propagation angles is available for transmission in waveguide 105 by specular reflection by the reflective coating and represents a range of propagation angles that would not be available for forming a virtual image in the absence of the reflective coating.

[0087] FIG. 8B shows an enlargement of Trace 210 in the region of high reflectance. The reflectance of the reflective coating is greater than or equal to 96% for propagation angles 0 greater than or equal to 25° and greater than or equal to 99.5% for propagation angles 0 greater than or equal to 30°. Trace 205 of FIG. 8A shows transmitance above 85% for incidence angles a between 0° and about 28°, which corresponds to a field of view of 56°. In the absence of theSP24-164 reflective coating, the mechanism of transmission is limited to total internal reflection and only a portion of this field of view would be diffracted by an in-coupling grating of a given configuration with a propagation angle above the minimum (41°) required for total internal reflection. The portion of the field of view diffracted to propagation angles below the minimum (41°) would be lost and would not contribute to the virtual image. Inclusion of the reflective coating in this example enables formation of a virtual image with imaging light that is diffracted to propagation angles at least as low as 30° (99.5% reflectivity) and expands the field of view by at least 22°. FIGS. 8A and 8B show results for positive values of the angles a and 0. Equivalent results apply for negative values of the angles a and 0. That is, the values for %T and %R are symmetric about the angles a = 0° and 0 = 0°.

[0088] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not actually recite an order to be followed by its steps or it is not otherwise specifically stated in the claims or description that the steps are to be limited to a specific order, it is no way intended that any particular order be inferred.

[0089] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the illustrated embodiments. Since modifications, combinations, sub-combinations, and variations of the disclosed embodiments that incorporate the spirit and substance of the illustrated embodiments may occur to persons skilled in the art, the description should be construed to include everything within the scope of the appended claims and their equivalents.

Claims

SP24-164CLAIMSWhat is claimed is:

1. An optical element comprising: a waveguide configured for transmission of light over a range of propagation angles from an in-coupling grating to an out-coupling grating, the transmission occurring within the waveguide between a first surface and a second surface, the range of propagation angles including a first interval of propagation angles over which the transmission occurs by total internal reflection and a second interval of propagation angles over which the transmission occurs by specular reflection, the first interval of propagation angles extending from a minimum angle of total internal reflection 0PTIR to a maximum angle of total internal reflection 0PMAX, the second interval of propagation angles extending from a minimum angle of specular reflection 0Rmin to a maximum angle of specular reflection 0Rmax, the second interval of propagation angles comprising propagation angles not included in the first interval of propagation angles; a first coating on the first surface, the first coating reflecting the light of the second interval of propagation angles with a reflectivity greater than or equal to 95%; and a second coating on the second surface, the second coating reflecting the light of the second interval of propagation angles with a reflectivity greater than or equal to 95%.

2. The optical element of claim 1, wherein the minimum angle of specular reflection 0Rminis less than the minimum angle of total internal reflection 0PTIR.

3. The optical element of claim 2, wherein the difference (0PTIR - 0Rmin) is greater than or equal to 5°.

4. The optical element of any of claims 1-3, wherein the first interval of propagation angles corresponds to a first interval of incidence angles extending from a first minimum incidence angle ocmR to a first maximum incidence angle otiMAX, the second interval of propagation angles corresponds to a second interval of incidence angles extending from a second minimum incidence angle a.Rminto a second maximum incidence angle a.Rmax, the second interval ofSP24-164 incidence angles comprising incidence angles not included in the first interval of incidence angles.

5. The optical element of claim 4, wherein the second minimum incidence angle a.Rminis less than the first minimum incidence angle amR.

6. The optical element of claim 5, wherein the difference (ocmR - aRmin) is greater than or equal to 5°.

7. The optical element of any of claims 4-6, wherein the first coating transmits the light of the first interval of incidence angles with a transmittance greater than or equal to 75%.

8. The optical element of any of claims 4-7, wherein the first coating transmits the light of the second interval of incidence angles with a transmittance greater than or equal to 75%.

9. The optical element of any of claims 1-8, wherein the reflectivity of the first coating is greater than or equal to 99%.

10. The optical element of claim 9, wherein the reflectivity of the second coating is greater than or equal to 99%.

11. The optical element of any of claims 1-10, wherein the first coating and the second coating comprise SiCh or a metal oxide.

12. The optical element of claim 11, wherein the metal oxide is Ta2Os or Nb2Os.

13. The optical element of any of claims 1-12, wherein the first coating includes a sequence of alternating high-index and low-index materials.

14. The optical element of claim 13, wherein each of the alternating high-index and low-index materials has a thickness in the range from 20 nm to 200 nm.SP24-16415. The optical element of claim 13 or 14, wherein the sequence comprises a periodic series of repeat units, each of the repeat units including a high-index layer and a low-index layer.

16. The optical element of claim 15, wherein the difference in refractive index between the high- index layer of the repeat unit and the low-index layer of the repeat unit is greater than or equal to 0.2.

17. The optical element of any of claims 1-16, wherein the first coating and the second coating differ in composition or thickness.

18. The optical element of any of claims 1-17, wherein the out-coupling grating diffracts the light of the first interval of propagation angles over a first range of output angles and the light of the second interval of propagation angles over a second range of output angles, the second range of output angles differing from the first range of output angles.

19. The optical element of any of claims 1-18, wherein the in-coupling grating and the out- coupling grating are disposed on or within the first coating.

20. The optical element of any of claims 1-19, wherein the spacing between the midpoint of the in-coupling grating and the midpoint of the out-coupling grating is greater than 10 mm.

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