Multilayer optical grating

By adopting the design of structured adhesive layer and inorganic layer in the optical waveguide, the efficiency limitations of existing optical waveguides in image light propagation and extraction are solved, and higher optical performance is achieved.

CN119768641APending Publication Date: 2025-04-043M INNOVATIVE PROPERTIES CO
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Patent Information

Application Number
CN202380062017.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2022-08-26
Filing Date
2023-08-09
Publication Date
2025-04-04

AI Technical Summary

Technical Problem

Existing optical waveguides have efficiency and performance limitations in extracting and propagating image light, especially in total internal reflection mode.

Method used

An optical waveguide structure is adopted including an optical core, a structured adhesive layer and an inorganic layer, wherein the inorganic layer is arranged on the optical core and is adapted to the top surface of the structured adhesive layer, and the adhesive layer fills the recesses and bonds to the optical core.

Benefits of technology

By optimizing the design of optical core and multi-layer structure, the light propagation efficiency and image extraction performance are improved, and the overall performance of optical waveguides is enhanced.

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Abstract

An optical waveguide (200) includes an optical core (20) configured to propagate an optical mode of a first wavelength along the optical core; and a multilayer grating (40) disposed on the optical core (30) and configured to extract the optical mode that would otherwise propagate along the optical core (30). The multilayer grating (30) includes an adhesive layer (50) and an inorganic layer (60). The adhesive layer (60) has a main bottom surface (51) facing the optical core and a structured main top surface (52) facing away from and spaced apart from the optical core (30). The structured main top surface (52) comprises a plurality of linear grating elements (53) extending in the same length direction of the grating elements (53) and arranged in orthogonal width directions. The inorganic layer (60) is conformable to the structured major top surface (52) of the adhesive layer (50) such that the inorganic layer (60) has a thickness standard deviation less than about 50% of an average thickness of the inorganic layer (60).
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Description

Summary of the invention

[0001] According to some aspects of the present specification, an optical waveguide is provided, comprising: an optical core configured to propagate an optical mode of a first wavelength along the optical core; and a multilayer grating disposed on the optical core and configured to extract the optical mode that would otherwise propagate along the optical core in a first direction. The multilayer grating comprises an adhesive layer and an inorganic layer. The adhesive layer has a main bottom surface facing the optical core and an opposite structured main top surface facing away from the optical core and spaced apart from the optical core. The structured main top surface comprises a plurality of substantially parallel linear grating elements extending in the same length direction of the grating elements and arranged in an orthogonal width direction of the grating elements. The inorganic layer is disposed on the structured main top surface of the adhesive layer and conforms to the structured main top surface so that the inorganic layer has a thickness standard deviation that is less than about 50% of the average thickness of the inorganic layer.

[0002] In some aspects of the present specification, an optical waveguide is provided, comprising: an optical core configured to propagate image light along the optical core primarily by total internal reflection; a structured adhesive layer; and an inorganic layer. The structured adhesive layer comprises a major bottom surface facing and bonded to the optical core and an opposite major structured top surface having a plurality of alternating ridges and grooves. The average spacing between the grooves and the optical core is greater than about 5 nm. The inorganic layer is conformally disposed on the major structured top surface of the structured adhesive layer, so that the opposite first major surface and the second major surface of the inorganic layer are substantially conformal to the major structured top surface of the structured adhesive layer, and define an average spacing between about 10 nm and about 100 nm therebetween.

[0003] In some aspects of the specification, an optical waveguide is provided, the optical waveguide comprising: an optical core (30) configured to propagate image light (20) along the optical core primarily by total internal reflection; an inorganic layer; and a structured adhesive layer. The inorganic layer is disposed on the optical core and defines a plurality of alternating first and second recesses. The first recesses are recessed toward the optical core, and the second recesses are convex toward the optical core. The structured adhesive layer is disposed between the optical core and the inorganic layer and bonds the optical core to the inorganic layer, and substantially fills the first recesses. For each pair of adjacent first and second recesses, the first and second recesses are separated by a common sidewall extending from a first rounded sidewall corner connecting the common sidewall to the bottom of the second recess to an opposite second rounded sidewall corner connecting the common sidewall to the bottom of the first recess. In a first planar cross-section substantially orthogonal to the common side wall, the first rounded side wall corner comprises a first outer circumferential surface facing the optical core and having a first radius of curvature R1, and the second rounded side wall corner has a second outer circumferential surface facing away from the optical core and having a second radius of curvature R2, such that for at least multiple pairs of adjacent first recesses and second recesses, R1>R2.

[0004] In some aspects of the present specification, an optical waveguide is provided, the optical waveguide comprising: an optical core configured to propagate image light along the optical core primarily by total internal reflection; and an inorganic layer; and a structured adhesive layer. The inorganic layer is disposed on the optical core and defines a plurality of alternating first and second recesses. The first recess is recessed toward the optical core, and the second recess is convex toward the optical core. The structured adhesive layer is disposed between the optical core and the inorganic layer and bonds the optical core to the inorganic layer. The structured adhesive layer substantially fills the first recess. For each pair of adjacent first and second recesses, the first recess and the second recess are separated by a common sidewall extending from a first rounded sidewall corner connecting the common sidewall to the bottom of the second recess to an opposite second rounded sidewall corner connecting the common sidewall to the bottom of the first recess. The first rounded sidewall corner is closer to the optical core and the second rounded sidewall corner is farther away from the optical core. In a first planar cross-section substantially orthogonal to the common side wall, the first rounded side wall corner comprises a first outer circumferential surface facing the optical core and having a first outer radius of curvature R1, and an inner first circumferential surface facing away from the optical core and having a first inner radius of curvature R1', wherein for at least multiple pairs of adjacent first recesses and second recesses, R1>R1'.

[0005] In some aspects of the present specification, a method of making an optical waveguide is provided, the method comprising: providing a temporary carrier including a main structured surface, the main structured surface having a plurality of alternating first ridges and first grooves; conformally disposing an inorganic layer on the main structured surface of the temporary carrier, such that a first main surface of the inorganic layer facing the temporary carrier and a second main surface of the inorganic layer facing away from the carrier both substantially conform to the main structured top surface of the temporary carrier. The first main surface and the second main surface of the inorganic layer define a spacing average value S therebetween. avg and the spacing standard deviation S sd , so that S sd / S avg less than about 0.5; disposing an adhesive layer on the second major surface of the inorganic layer and substantially flattening the inorganic layer to form a structured adhesive layer having a major structured top surface facing and substantially conforming to the second major surface of the inorganic layer and an opposite substantially flat major surface; bonding the substantially flat major surface of the structured adhesive layer to a major surface of an optical core configured to propagate image light along the optical core primarily by total internal reflection; and removing the temporary carrier from the first major surface of the inorganic layer. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1A and Figure 1B A side view of a portion of an optical waveguide including a multilayer grating according to an embodiment of the present specification;

[0007] Figure 2 is a scanning electron microscope of a multilayer grating according to an embodiment of the present specification;

[0008] Figure 3 is a process flow illustrating a method of fabricating an optical waveguide having a multilayer grating according to an embodiment of the present specification;

[0009] Figure 4 is a side view of an optical waveguide including two multilayer grating segments according to an embodiment of the present specification;

[0010] Figure 5 According to the embodiments of the present invention, Figure 4 Alternative views of an optical waveguide;

[0011] Fig. 6A and Figure 6B A side view of an architecture including a multilayer grating according to an embodiment of the present specification;

[0012] Figure 7 is a side view of an optical waveguide including multilayer grating segments on opposite sides of an optical core according to an alternative embodiment of the present specification;

[0013] Figure 8 is a side view of an optical waveguide according to another alternative embodiment of the present specification;

[0014] Fig.9A and Fig. 9B A top view and a side view are respectively provided of an optical waveguide including three multilayer grating segments according to an alternative embodiment of the present specification;

[0015] Fig. 10A and Fig. 10B Illustrative examples of alternative shapes for features on multilayer gratings according to embodiments of the present specification are provided;

[0016] Fig.11A and Fig. 11B Additional illustrative examples of alternative shapes for features on multilayer gratings according to embodiments of the present description are provided; and

[0017] Fig.12 is an illustrative example of a method for measuring dimensions on a relief layer of a multilayer grating according to an embodiment of the present specification. DETAILED DESCRIPTION

[0018] In the following description, reference is made to the accompanying drawings, which form a part of the present disclosure and in which various embodiments are shown by way of example. The drawings are not necessarily drawn to scale. It should be understood that other embodiments may be conceived and made without departing from the scope or essence of the present specification. Therefore, the following specific embodiments should not be considered to have a limiting meaning.

[0019] Nanostructured films can be used in optical laminates or as transfer films based on subwavelength optical devices such as diffractive optical elements and optical metasurfaces. The transfer films can be used to make image-retaining waveguides for augmented reality devices. The optical performance of these waveguides depends on the refractive index contrast (i.e., refractive index difference) between the grating structure and the surrounding medium, which can be a template film (e.g., a polymer with a refractive index of about 1.5) or air (in the case where the template is removed in a subsequent processing step). Therefore, methods are needed to maximize the refractive index of templated nanostructures used in the final article of the templated nanostructures.

[0020] The fabrication of high-refractive-index, sub-wavelength gratings and nanostructures is typically done using “batch processing” and methods developed for the semiconductor industry. The process involves depositing a dense layer of TiO on a substrate (e.g., a high-refractive-index glass wafer). 2 TiO 2The layer is coated with a polymer resist which is then patterned via a lithography technique (such as photolithography, nanoimprint lithography, or electron beam lithography) to define a desired pattern in the resist. The pattern in the resist is then transferred to the TiO 2 layer, and finally the resist is removed, leaving the patterned TiO 2 .

[0021] The transfer film method described in this paper is fundamentally different from the commonly used batch processing methods and may be more suitable for high-volume and low-cost production of subwavelength optical structures. The transfer film method fabricates high-refractive-index TiO on a polymer template structure on a support film. 2 This is accomplished by using a sub-wavelength structure. Once the structure is made, it is transferred to the final substrate (e.g., a high refractive index glass wafer) with an ultra-thin adhesive (less than 500 nm and preferably less than 100 nm thick to maintain good optical coupling), and the carrier substrate and optionally the template layer are removed. This enables the use of high-volume roll-to-roll processing to produce high refractive index structures on the final substrate.

[0022] According to some aspects of the present specification, an optical waveguide includes: an optical core configured to propagate an optical mode of a first wavelength along the optical core; and a multilayer grating disposed on the optical core and configured to extract the optical mode that would otherwise propagate along the optical core in a first direction (e.g., on an x-axis relative to the waveguide).

[0023] In some embodiments, the multilayer grating may include an adhesive layer and an inorganic layer. In some embodiments, the adhesive layer may include a main bottom surface facing the optical core and an opposite structured main top surface facing away from the optical core and spaced apart from the optical core. In some embodiments, the structured main top surface may include a plurality of substantially parallel linear grating elements extending along the same length direction of the grating element (e.g., y-axis) and arranged along the orthogonal width direction of the grating element (e.g., x-axis). In some embodiments, a plurality of substantially parallel linear grating elements may form a periodic pattern along the width direction of the grating element. In some such embodiments, the periodic pattern may have a period in the range of about 100 nm to about 1000 nm, or about 150 nm to about 750 nm, or about 200 nm to about 700 nm, or about 250 nm to about 600 nm, or about 300 nm to about 550 nm, or about 300 nm to about 500 nm, or about 300 nm to about 450 nm. In some implementations, a width direction of the grating element can be substantially parallel to the first direction.

[0024] In some embodiments, the inorganic layer may be disposed on the structured major top surface of the adhesive layer and may conform to the structured major top surface such that the inorganic layer has a thickness standard deviation of less than about 50%, or less than about 45%, or less than about 40%, or less than about 35%, or less than about 30%, or less than about 25%, or less than about 20% of the average thickness of the inorganic layer.

[0025] In some embodiments, the optical core can have an average thickness between about 100 microns and about 2000 microns, or between about 150 microns and about 1500 microns, or between about 200 microns and about 1250 microns, or between about 250 microns and about 1250 microns, or between about 300 microns and about 1000 microns. In some embodiments, the optical core can have a thickness of at most 5000 microns, or at most 7500 microns, or at most 10,000 microns.

[0026] In some embodiments, the minimum spacing between the optical core and the major top surface of the adhesive layer may be greater than about 5 nm, or greater than about 10 nm, or greater than about 15 nm, or greater than about 20 nm, or greater than about 25 nm, or greater than about 30 nm, or greater than about 35 nm, or greater than about 40 nm, or greater than about 45 nm, or greater than about 50 nm.

[0027] In some embodiments, the optical waveguide may further include a capping layer disposed on the inorganic layer and substantially planarizing the inorganic layer. In some embodiments, the inorganic layer may include titanium dioxide (TiO 2 ), zirconium oxide (ZrO x ), titanium oxide (TiO x )、SiO 2 、Al 2 O 3 、CeO 2 、ZnO、Nb 2 O 5 、 2 O 5 , HfO 2 、SiAlOxNy、Si 3 N 4 , Nb-doped TiO 2 and ZrO 2 In some implementations, at the first wavelength, the refractive index of the capping layer can be at least 0.5, or at least 0.6, or at least 0.7, or at least 0.8, or at least 0.9, or at least 1.0, or at least 1.2 less than the refractive index of the inorganic layer.

[0028] In some embodiments, an optical system may include any of the optical waveguides described herein; and at least one light source configured to introduce light at a first wavelength into an optical core of the optical waveguide such that the introduced light propagates along the optical core in a first direction as an optical mode.

[0029] According to some aspects of the present specification, an optical waveguide includes: an optical core configured to propagate image light along the optical core primarily by total internal reflection; a structured adhesive layer; and an inorganic layer. In some embodiments, the structured adhesive layer may include a major bottom surface facing and bonded to the optical core and an opposite major structured top surface including a plurality of alternating ridges and grooves. In some embodiments, the average spacing between the grooves and the optical core may be greater than about 5nm, or about 10nm, or about 15nm, or about 20nm, or about 25nm, or about 30nm, or about 35nm, or about 40nm, or about 45nm, or about 50nm. In some embodiments, the average spacing between the grooves and the optical core may be less than about 500nm, or about 450nm, or about 400nm, or about 350nm, or about 300nm, or about 250nm, or about 200nm, or about 150nm, or about 100nm. In some implementations, the minimum spacing between the trench and the optical core can be greater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm.

[0030] As used herein, the terms "ridge" and "groove" shall be defined as follows. A ridge is any undulation in a layer for which the material of the layer is pushed "upward" away from the optical core, thereby forming a protrusion extending in a direction away from the optical core. Conversely, a groove is any undulation in a layer for which the material of the layer is pushed "downward" toward the optical core, thereby forming a recess extending in a direction toward the optical core.

[0031] Both ridges and grooves can be considered "depressions" in a layer, but the depressions face different directions. For example, each depression has an open end and a closed end (e.g., a "cup-like" shape). In a "ridge" depression, the open end of the depression faces "downward" toward the optical core (negative z-direction of FIG. 1 ), and the closed end protrudes "upward" away from the optical core (positive z-direction of FIG. 1 as shown by arrows on the coordinate system graphic). Conversely, a "groove" depression has an open end facing "upward" away from the optical core and a closed end facing "downward" toward the optical core. These definitions are provided for clear understanding of the drawings and language of this specification.

[0032] In some embodiments, the structured adhesive has a refractive index of between about 1.35 and about 2.5 for at least one visible wavelength in the visible (human visible) wavelength range extending from about 420 nm to about 680 nm. In some embodiments, the structured adhesive has a refractive index of about 1.5 for at least one visible wavelength in the visible wavelength range extending from about 420 nm to about 680 nm.

[0033] In some embodiments, the inorganic layer may be conformally disposed on the major structured top surface of the structured adhesive layer such that the opposing first and second major surfaces of the inorganic layer substantially conform to the major structured top surface of the structured adhesive layer, and the first and second major surfaces of the inorganic layer define an average spacing therebetween of from about 10 nm to about 100 nm, or from about 20 nm to about 90 nm, or from about 30 nm to about 80 nm, or from about 40 nm to about 70 nm, or from about 40 nm to about 60 nm. In some embodiments, the inorganic layer may have a refractive index greater than about 1.5, or about 1.6, or 1.7, or 1.8, or 1.9, or 2.0, or 2.1, or 2.2, or 2.3, or 2.4 at a wavelength of about 580 nm.

[0034] In some embodiments, the optical core may have a refractive index greater than about 1.5, or greater than about 1.6, or greater than about 1.7, or greater than about 1.8, or greater than about 1.9, or greater than about 2.0 at a wavelength of about 580 nm. In some embodiments, the optical core may include one or more of tantalum, niobium, lanthanum, lead, barium, titanium, zirconium, and bismuth. In some embodiments, the optical core may be a polymer. In some embodiments, the optical core may include, but is not limited to, one or more of polymethacrylate, polycarbonate, polyester, polyphosphonate, polysulfone, siloxane, epoxy, or polyimide components. In some embodiments, the optical core may include nanoparticles. In some embodiments, the optical core may include nanoparticles of titanium dioxide or zirconium oxide.

[0035] According to some aspects of the present specification, an optical waveguide includes: an optical core configured to propagate image light along the optical core primarily by total internal reflection; an inorganic layer; and a structured adhesive layer. In some embodiments, the inorganic layer may be disposed on the optical core and may define a plurality of alternating first and second recesses, wherein the first recesses are recessed toward the optical core and the second recesses are convex toward the optical core. In some embodiments, the structured adhesive layer may be disposed between the optical core and the inorganic layer and bond them to each other. In some embodiments, the structured adhesive layer may substantially fill the first recess.

[0036] For each pair of adjacent first and second recessed portions, the first and second recessed portions may be separated by a common sidewall extending from a first rounded sidewall corner connecting the common sidewall to the bottom of the second recessed portion to an opposite second rounded sidewall corner connecting the common sidewall to the bottom of the first recessed portion. In a first planar cross-section substantially orthogonal to the common sidewall (e.g., in the xz plane of the optical waveguide), the first rounded sidewall corner may include a first outer circumferential surface facing the optical core and having a first radius of curvature R1. In some embodiments, the second rounded sidewall corner may include a second outer circumferential surface facing away from the optical core and having a second radius of curvature R2. In some embodiments, for at least a plurality of adjacent pairs of first and second recessed portions, R1 may be greater than R2.

[0037] According to some aspects of the present specification, an optical waveguide may include: an optical core configured to propagate image light along the optical core primarily by total internal reflection; an inorganic layer; and a structured adhesive layer. In some embodiments, the inorganic layer may be disposed on the optical core and may define a plurality of alternating first and second recessed portions. In some embodiments, the first recessed portion may be recessed toward the optical core, and the second recessed portion may be convex toward the optical core.

[0038] In some embodiments, the structured adhesive layer may be disposed between the optical core and the inorganic layer, and may bond the optical core to the inorganic layer. In some embodiments, the structured adhesive layer may substantially fill the first recess. In some embodiments, for each pair of adjacent first and second recesses, the first recess and the second recess may be separated by a common sidewall extending from a first rounded sidewall corner that joins the common sidewall to the bottom of the second recess to an opposite second rounded sidewall corner that joins the common sidewall to the bottom of the first recess. In some embodiments, the first rounded sidewall corner may be closer to the optical core and the second rounded sidewall corner may be farther away from the optical core.

[0039] In some embodiments, in a first planar cross-section substantially orthogonal to the common sidewall (e.g., an xz plane of the optical waveguide), the first rounded sidewall corner may include a first outer circumferential surface facing the optical core and having a first outer radius of curvature R1 and an inner first circumferential surface facing away from the optical core and having a first inner radius of curvature R1. In some embodiments, for at least a plurality of adjacent first and second recessed portions, R1 may be greater than R1'. In some embodiments, the value of R1-R1' may be at least 10 nm, or at least 20 nm, or at least 30 nm, or at least 40 nm, or at least 50 nm.

[0040] According to some aspects of the present description, a method of making an optical waveguide may include: providing a temporary carrier including a main structured surface having a plurality of alternating first ridges and first grooves; conformally disposing an inorganic layer on the main structured surface of the temporary carrier, such that a first main surface of the inorganic layer facing the temporary carrier and a second main surface of the inorganic layer facing away from the carrier both substantially conform to the main structured top surface of the temporary carrier, such that the first main surface and the second main surface of the inorganic layer define a spacing average value S therebetween. avg and the spacing standard deviation S sd , S sd / S avg less than about 0.5, or about 0.4, or about 0.3, or about 0.2, or about 0.17, or about 0.15, or about 0.12, or about 0.1; disposing an adhesive layer on the second major surface of the inorganic layer and substantially planarizing the inorganic layer to form a structured adhesive layer having a major structured top surface facing and substantially conforming to the second major surface of the inorganic layer and an opposing substantially planar major surface; and bonding the substantially planar major surface of the structured adhesive layer to a major surface of an optical core configured to propagate image light along the optical core primarily by total internal reflection; and removing the temporary carrier from the first major surface of the inorganic layer. For S avg and S sd For additional details on the value of and how the measurement can be determined, refer to the Fig.12 Discussion.

[0041] In some embodiments, the method of making an optical waveguide may further include: disposing a cover material on a first major surface of the inorganic layer; and substantially planarizing the inorganic layer to form a structured cover layer having a main structured surface facing and substantially conforming to the first major surface of the inorganic layer and an opposite substantially planar major surface. In some embodiments, the step of providing a temporary carrier includes providing a tool having a main structured surface, the main structured surface comprising a plurality of alternating ridges and grooves; and disposing a temporary carrier material on the main structured surface of the tool to form a temporary carrier having a main structured surface facing and substantially conforming to the main surface of the tool and comprising a plurality of alternating first ridges and first grooves.

[0042] In some embodiments, removing the temporary carrier from the first major surface of the inorganic layer can include removing the temporary carrier by plasma etching, wet etching, solvent dissolution, laser ablation, chemical mechanical polishing (CMP), or any other suitable method.

[0043] In some embodiments, the temporary carrier may include a carrier substrate having a detachable release layer, wherein the primary structured surface is deposited on the detachable release layer. Examples of carriers having a detachable release layer are described in co-pending U.S. patent application No. 63 / 265,650 filed on December 17, 2021.

[0044] In such embodiments, the step of removing the temporary carrier involves removing the carrier substrate and then removing the remaining "primary structured surface" by plasma etching, wet etching, solvent dissolution, laser ablation, chemical mechanical polishing (CMP), or any other suitable method.

[0045] According to some aspects of the present specification, an optical waveguide may include an optical core configured to propagate image light along the optical core; and a first multilayer grating and a second multilayer grating disposed on the optical core. In some embodiments, the first multilayer grating may be configured to receive image light from an image projector and to direct at least a portion of the received image light into the optical core. In some embodiments, the directed image light may propagate along the optical core primarily by total internal reflection. In some embodiments, the second multilayer grating may be configured to receive at least a portion of the directed image light and to extract at least a portion of the received directed image light from the optical core for viewing by a viewer (e.g., a human observer). In some embodiments, the first multilayer grating and the second multilayer grating may have different width directions (e.g., an x-axis relative to each multilayer grating may define a non-zero angle therebetween in the case of overlap). In some embodiments, the optical core may have a refractive index greater than about 1.5, or greater than about 1.6, or greater than about 1.7, or greater than about 1.8, or greater than about 1.9, or greater than about 2.0 at a wavelength of about 580 nm. In some embodiments, the optical core may include one or more of tantalum, niobium, lanthanum, lead, barium, titanium, zirconium, and bismuth. In some embodiments, the optical core may be a polymer. In some embodiments, the optical core may include one or more of polymethacrylate, polycarbonate, polyester, polyphosphonate, polysulfone, siloxane, epoxy, or polyimide components. In some embodiments, the optical core may include nanoparticles. In some embodiments, the optical core may include nanoparticles of titanium dioxide or zirconium oxide. In some embodiments, each of the first multilayer grating and the second multilayer grating may include an inorganic undulating layer and a planarizing adhesive layer. In some embodiments, the inorganic undulating layer may include opposing outermost undulating major surfaces that are nestedly aligned with each other to have a wavy shape along a width direction of the inorganic undulating layer (e.g., along the x-axis) and form a plurality of substantially parallel ridges and grooves. In some embodiments, the ridges and grooves may extend along an orthogonal length direction of the inorganic undulating layer (e.g., the y-axis). In some embodiments, the undulation amplitude of at least one of the first multilayer grating and the second multilayer grating may vary along its width direction.

[0046] As used herein, the phrase "undulating layer" refers to a layer having a wavy pattern, shape or profile in the width direction of the layer, wherein connected curves in alternating directions in the layer form alternating peaks and valleys or ridges and grooves on each major side of the layer in the width direction and extend along the length direction of the layer. Examples of undulating layers include, but are not limited to, layers having sinusoidal wave patterns, shapes or profiles, and layers having triangular wave, tilted or shimmering patterns, shapes or profiles. Other examples of undulating layers include layers characterized by a two-dimensional (2D) pattern of posts and / or holes, wherein a cross section taken through a linear collection of posts or holes (e.g., a row of posts or holes) produces an undulating pattern across the layer.

[0047] In some embodiments, a planarizing adhesive layer can be disposed between the inorganic relief layer and the optical core and substantially planarizes one of the relief major surfaces of the inorganic relief layer and bonds the inorganic relief layer to the optical core.

[0048] In some embodiments, the planarized adhesive layer can define a minimum distance d between the inorganic relief layer and the optical core. min In some such embodiments, d min The minimum spacing between the optical core and the groove of the multilayer grating may be greater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm. In some implementations, for at least one of the first multilayer grating and the second multilayer grating, the minimum spacing between the optical core and the groove of the multilayer grating may vary along the width of the multilayer grating.

[0049] In some embodiments, for at least one of the first multilayer grating and the second multilayer grating, in a planar cross section (e.g., an xz plane) of the multilayer grating orthogonal to a length direction (e.g., a y-axis) of the multilayer grating, for two different positions L1 and L2 on the multilayer grating, each position includes a ridge and a directly adjacent groove, wherein the area between the optical core and the ridge at L1 is A r1 , the area between the optical core and the groove at L1 is A g1 , the area between the optical core and the ridge at L2 is A r2 , and the area between the optical core and the groove at L2 is A g2 , A r1 +A g1 In A r2 +A g2 within 30%, or within 20%, or within 10%, or within 5%, or within 2%.

[0050] In some embodiments, for at least one of the first multilayer grating and the second multilayer grating, the multilayer grating may further include a planarization cover layer that conformally covers the inorganic undulation layer opposite the planarization adhesive layer and substantially planarizes the inorganic undulation layer. In some embodiments, the first multilayer grating and the second multilayer grating may be disposed on the same side of the optical core, or may be disposed on opposite major sides of the optical core. In some embodiments, the first multilayer grating and the second multilayer grating may be spaced apart, while in other embodiments, the first multilayer grating and the second multilayer grating may contact or overlap.

[0051] In some embodiments, the optical waveguide may further include: a connecting adhesive portion disposed between the planarizing adhesive layers of the first multilayer grating and the second multilayer grating and continuously and seamlessly connecting the planarizing adhesive layers. In some embodiments, the optical waveguide may further include: a connecting substantially non-relief inorganic layer disposed between the inorganic undulation layers of the first multilayer grating and the second multilayer grating and continuously and seamlessly connecting the inorganic undulation layers.

[0052] In some embodiments, each of the first multilayer grating and the second multilayer grating may further include a planarization cover layer that conformally covers the inorganic undulation layer opposite to the planarization adhesive layer and substantially planarizes the inorganic undulation layer. In some such embodiments, the optical waveguide may further include: a substantially planarized connection cover layer that is disposed between the planarization cover layers of the first multilayer grating and the second multilayer grating and continuously and seamlessly connects the planarization cover layers.

[0053] In some embodiments, for at least one visible wavelength in the human visible wavelength range extending from about 420 nm to about 680 nm, the refractive index of the planarized capping layer is at least 0.5, or at least 0.6, or at least 0.7, or at least 0.8, or at least 0.9, or at least 1.0, or at least 1.2 less than the refractive index of the inorganic undulating layer.

[0054] In some embodiments, for at least one of the first multilayer grating and the second multilayer grating, the plurality of substantially parallel ridges and grooves may form a periodic pattern along the width direction of the inorganic relief layer. In some such embodiments, the periodic pattern may have a period in the range of about 100 nm to about 1000 nm, or about 150 nm to about 750 nm, or about 200 nm to about 700 nm, or about 250 nm to about 600 nm, or about 300 nm to about 550 nm, or about 300 nm to about 500 nm, or about 300 nm to about 450 nm.

[0055] In some embodiments, the optical core may have an average thickness between about 100 microns and about 2000 microns, or about 150 microns and about 1500 microns, or about 200 microns and about 1250 microns, or about 250 microns and about 1250 microns, or about 300 microns and about 1000 microns. In some embodiments, the optical core may have a thickness of at most 5000 microns, or at most 7500 microns, or at most 10,000 microns. In some embodiments, the minimum thickness of the planarization adhesive layer may be greater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm.

[0056] In some embodiments, the inorganic relief layer may include titanium dioxide (TiO 2 ), zirconium oxide (ZrO x ), titanium oxide (TiO x )、SiO 2 、Al 2 O 3 、CeO 2 、ZnO、Nb 2 O 5 、 2 O 5 , HfO 2 、SiAlOxNy、Si 3 N 4 , Nb-doped TiO 2 and zirconium dioxide (ZrO 2 )

[0057] In some embodiments, an optical system may include any of the optical waveguides described herein and an image projector configured to emit image light, wherein the first multilayer grating may be configured to receive the emitted image light and direct at least a portion of the received image light into an optical core of the optical waveguide.

[0058] In some embodiments, the planarizing adhesive layer may have a refractive index between about 1.35 and about 2.5 for at least one visible wavelength in the visible wavelength range extending from about 420 nm to about 680 nm. In some embodiments, the planarizing adhesive layer may have a refractive index of about 1.5 for at least one visible wavelength in the visible wavelength range extending from about 420 nm to about 680 nm. In some embodiments, the inorganic undulation layer may have a refractive index greater than about 1.5, or greater than about 1.6, or greater than about 1.7, or greater than about 1.8, or greater than about 1.9, or greater than about 2.0, or greater than about 2.1, or greater than about 2.2, or greater than about 2.3, or greater than about 2.4 at a wavelength of about 580 nm.

[0059] In some embodiments, the minimum spacing between the optical core and the plurality of substantially parallel ridges and grooves can be greater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm. In some embodiments, the average spacing between the grooves and the optical core can be less than about 500 nm, or about 450 nm, or about 400 nm, or about 350 nm, or about 300 nm, or about 250 nm, or about 200 nm, or about 150 nm, or about 100 nm.

[0060] According to some aspects of the present description, an optical waveguide may include: an optical core configured to propagate image light along the optical core; and a continuous seamless multilayer disposed on a major side of the optical core.

[0061] In some embodiments, the continuous seamless multilayer may include a continuous seamless inorganic layer and a continuous seamless adhesive layer. In some embodiments, the continuous seamless inorganic layer may be undulated in a plurality of discrete spaced-apart regions of the inorganic layer to form a plurality of spaced-apart undulated inorganic layer portions of an otherwise non-undulated inorganic layer.

[0062] In some embodiments, each of the undulating inorganic layer portions may include opposite outermost undulating major surfaces that are nested and aligned with each other and form a plurality of substantially parallel ridges and grooves extending along the length direction (e.g., the x-axis) of the undulating inorganic layer portion and arranged along an orthogonal width direction (e.g., the y-axis) of the undulating inorganic layer portion.

[0063] In some embodiments, a continuous seamless adhesive layer can be disposed between the inorganic layer and the optical core and can substantially conform to the ridges and grooves of each of the undulating inorganic layer portions and bond the inorganic layer to the optical core.

[0064] In some embodiments, a first undulating inorganic layer portion in the undulating inorganic layer portions is configured to receive image light from an image projector and direct at least a portion of the received image light into an optical core. In some embodiments, the directed image light may propagate along the optical core primarily by total internal reflection. In some embodiments, a second undulating inorganic layer portion in the undulating inorganic layer portions may be configured to receive at least a portion of the directed image light along a first direction and redirect the directed image light into redirected image light that propagates along the optical core in a different second direction primarily by total internal reflection. In some embodiments, a third undulating inorganic layer portion in the undulating inorganic layer portions may be configured to receive at least a portion of the redirected image light and extract at least a portion of the received redirected image light from the optical core for viewing by a viewer.

[0065] As used herein, the term "seamless" used in conjunction with the term "layer" (e.g., in "seamless adhesive layer") shall be defined to mean a layer that is formed as a continuous piece and contains substantially no gaps within the layer. In some embodiments, a "seamless" layer may contain small cracks (e.g., cracks that are unintentionally formed as a result of a manufacturing or processing step) that do not significantly affect the intended function of the otherwise continuous layer. In addition, a layer that contains an intentional discontinuity between two substantially similar sections of the layer shall be considered seamless, where the two sections are otherwise in direct contact with each other (e.g., a butt joint between the two sections) and where the layer otherwise functions substantially as a continuous layer.

[0066] According to some aspects of the present specification, a method of making an optical waveguide may include the following steps: providing a temporary carrier including a major structured surface having a plurality of alternating first ridges and first grooves in a plurality of discretely spaced-apart regions; conformally disposing an inorganic layer on the major structured surface of the temporary carrier such that a first major surface of the inorganic layer facing the temporary carrier and a second major surface of the inorganic layer facing away from the carrier substantially conform to the major structured top surface of the temporary carrier to form a continuous seamless inorganic layer having a plurality of undulating inorganic layer portions in an otherwise non-undulating inorganic layer, such that in each of the undulating inorganic layer portions, the first major surface and the second major surface of the layer portion define a spacing average value S therebetween; avg and the spacing standard deviation S sd , S sd / S avgless than about 0.5, or less than about 0.4, or less than about 0.3, or less than about 0.2, or less than about 0.17, or less than about 0.15, or less than about 0.12, or less than about 0.1; substantially conformally coating the second major surface of the inorganic layer with an adhesive layer and substantially flattening the inorganic layer to form a structured adhesive layer having a major structured top surface facing and substantially conforming to the second major surface of the inorganic layer and an opposite substantially flat major surface; bonding the substantially flat major surface of the structured adhesive layer to a major surface of an optical core, the optical core being configured to propagate image light along the optical core primarily by total internal reflection; and removing the temporary carrier from the first major surface of the inorganic layer.

[0067] Turning now to the accompanying drawings, Figure 1A and Figure 1B A side view of an embodiment including an optical waveguide according to the present specification. Figure 1A , an embodiment of an optical system 300 is shown. In some embodiments, the optical system 300 includes an optical waveguide 200 and at least one light source 70 / 71.

[0068] In some embodiments, the optical waveguide 200 includes an optical core 30 and a multilayer grating 40. In some embodiments, the multilayer grating 40 can be disposed on the optical core 30 and configured to extract an optical mode that would otherwise propagate along the optical core 30.

[0069] In some embodiments, the light source 70 / 71 can be configured to direct light 20 / 21 at a first wavelength within a human-visible (visible) wavelength range into the optical core 30, wherein the directed light 20 / 21 is directed along the optical core 30 in a first direction of the optical core 30 (e.g., in a direction along the x-axis, such as Figure 1A The light 20 / 21 propagates along the optical core 30 until the light impinges on the multilayer grating 40, where the light can enter the multilayer grating 40 and can be extracted from the optical core 30 (where the light can be viewed by a viewer, in Figure 1A , but shown elsewhere herein). It should be noted that the first wavelength may also be outside the visible wavelength range (eg, may be an infrared wavelength).

[0070] In some embodiments, the multilayer grating 40 may include an adhesive layer 50 and an inorganic layer 60. In some embodiments, the adhesive layer 50 may include a major bottom surface 51 facing the optical core 30 and an opposite structured major top surface 52 facing away from the optical core 30 and spaced apart from the optical core. In some embodiments, the structured major top surface 52 may include a plurality of substantially parallel linear grating elements 53 extending along the same length direction of the grating elements 53 (e.g., as shown in FIG. 1 ). Figure 1AThe y-axis shown in FIG. 5A ) extends along an orthogonal width direction of the grating element 53 (e.g., as shown in FIG. Figure 1A The x-axis is shown).

[0071] In some embodiments, the plurality of substantially parallel linear grating elements 53 are arranged along the width direction of the grating element 53 (e.g., Figure 1A In some embodiments, the grating elements are provided with a periodic pattern in the x-direction shown in FIG. 1 . In some embodiments, the width direction of the grating elements is substantially parallel to the first direction. In some such embodiments, the periodic pattern may have a period in the range of about 100 nm to about 1000 nm, or about 150 nm to about 750 nm, or about 200 nm to about 700 nm, or about 250 nm to about 600 nm, or about 300 nm to about 550 nm, or about 300 nm to about 500 nm, or about 300 nm to about 450 nm.

[0072] In some embodiments, the optical core may have an average thickness t between about 100 microns and about 2000 microns, or about 150 microns and about 1500 microns, or about 200 microns and about 1250 microns, or about 250 microns and about 1250 microns, or about 300 microns and about 1000 microns. c In some embodiments, the minimum spacing d between the optical core and the major top surface of the adhesive layer is b Greater than about 5 nm, or greater than about 10 nm, or greater than about 15 nm, or greater than about 20 nm, or greater than about 25 nm, or greater than about 30 nm, or greater than about 35 nm, or greater than about 40 nm, or greater than about 45 nm, or greater than about 50 nm.

[0073] In some embodiments, the inorganic layer 60 can be disposed on the structured major top surface 52 of the adhesive layer 50 and can conform to the structured major top surface such that the inorganic layer 60 has a thickness standard deviation of less than about 50%, or about 45%, or about 40%, or about 35%, or about 30%, or about 25%, or about 20% of the average thickness of the inorganic layer 60. In some embodiments, the inorganic layer 60 can have a first major surface 61 facing away from the optical core 30 and a second major surface 62 facing toward the optical core 30 and substantially conforming to the major structured top surface 52 of the adhesive layer 50. In some embodiments, the inorganic layer 60 can define a plurality of alternating first recesses 63 and second recesses 64, wherein the first recesses 63 are recessed toward the optical core 30 and the second recesses 64 are convex toward the optical core 30. In some embodiments, the inorganic layer 60 can include titanium dioxide (TiO 2 ), zirconium oxide (ZrO x ), titanium oxide (TiO x )、SiO 2 、Al 2 O3 、CeO 2 、ZnO、Nb 2 O 5 、 2 O 5 , HfO 2 、SiAlO x N y 、Si 3 N 4 , Nb-doped TiO 2 and zirconium dioxide (ZrO 2 )

[0074] In some embodiments, the multilayer grating 40 of the optical waveguide 200 may further include a capping layer 80 disposed on and substantially planarizing the inorganic layer 60. In some embodiments, the refractive index of the capping layer 80 may be at least 0.5 less than the refractive index of the inorganic layer 60 at the first wavelength.

[0075] Figure 1B Additional details about adhesive layer 50 are shown. Adhesive layer 50 can be structured and include a major bottom surface 51 and an opposing major structured top surface 52. In some embodiments, major structured top surface 52 can include a plurality of alternating ridges 54 and grooves 55. In some embodiments, the average spacing d between the bottom of grooves 55 and optical core 30 is 1.5 Å. a It may be greater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm.

[0076] Figure 2 is a scanning electron microscope (SEM) image of a multilayer grating on an optical core according to an embodiment of the present specification. The multilayer grating 40 is disposed on the optical core 30. Figure 2 In the illustrated embodiment, the multilayer grating 40 includes an adhesive layer 50 , an inorganic layer 60 conforming to the adhesive layer 50 , and a capping layer 80 that planarizes the top of the multilayer grating 40 .

[0077] The inorganic layer 60 is disposed on the optical core 30 and defines a plurality of alternating first recesses 63 and second recesses 64. In this embodiment, the first recesses 63 are recessed toward the optical core 30 and the second recesses 64 are convex toward the optical core 30. The structured adhesive layer 50 is disposed between the optical core 30 and the inorganic layer 60 and bonds the optical core to the inorganic layer such that the structured adhesive layer 50 substantially fills the first recesses 63.

[0078] For each pair of adjacent first recesses 63a and second recesses 64a, the first recess 63a and the second recess 64a are separated by a common side wall 65 extending from a first rounded side wall corner 65a connecting the common side wall 65 to the bottom 64a1 of the second recess 64a to an opposite second rounded side wall corner 65b1 connecting the common side wall 65 to the bottom 63a1 of the first recess 63a.

[0079] In a first planar cross-section substantially orthogonal to the common side wall 65 (eg, Figure 2 In the xz plane shown in , the first rounded side wall corner 65a includes a first outer circumferential surface 65a1 facing the optical core 30 and having a first curvature radius R1, and the second rounded side wall corner 65b includes a second outer circumferential surface 65b1 facing away from the optical core 30 and having a second curvature radius R2, so that for at least multiple pairs of adjacent first recesses 63a and second recesses 64a, R1 is greater than R2.

[0080] In addition, in the same first plane cross-section (i.e., xz plane), the first rounded side wall corner 65a has an inner first circumferential surface 65a2 facing away from the optical core and having a first inner curvature radius R1', so that for at least multiple pairs of adjacent first recessed portions 63a and second recessed portions 64a, R1 is greater than R1'.

[0081] Figure 3 is a process flow illustrating one embodiment of a method of making an optical waveguide with a multilayer grating according to the present specification. The method may include steps A to J as outlined herein. It should be noted that Figure 3 The process flow shown in Figure 3 The arrows are set between the steps and the Figure 3 Move to the top of Figure 3 at the bottom of the flowchart (i.e., the steps are performed sequentially based on their letter labels from Step A to Step J).

[0082] A temporary carrier 90 having a primary structured surface 91 having a plurality of alternating first ridges 92 and first grooves 93 is provided (step D). In some embodiments, step D may include: providing a tool 100 having a primary structured surface 101 having a plurality of alternating ridges 102 and grooves 103 (step A); disposing a temporary carrier material 90a on the primary structured surface 101 of the tool 100 to form a temporary carrier 90 having a primary structured surface 91 facing and substantially conforming to the primary structured surface 101 of the tool 100 and including a plurality of alternating first ridges 92 and first grooves 93 (step B); removing the temporary carrier 90 from the tool 100 (step C). In some embodiments, the temporary carrier 90 may include a detachable substrate 97 for handling and / or transfer. In some embodiments, the landing area (labeled L in step D, representing the thickness between the bottom of a groove on the primary structured surface 91 and the opposite surface of the temporary support) may be less than 10 microns, or less than 5 microns, or less than 2 microns, or less than 1 micron, or less than 0.5 microns thick.

[0083] In step E, the inorganic layer 60 is conformally disposed on the major structured surface 91 of the temporary carrier 90 such that both the first major surface 61 of the inorganic layer facing the temporary carrier 90 and the second major surface 62 of the inorganic layer facing away from the carrier 90 substantially conform to the major structured top surface 91 of the temporary carrier 90. In some embodiments, the first major surface 61 and the second major surface 62 of the inorganic layer 60 may define a spacing average S therebetween. avg and the spacing standard deviation S sd , so that S sd / S avg Less than about 0.5, or about 0.4, or about 0.3, or about 0.2, or about 0.17, or about 0.15, or about 0.12, or about 0.1. In some embodiments, suitable deposition methods may include chemical vapor deposition (CVD) methods, sputter coating methods, physical vapor deposition (PVD) methods, atomic layer deposition (ALD) methods, or any suitable combination thereof.

[0084] In step F, an adhesive material layer is disposed on the second major surface 62 of the inorganic layer 60, the adhesive material layer substantially flattening the inorganic layer 60 to form a structured adhesive layer 50 having a main structured top surface 52 facing the second major surface 62 of the inorganic layer 60 and substantially conforming to the second major surface, and an opposite substantially flat major surface 51.

[0085] In some embodiments, the adhesive material layer can be a polymer or monomer adhesive layer, and / or can be an optically clear adhesive layer. Suitable optically clear adhesives include, but are not limited to, for example, those available from Norland Products Inc. (Cranbury, NJ) in Cranbury, New Jersey. Other suitable adhesives include thermosetting materials, such as those available from Dow Chemical Company (Midland, MI) in Midland, Michigan under the trade name CYCLOTENE. Other suitable adhesives also include heat-activated adhesives, such as those available from KRATON Polymers (Huston, TX) in Houston, Texas under the trade name KRATON. Suitable adhesive layers, including thin adhesive layers (e.g., less than 50 nm thick) are described, for example, in the following U.S. Patents: U.S. Patents 7,521,727 (Khanarian et al.); 7,53,419 (Camras et al.); U.S. Patent 6,709,883 (Yang et al.); and U.S. Patent 6,682,950 (Yang et al.).

[0086] In step G, substantially planar major surface 51 of structured adhesive layer 50 is bonded to major surface 31 of optical core 30, which is configured to propagate image light along the optical core primarily by total internal reflection. In step H, the removable substrate (if present) is removed from temporary carrier 90. In step I, temporary carrier 90 is removed from first major surface 61 of inorganic layer 60.

[0087] In some embodiments, a capping material may be disposed on first major surface 61 of inorganic layer 60 to substantially planarize inorganic layer 60, thereby forming structured capping layer 80 (step J). In some embodiments, structured capping layer 80 may have a major structured surface 81 facing and substantially conforming to first major surface 61 of inorganic layer 60 and an opposite substantially planar major surface 82.

[0088] Figure 4 4 is a side view of an embodiment of an optical system having an optical waveguide featuring at least a first microlayer grating and a second microlayer grating according to the present specification. In some embodiments, optical system 400 includes optical waveguide 305 (including first multilayer grating 40a, second multilayer grating 40b and optical core 30a) and image projector 70a.

[0089] In some embodiments, the optical core 30a of the optical waveguide 305 can be configured to propagate light along the optical core by total internal reflection. In some embodiments, the spaced-apart first multilayer grating 40a and the second multilayer grating 40b are disposed on the optical core 30a. In some embodiments, the first multilayer grating 40a can be configured to receive the image light 20 from the image projector 70a and direct at least a portion 21 of the received image light into the optical core 30a.

[0090] In some embodiments, the induced image light 21 propagates along the optical core primarily by total internal reflection as propagated image light 22. In some embodiments, the second multilayer grating 40b can be configured to receive at least a portion 23 of the propagated image light 22 and extract at least a portion 24 of the received induced image light from the optical core 30a for viewing by the viewer 55.

[0091] In some embodiments, each of the first multilayer grating 40a and the second multilayer grating 40b may include an inorganic relief layer 60a, 60b and a planarized adhesive layer 50a, 50b. In some embodiments, the inorganic relief layers 60a, 60b may include opposite outermost relief major surfaces 61a, 61b, 62a, 62b that are nestedly aligned with each other to extend in a width direction of the inorganic relief layers 60a, 60b (e.g., as shown in FIG. 1 ). Figure 4 for the x-axis shown at 40a, or Figure 5 The inorganic undulating layers 60a, 60b have a wavy shape (i.e., the x' axis shown in FIG. 40b) and form a plurality of substantially parallel ridges 62a, 62b and grooves 63b, 63b. In some embodiments, the ridges 62a, 62b and grooves 63b, 63b are arranged along the orthogonal length directions (e.g., Figure 4 The y-axis or Figure 5 y' axis) extends.

[0092] In some embodiments, the planarizing adhesive layer 50a, 50b may be disposed between the inorganic undulating layers 60a, 60b and the optical core 30a, and may substantially planarize one of the undulating major surfaces 62a, 62b of the inorganic undulating layers 60a, 60b and bond the inorganic undulating layers 60a, 60b to the optical core 30a.

[0093] In some embodiments, for at least one of the first multilayer grating 40a and the second multilayer grating 40b, the multilayer grating may also include a planarization cover layer 80a, 80b, which conformally covers the inorganic undulation layer 60a, 60b opposite to the planarization adhesive layer 50a, 50b and substantially planarizes the inorganic undulation layer 60a, 60b.

[0094] Figure 5 supply Figure 4 Unless otherwise specifically stated, Figure 4 and Figure 5 Like numbered components common to both should be assumed to have similar functions. Figure 4 The description given for the components in the Figure 5 Like numbered parts in the Figure 5 These descriptions are repeated in the description of FIG. 1 . In some embodiments, image light 20 is emitted by image projector 70a and enters optical core 30 via first multilayer grating 40a. This image light propagates as propagating image light 22 (via total internal reflection within optical core 30a) until at least a portion of the light is extracted from optical core 30a via second multilayer grating 40b as extracted image light 24 for viewing by viewer 55. Figure 5 As shown, the orientations of the first multilayer grating 40a and the second multilayer grating 40b (i.e., the width directions of the two gratings) may be different, as required by the application to direct the image light in the appropriate direction. In some embodiments, the ridges and grooves of the first multilayer grating 40a may be aligned with the ridges and grooves of the second multilayer grating 40b. Figure 5 The x direction shown ( Figure 5 The ridges and grooves of the second multilayer grating 40b may be aligned with the left side of the multilayer grating 40a and extend in the x direction. Figure 5 The x' direction ( Figure 5 ) and extends in the x' direction.

[0095] Fig. 6A and Figure 6B Including multi-layer gratings (such as Figure 4 and Figure 5 A side view of the architecture of an embodiment of the multilayer grating 40a, 40b). Fig. 6A and Figure 6B In some embodiments, at least one of the multilayer gratings 40a, 40b may have a plurality of gratings having ... FIG. 6A to FIG. 6B The fluctuation amplitude A of the change in the x direction) m (eg, the distance between the bottom of a groove and the top of an adjacent ridge). In some embodiments, planarization adhesive layers 50a, 50b can define a minimum distance d between inorganic relief layer 60 and optical core 30a. min , so that d minGreater than about 5 nm, or about 10 nm, or about 15 nm, or about 20 nm, or about 25 nm, or about 30 nm, or about 35 nm, or about 40 nm, or about 45 nm, or about 50 nm. In some implementations, for at least one of the first multilayer grating 40 a and the second multilayer grating 40 b, the minimum spacing d between the optical core 30 a and the bottom of the grooves of the multilayer gratings 40 a, 40 b can vary along the width of the multilayer gratings 40 a, 40 b.

[0096] In some embodiments, for at least one of the first multilayer grating 40a and the second multilayer grating 40b, a plane cross section (e.g., FIG. 6A to FIG. 6B ), and for two different locations L1 and L2 on the multilayer grating, each location includes a single ridge and a single directly adjacent groove, where the area between the optical core and the ridge at L1 is A r1 , the area between the optical core and the groove at L1 is A g1 , the area between the optical core and the ridge at L2 is A r2 , and the area between the optical core and the groove at L2 is A g2 , A r1 +A g1 In A r2 +A g2 30% or within A r2 +A g2 30% or within A r2 +A g2 Within 10% of A r2 +A g2 Within 5% or in A r2 +A g2 Within 2%. Figure 7 is a side view of an alternative embodiment of an optical system including an optical waveguide having a first multilayer grating and a second multilayer grating disposed on opposite sides of an optical core. Figure 7 The embodiment shown is similar to that discussed elsewhere herein Figure 4 Therefore, unless otherwise specifically stated, like-numbered components common to both figures should be assumed to have the same function and may not be used in the same manner. Figure 7 The discussion is repeated from Figure 4 The definition of the discussion. Figure 7 In the embodiment of the present invention, the spaced-apart first multilayer grating 40a and the second multilayer grating 40b are disposed on opposite major sides 11a and 11b of the optical core 30a (as shown in FIG. Figure 4 Differently shown on the same main side). Figure 7The basic function of the optical waveguide 305 is essentially the same as Figure 4 The basic functionality of the optical waveguide 305 is the same (i.e., the second multilayer grating 40b extracts a portion of the light 23 and guides the portion of the light as image light 24 for viewing by the viewer 55, but the viewer 55 is now on the main side 11b of the optical waveguide 305, and the image projector 70a is on the side 11a of the optical waveguide 305).

[0097] Figure 8 is a side view of another alternative embodiment of the optical waveguide 305, and is also similar to Figure 4 and Figure 7 If the two devices share common like-numbered components, these common like-numbered components should be assumed to have similar functions unless otherwise specifically stated. Figure 8 In an embodiment of the optical waveguide 305, the optical waveguide 305 further comprises a connecting adhesive portion 110 disposed between the planarizing adhesive layers 50a, 50b of the first multilayer grating 40a and the second multilayer grating 40b and continuously and seamlessly connects the planarizing adhesive layers. In some embodiments, the optical waveguide 305 further comprises a connecting substantially non-relief inorganic layer 111 disposed between the inorganic relief layers 60a, 60b of the first multilayer grating 40a and the second multilayer grating 40b and continuously and seamlessly connects the inorganic relief layers. In some embodiments, wherein each of the first multilayer grating 40a and the second multilayer grating 40b further comprises a planarizing cover layer 80a, 80b that conformally covers and substantially planarizes the inorganic relief layers 60a, 60b opposite the planarizing adhesive layer 50a, 50b, the optical waveguide 305 may further comprise a substantially planarizing connecting cover layer 112 disposed between and continuously and seamlessly connecting the planarizing cover layers 80a, 80b of the first multilayer grating 40a and the second multilayer grating 40b. In some such embodiments, the planarizing cover layer 112, 80a, 80b has a refractive index that is at least 0.5 less than the refractive index of the inorganic relief layers 60a, 60b for at least one visible wavelength within a human visible wavelength range extending from about 420 nm to about 680 nm.

[0098] Fig.9A and Fig. 9B A top view and a side view of another embodiment of an optical waveguide are provided, respectively. Fig.9A and Fig. 9BFor the following discussion. In some embodiments, the optical waveguide 310 may include an optical core 30a configured to propagate image light along it and a continuous seamless multilayer 40s disposed on the major side 11a of the optical core 30a. In some embodiments, the continuous seamless multilayer 40s may include a continuous seamless inorganic layer 60 and a continuous seamless adhesive layer 50.

[0099] In some embodiments, the continuous seamless inorganic layer 60 may be formed in a plurality of discretely spaced apart regions 100a, 100b, 100c ( Fig. 9B ) to form a plurality of spaced-apart undulating inorganic layer portions 60a, 60b, 60c of the otherwise non-undulating inorganic layer 60. In some embodiments, each of the undulating inorganic layer portions 60a, 60b, 60c may include opposite outermost undulating major surfaces 61a, 61b, 61c; 62a, 62b, 62c that are nestedly aligned with one another and form a plurality of substantially parallel ridges 63a, 63b, 63c and grooves 64a, 64b, 64c of the undulating inorganic layer portions 60a, 60b, 60c that extend in a length direction (see, e.g., Fig.9A y-axis, y'-axis and y"-axis) extend and are arranged along the orthogonal width directions (eg, y-axis, y'-axis and y"-axis) of the undulating inorganic layer portions 60a, 60b, 60c.

[0100] In some embodiments, a continuous seamless adhesive layer 50 can be disposed between the inorganic layer 60 and the optical core 30a and can substantially conform to the ridges 63 and grooves 64 of each of the undulating inorganic layer portions 60a, 60b, 60c and bond the inorganic layer 60 to the optical core 30a.

[0101] In some embodiments, the first relief inorganic layer portion 40a can be configured to receive image light 20 from the image projector 70a and to direct at least a portion 21 of the received image light into the optical core 30a. In some embodiments, the directed image light 21 can propagate along the optical core 30a primarily by total internal reflection.

[0102] In some embodiments, the second undulating inorganic layer portion 40c can be configured to receive at least a portion 25 of the directed image light 21 along the first direction 25a and redirect the directed image light as redirected image light 26 that propagates in a different second direction 26a along the optical core 30a primarily by total internal reflection.

[0103] In some embodiments, the third relief inorganic layer portion 40b can be configured to receive at least a portion of the redirected image light 27 and extract at least a portion of the received redirected image light 24 from the optical core 30a for viewing by the viewer 55 .

[0104] Fig. 10A and Fig. 10B Illustrative examples of alternative shapes for features on multilayer gratings are provided. Fig. 10A A multilayer grating 40c is shown disposed on the optical core 30. In some embodiments, the multilayer grating 40c may include an adhesive layer 50 and an inorganic layer 60. In some embodiments, the inorganic layer 60 may define a plurality of alternating first recesses 63 and second recesses 64, wherein the first recesses 63 are recessed toward the optical core 30 and the second recesses 64 are convex toward the optical core 30. Fig. 10A In the embodiment 40c, the first recessed portion 63 and the second recessed portion 64 may have an inclined square wave shape. Fig. 10B In FIG. 4 , the plurality of alternating first recesses 63 and second recesses 64 of the multilayer grating 40 d may have a triangular or “blazed” shape.

[0105] Although the examples discussed herein thus far have shown one-dimensional relief patterns, multilayer gratings exhibiting two-dimensional arrays of features are also within the scope of this specification. Fig.11A An example of a grating 40e is shown which exhibits a two-dimensional array of pillars comparable to ridges 63, and the areas between the pillars are comparable to grooves 64. Similarly, Fig. 11B A grating 40f is shown having a two-dimensional array of holes, wherein each hole is functionally similar to a groove 64 and the area between the holes is comparable to a ridge 63. Fig.11A and Fig. 11B In both, the cross-sections of gratings 40 e and 40 f (disposed on the optical core 30 ) shown in the figures illustrate the same undulating pattern of the inorganic layer 60 and the adhesive layer 50 .

[0106] As discussed elsewhere herein, the ridges and grooves (or first and second recesses) of the multilayer gratings discussed herein may have any suitable shape. Fig. 10A , Fig. 10B , Fig.11A and Fig. 11B The embodiments described are merely examples and are not intended to be limiting in any way.

[0107] at last, Fig.12 is an illustrative example of a possible method for measuring dimensions on a relief layer of a multilayer grating according to the present specification. For example, one method of measuring the thickness of a relief inorganic layer is to make multiple measurements of the distance between the first major surface and the second major surface of the inorganic layer 60, such as Fig.12One way to do this is to randomly select a number of points on the first major surface 61 of the inorganic layer 60 and then draw straight lines to the closest corresponding points on the second major surface 62. The spacing average S is then determined by taking the average of these measurements. avg , and determine the spacing standard deviation S sd .

[0108] Example

[0109] Substrate with separation package

[0110] The substrate with the separation package was prepared by depositing the separation package on ST504 PET film according to the method described in co-pending U.S. patent application No. 63 / 265,650 (Gotrik et al.) filed on December 17, 2021. x The acrylate coating of the first layer of the release package for release was prepared on a roll-to-roll vacuum coater similar to the coater described in U.S. Patent Application No. 2010 / 0316852 (Condo et al.), by adding a second evaporator and curing system between the plasma pretreatment station and the first sputtering system, and using an evaporator as described in U.S. Patent No. 8,658,248 (Anderson et al.).

[0111] The coater was equipped with a substrate in the form of an infinite length roll of 0.05 mm thick, 9 inch (22.86 cm) wide ST504. The substrate was prepared for coating by subjecting it to a nitrogen plasma treatment to improve the adhesion of the planarized acrylate layer to the PET. The film was treated with a nitrogen plasma operating at 50 W using a titanium cathode, using a web speed of 8.0 m / min and keeping the back side of the film in contact with the coating drum cooled to 0°C.

[0112] On the prepared ST504 PET substrate, a planarized acrylate layer of SR833 was formed. The acrylate layer was applied by ultrasonic atomization and flash evaporation to a coating width of 9 inches (22.68 cm). The flow rate of the mixture into the atomizer was 0.67 ml / min, resulting in a layer of 375 nm, the gas flow rate was 60 standard cubic centimeters per minute (SCCM), and the evaporator temperature was 260° C. Once condensed onto the PET substrate, the monomer coating was immediately cured using an electron beam curing gun operating at 7.0 kV and 4.0 mA.

[0113] SiAlO xThe release layer was deposited in-line with the previous acrylate coating step. The silicon aluminum oxide layer was laid down from a SiAl target using an AC reactive sputtering deposition process using a 40kHz alternating current (AC) power supply. During the sputtering process, the voltage of the cathode was controlled by a feedback control loop that monitored the voltage and controlled the oxygen flow so that the voltage would remain constant. The system was operated at a power of 16kW to deposit a 11nm thick silicon aluminum oxide layer onto the planarized organic acrylate layer.

[0114] The transferable acrylate layer (separation package) of SR833 is different from the previous SiAlO x Deposition was in-line. The acrylate layer was applied by ultrasonic atomization and flash evaporation to a coating width of 9 inches (22.68 cm). The flow rate of the mixture into the atomizer was 0.67 ml / min, giving a layer of 375 nm, the gas flow rate was 60 standard cubic centimeters per minute (SCCM), and the evaporator temperature was 260°C. Once condensed onto the SiAlO x Once the monomer coating was applied, the monomer coating was immediately cured using an electron beam curing gun operated at 7.0 kV and 4.0 mA.

[0115] Nanostructured mold film

[0116] The nanostructured mold film was prepared by die coating a photocurable acrylate resin mixture (prepared by combining and mixing PHOTOMER6210, SR238, SR351 and TPO in a weight ratio of 60 / 20 / 20 / 0.5) onto an ST505 film. The coated film was pressed onto a nanostructured nickel surface, which was attached to a steel roll controlled at a speed of 15.2 meters per minute using a rubber-covered roller at 60°C. The nanostructured nickel surface consists of sub-wavelength gratings arranged in a 2D exit pupil expander pattern. The pattern has three grating regions that act as input couplers, exit pupil expanders, and output couplers when attached to an appropriate substrate.

[0117] The coating thickness of the acrylate resin mixture on the film was sufficient to completely wet the nickel surface and form a rolling bead of resin when the coated film was pressed against the nanostructured nickel surface. The film was exposed to radiation from two Fusion UV lamp systems equipped with D bulbs (obtained from Fusion UV Systems, Gaithersburg, MD under the trade designation "F600"), both operating at 142 W / cm, while in contact with the nanostructured nickel surface. After the film was peeled off the nanostructured nickel surface, the nanostructured side of the film was again exposed to radiation from a single Fusion UV lamp system.

[0118] A silicon-containing release film layer assembled according to the methods described in U.S. Pat. Nos. 6,696,157 (David et al.) and 8,664,323 (Iyer et al.) and U.S. Patent Application Publication No. 2013 / 0229378 (Iyer et al.) was applied to the nanostructured mold film in a parallel plate capacitively coupled plasma reactor. The chamber had a surface area of ​​1.7 m 2 (18.3ft 2 )’s central cylindrical powered electrode.

[0119] The nanostructured mold was placed on the powered electrodes and the reaction chamber was pumped down to a base pressure of less than 1.3 Pa (2 mTorr). 2 Gases flowed into the chamber at a rate of 1000 SCCM. The plasma enhanced CVD method was used to couple radio frequency (RF) power into the reactor at a frequency of 13.56 MHz and an applied power of 2000 watts. The treatment time was controlled by moving the nanostructured mold film through the reaction zone at a rate of 9.1 meters per minute (30 ft / min), resulting in an exposure time of about 10 seconds. After the deposition was completed, the RF power was turned off and the gas was exhausted from the reactor.

[0120] After the first treatment, the second plasma treatment is carried out in the same reactor without returning the reaction chamber to atmospheric pressure. HMDSO gas is made to flow into the chamber with about 1750SCCM to achieve a pressure of 9 mTorr. Subsequently, 13.56MHz RF power is coupled to the reactor with an applied power of 1000W. Then the film is transported through the reaction zone at a speed of 9.1 meters per minute (30ft / min), thereby obtaining an exposure time of about 10 seconds. When the treatment time ends, RF power and gas supply are stopped, the chamber is returned to atmospheric pressure, and the nanostructured mold film through the release treatment is removed from the chamber.

[0121] Template substrate

[0122] The substrate with the separation bag was corona treated at an energy density of 1,000 J / cm^2. The acrylate solution was prepared by adding 74 wt% PHOTOMER 6210 with 25 wt% SR238 and 0.014% TPO to produce acrylate resin A. Acrylate resin A was diluted to make a solution of 10 wt% acrylate resin A, 54 wt% PGME and 36% MEK. The diluted solution was slot-die coated onto the corona treated substrate with a separation bag at a rate of 3 m / min. The solution was coated to 10.16 cm wide and pumped at a rate of 3 SCCM using a syringe pump (Harvard Apparatus, Holliston, MA, USA).

[0123] The film was then dried for 3 minutes at ambient conditions before entering the nip. At the nip, the coated substrate with the release pack was laminated to the release treated nanostructured tooling film produced in the previous step.

[0124] The nip consisted of a 90 durometer rubber roll and a steel roll set at 54° C. The nip was joined by two Bimba cylinders (Bimba, University Park, IL) pressurized to 0.55 MPa.

[0125] The applied acrylate solution was cured using a Fusion D bulb (Fusion UV Systems, Gaithersburg, MD), and the cured acrylate mixture was separated from the release treated template film, leaving a cured acrylate coating with a sub-wavelength grating replica on the substrate with the separation package. The web tension was set to about 0.0057 N / m.

[0126] Transfer film

[0127] The exemplary transfer film uses a sputtering coater to coat high refractive index (n~2.4) TiO x The TiO layers were deposited onto the above template substrates. x The target was used with an argon / oxygen gas mixture (about 2% O 2 ) was used to sequentially deposit 15 nm TiO at 0.9 m / min in four passes. x , to produce a nominally 60nm thick TiO x layer (after deposition, x is approximately equal to 2). x The transferable acrylate film of the coating had a thickness of nominally 350 nm - 550 nm.

[0128] Individual patterns were cut from the transfer film roll. A thin layer of FG1901 was applied on the TiO by spin coating at 200 rpm for 5 seconds at a 0.48% solids dilution in cyclohexane / toluene (9.05%:90.95% by weight) followed by spin coating at 4000 rpm for 30 seconds. x surface to obtain a layer of about 45 nm thick.

[0129] waveguide

[0130] The above binder-coated TiO xThe gratings were laminated onto a high-refractive-index glass wafer by placing the paired substrates in a 120 mm CNI nanoimprint tool (NIL Technologies ApS, Lyngby, Denmark) at a temperature of 140°C and a pressure of 6 bar for 5 minutes. Once the laminated pair had cooled to room temperature, the template substrate was pulled away from the surface of the glass wafer, inducing a crack at the separation interface between the carrier substrate and the transfer acrylate. This resulted in the transfer acrylate and TiO x / The grating remains on the glass wafer.

[0131] O was generated by plasma ionization at 500 W and 230 mTorr oxygen pressure on a grounded electrode using a 40 kHz YES G-1000 plasma system (Yield Engineering Systems, Fremont, CA). 2 Plasma etching was continued for 140 min to remove the remaining acrylate template from the TiO x Grating removed.

[0132] The completed waveguide was illuminated with a projector (Venus III 40D, Coretronic Corporation, Hsinchu, Taiwan, China) directed onto the input coupler grating, and the image was observed at the output coupler to confirm that the completed waveguide functioned as an image-preserving waveguide.

[0133] Material

[0134]

[0135]

[0136]

[0137] Terms such as "about" will be understood by one of ordinary skill in the art in the context of use and description in this specification. If it is not clear to one of ordinary skill in the art in the context of use and description in this specification that "about" should be used to express the amount of feature size, quantity, and physical properties, then "about" will be understood to mean within 10% of the specified value. A quantity given as about a specified value may be exactly the specified value. For example, if it is not clear to one of ordinary skill in the art in the context of use and description in this specification, a quantity having a value of about 1 means that the quantity has a value between 0.9 and 1.1, and the value may be 1.

[0138] One of ordinary skill in the art will understand terms such as "substantially" in the context of use and description in this specification. If the use of "substantially equal" in the context of use and description in this specification is unclear to one of ordinary skill in the art, "substantially equal" will refer to approximately the situation of approximately as described above. If the use of "substantially parallel" in the context of use and description in this specification is unclear to one of ordinary skill in the art, "substantially parallel" will refer to within 30 degrees of parallel. In some embodiments, directions or surfaces described as being substantially parallel to each other may be within 20 degrees or within 10 degrees of parallel, or may be parallel or nominally parallel. If the use of "substantially aligned" in the context of use and description in this specification is unclear to one of ordinary skill in the art, "substantially aligned" will refer to alignment within 20% of the width of the object of alignment. In some embodiments, the objects described as being substantially aligned may be aligned within 10% or within 5% of the width of the object of alignment.

[0139] All references, patents, and patent applications cited above are hereby incorporated by reference in their entirety in a consistent manner. In the event of inconsistencies or conflicts between an incorporated reference portion and the present application, the information in the foregoing description shall prevail.

[0140] Unless otherwise indicated, the description of the elements in the drawings should be understood to be equally applicable to the corresponding elements in the other drawings. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that the specific embodiments shown and described may be replaced with a variety of alternative and / or equivalent implementations without departing from the scope of the present disclosure. The present application is intended to cover any modification or variation of the specific embodiments discussed herein. Therefore, the present disclosure is intended to be limited only by the claims and their equivalents.

Claims

1. An optical waveguide, comprising: an optical core configured to propagate an optical mode of a first wavelength along the optical core; and a multilayer grating disposed on the optical core and configured to extract the optical mode that would otherwise propagate along the optical core in a first direction, the multilayer grating comprising: an adhesive layer comprising a major bottom surface facing the optical core and an opposing structured major top surface facing away from and spaced apart from the optical core, the structured major top surface comprising a plurality of substantially parallel linear grating elements extending in a same length direction of the grating elements and arranged in an orthogonal width direction of the grating elements; and An inorganic layer is disposed on and conformed to the structured major top surface of the adhesive layer such that the inorganic layer has a thickness standard deviation that is less than about 50% of an average thickness of the inorganic layer.

2. The optical waveguide of claim 1, wherein the plurality of substantially parallel linear grating elements form a periodic pattern along the width direction of the grating elements.

3. The optical waveguide of claim 1, wherein the periodic pattern has a period in the range of about 100 nm to about 1000 nm.

4. The optical waveguide of claim 1, wherein the optical core has an average thickness between about 100 microns and about 2000 microns.

5. The optical waveguide of claim 1, wherein a minimum spacing between the optical core and the major top surface of the adhesive layer is greater than about 5 nm.

6. The optical waveguide of claim 1, wherein the width direction of the grating element is substantially parallel to the first direction.

7. The optical waveguide according to claim 1, further comprising: A cover layer is disposed on the inorganic layer and substantially planarizes the inorganic layer.

8. The optical waveguide of claim 7, wherein at the first wavelength, the refractive index of the capping layer is at least 0.5 less than the refractive index of the inorganic layer.

9. The optical waveguide according to claim 1, wherein the inorganic layer comprises titanium dioxide (TiO2), zirconium oxide (ZrO x ), titanium oxide (TiOx), SiO2, Al2O3, CeO2, ZnO, Nb2O5, Ta2O5, HfO2, SiAlO x N y , Si3N4, Nb-doped TiO2 and ZrO2, one or more.

10. An optical system comprising: The optical waveguide according to claim 1; At least one light source is configured to introduce light at the first wavelength into the optical core, the introduced light propagating along the optical core in the first direction as the optical mode.

11. An optical waveguide comprising: an optical core configured to propagate image light along the optical core primarily by total internal reflection; a structured adhesive layer comprising a major bottom surface facing and bonded to the optical core and an opposing major structured top surface comprising a plurality of alternating ridges and grooves, the average spacing between the grooves and the optical core being greater than about 5 nm; and An inorganic layer is conformally disposed on the major structured top surface of the structured adhesive layer such that the opposite first major surface and second major surface of the inorganic layer substantially conform to the major structured top surface of the structured adhesive layer and define an average spacing between about 10 nm and about 100 nm.

12. The optical waveguide of claim 11, wherein the optical core has a refractive index greater than about 1.5 at a wavelength of about 580 nm.

13. The optical waveguide of claim 11, wherein the optical core comprises one or more of tantalum, niobium, lanthanum, lead, barium, titanium, zirconium, and bismuth.

14. The optical waveguide of claim 11, wherein the structured adhesive has a refractive index of between about 1.35 and about 2.5 for at least one visible wavelength within a visible wavelength range extending from about 420 nm to about 680 nm.

15. The optical waveguide of claim 11, wherein the structural adhesive has a refractive index of about 1.5 for at least one visible wavelength within a visible wavelength range extending from about 420 nm to about 680 nm.

16. The optical waveguide of claim 11, wherein a minimum spacing between the trench and the optical core is greater than about 5 nm.

17. The optical waveguide of claim 11, wherein the average spacing between the trenches and the optical core is less than about 500 nm.

18. The optical waveguide of claim 11, wherein the inorganic layer has a refractive index greater than about 1.5 at a wavelength of about 580 nm.

19. An optical waveguide comprising: an optical core configured to propagate image light along the optical core primarily by total internal reflection; an inorganic layer disposed on the optical core and defining a plurality of alternating first recessed portions and second recessed portions, wherein the first recessed portions are recessed toward the optical core and the second recessed portions are convex toward the optical core; and a structured adhesive layer disposed between the optical core and the inorganic layer and bonding the optical core to the inorganic layer, the structured adhesive layer substantially filling the first recess, For each pair of adjacent first and second recessed portions, the first recessed portion and the second recessed portion are separated by a common sidewall, the common sidewall extending from a first rounded sidewall corner connecting the common sidewall to the bottom of the second recessed portion to an opposite second rounded sidewall corner connecting the common sidewall to the bottom of the first recessed portion, such that in a first planar cross-section substantially orthogonal to the common sidewall, The first rounded side wall corner includes a first outer circumferential surface facing the optical core and having a first curvature radius R1, and the second rounded side wall corner includes a second outer circumferential surface facing away from the optical core and having a second curvature radius R2, wherein for at least multiple pairs of adjacent first recessed portions and second recessed portions, R1>R2.

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