Plate-shaped waveguide layer for enhanced near-eye display surface relief grating light guide

Abstract

Embodiments of the present disclosure generally relate to augmented reality waveguide assemblies. The waveguide includes: a waveguide substrate having a substrate refractive index (RI) nsub; a plate-shaped waveguide layer disposed over the waveguide substrate, the plate-shaped waveguide layer having a plate-shaped RI nswg and a plate-shaped depth dswg, the plate-shaped depth dswg being from a lower surface of the plate-shaped waveguide layer to an upper surface of the plate-shaped waveguide layer; at least one grating, the at least one grating being defined by a plurality of grating structures, the grating structures being disposed in, on, or above the plate-shaped waveguide layer; and a top plate between and above the grating structures, the top plate having a top plate RI n top plate and an interface with the plate-shaped waveguide layer. The plate-like RI nswg is larger than the substrate RI nsub and the plate-like RI nswg is larger than the top plate RI n top plate.

Description

Technical Field

[0001]

[0013] Embodiments of the present disclosure generally relate to augmented reality waveguide assemblies. Background Art

[0002] Virtual reality is generally considered to be a computer-generated simulated environment in which the user has an apparent physical presence. The virtual reality experience can be generated in 3D and viewed using a head-mounted display (HMD), such as glasses, or other wearable display devices that have near-eye display panels as lenses to display the virtual reality environment in place of the actual environment.

[0003] However, augmented reality enables an experience in which the user can still see the surrounding environment through the display lenses of the glasses or other HMD device, and can also see images of virtual objects that are generated to be displayed and appear as part of the environment. Augmented reality can include any type of input, such as audio and tactile input, as well as virtual images, graphics, and videos of the environment that enhance or augment the user's experience. As an emerging technology, augmented reality faces many challenges and design constraints.

[0004] One such challenge is to display a virtual image superimposed on the surrounding environment. Waveguide assemblies are used to help superimpose images. Generated light is input coupled into the waveguide assembly, propagated through the amplification waveguide assembly, output coupled from the amplification waveguide assembly, and superimposed on the surrounding environment. Surface relief gratings are used to couple light into and out of the amplification waveguide assembly. Therefore, what is needed in the art is a waveguide assembly. Summary of the invention

[0005] In one embodiment, a waveguide is provided. The waveguide comprises: a waveguide substrate having a substrate refractive index (RI) n sub ; a slab waveguide layer, the slab waveguide layer being arranged above the waveguide substrate, the slab waveguide layer having a slab RI n swg and plate depth d swg , the plate depth d swg From the lower surface to the upper surface of the slab waveguide layer; at least one grating, the at least one grating is defined by a plurality of grating structures, the grating structures are arranged in, on or above the slab waveguide layer; and a top plate, the top plate is between and above the grating structures, the top plate having a top plate RIn 顶板 and the interface with the slab waveguide layer. swg Greater than the substrate RI n sub And the plate-like RI n swg Greater than the top plate RIn 顶板 .

[0006] In one embodiment, a waveguide is provided. The waveguide includes: a waveguide substrate having a substrate refractive index (RI) n sub ; a slab waveguide layer disposed above the waveguide substrate, the slab waveguide layer having a slab RI n swg and a slab depth d swg , the slab depth d swg from the lower surface to the upper surface of the slab waveguide layer; at least one grating defined by a plurality of grating structures disposed in, on, or above the slab waveguide layer; a top plate between and above the grating structures, the top plate having a top plate RI n 顶板 and an interface with the slab waveguide layer. The slab RI n swg is greater than the substrate RI n sub and the slab RI n swg is greater than the top plate RI n 顶板 , and the slab depth d swg is: 75 nm to 110 nm when the slab RI n swg at 620 nm is 2.1; 55 nm to 100 nm when the slab RI n swg at 620 nm is 2.2; 35 nm to 85 nm when the slab RI n swg at 620 nm is 2.3; 30 nm to 70 nm when the slab RI n swg at 620 nm is 2.4; 25 nm to 60 nm when the slab RI n swg at 620 nm is 2.5; and 15 nm to 50 nm when the slab RI n swg at 620 nm is 2.6.

[0007] In one embodiment, a waveguide is provided. The waveguide includes: a waveguide substrate having a substrate refractive index (RI) n sub ; a slab waveguide layer disposed above the waveguide substrate, the slab waveguide layer having a slab RI n swg and a slab depth d swg ; a folded grating defined by grating structures disposed in the slab waveguide layer, the slab depth d swg being from the lower surface to the upper surface of the slab waveguide layer between the grating structures; and a top plate between and above the grating structures, the top plate having a top plate RI n 顶板 and an interface with the slab waveguide layer, wherein the slab RI n swg is greater than the substrate RI n sub and the slab RI nswg Greater than the top plate RIn 顶板 。 BRIEF DESCRIPTION OF THE DRAWINGS

[0008] To enable a detailed understanding of the above features of the present disclosure, the present disclosure briefly summarized above may be described more particularly with reference to the embodiments, some of which are illustrated in the drawings. It should be noted, however, that the drawings illustrate only exemplary embodiments and should not be considered as limiting its scope, and other equally effective embodiments may be permitted.

[0009] Figure 1A is a cross-sectional view of a waveguide according to an embodiment.

[0010] Figure 1B is a k-space diagram of a waveguide according to an embodiment.

[0011] Figure 2 is a cross-sectional view of a waveguide according to an embodiment.

[0012] Figure 3 is a graph of the simulated diffraction efficiency of three waveguides.

[0013] Figures 4A to 4C is a cross-sectional view of a waveguide according to different configurations.

[0014] Figures 5A to 5E is a cross-sectional view of a grating according to an embodiment.

[0015] To facilitate understanding, wherever possible, the same reference numerals are used to denote common elements in the drawings. It is contemplated that elements and features of one embodiment may be beneficially incorporated into other embodiments without further recitation. DETAILED DESCRIPTION

[0016] Embodiments of the present disclosure generally relate to augmented reality waveguide assemblies.

[0017] Figure 1A is a cross-sectional view of waveguide 100. Waveguide 100 includes waveguide substrate 101. Input coupler 102, first grating (e.g., folded grating) 104, and second (e.g., output coupler) grating 106 are disposed above waveguide substrate 101. Input coupler 102, first grating 104, and second grating 106 include grating structure 108. Grating structure 108 includes device material 103 disposed above waveguide substrate 101.

[0018] Figure 1BIt is the k-space diagram of waveguide 100. In operation, white light is input-coupled by input coupler 102 and undergoes total-internal-reflection (TIR) through waveguide 100 to the folded grating. Blue channel light (wavelength from about 380 nm to about 495 nm), green channel light (wavelength from about 495 nm to about 590 nm), and red channel light (wavelength from about 590 nm to about 750 nm) propagate under TIR with different attenuation rates. The beams of the optical channels (blue, green, and red channel light) undergo TIR in the folded grating until the beams of the optical channels are coupled to output coupler 106. The beams output-coupled from waveguide 100 by output coupler 106 result in the field of view of the virtual image projected onto the user's eyes. These fields of view include the blue field of view (FOV), the green FOV, and the red FOV.

[0019] Due to the dispersion of the diffraction angle in the propagation inside waveguide 100, the density of interaction with the grating surface is lower for longer wavelengths (red channel light) than for shorter wavelengths (blue channel light). The angular dispersion caused by diffraction is shown by the following diffraction equation:

[0020]

[0021] where θ 0 is the output diffraction angle, θ i is the input angle, λ 0 is the free-space wavelength, Λ is the grating period, n 0 is the refractive index of the output medium, n i is the refractive index of the input medium, and m is the diffraction order (...,-2,-1,0,+1,+2,...). As the wavelength increases, the diffraction angle increases.

[0022] As Figure 1B shown, in the first TIR state 107 and the second TIR state 109, the propagation angular dispersion in TIR among blue channel light, green channel light, and red channel light causes the blue FOV 111, the green FOV 113, and the red FOV 115 to be offset from each other. As the blue channel light propagates to the output coupler 106 farthest from the projector, there is a stronger output coupling of the blue channel light at the corner of the display field of view closest to the projector 105, and the attenuation of the blue light is faster. When the red light propagates, the red channel light attenuates more slowly and thus dominates the image in the part of the field of view farthest from the projector 105. It is desired to minimize the number of substrates required in the near-eye display. However, when multiple display channels (blue, green, red channels) are intended to propagate through the waveguide substrate 101, it is necessary to improve the diffraction efficiency of the multiple display channels.

[0023] Figure 2It is a cross-sectional view of the waveguide 200. Figure 2 The waveguide 200 has a first configuration 401. The waveguide 200 includes a waveguide substrate 201. The waveguide substrate 201 has a substrate refractive index (RI) n sub .

[0024] The waveguide 200 includes at least one grating defined by a plurality of grating structures 208. The waveguide 200 includes an input coupler 202, a first grating (e.g., a folded grating) 204, and a second grating (e.g., an output coupler) 206. The input coupler 202, the first grating 204, and the second grating 206 include the grating structures 208. A slab waveguide layer 210 is disposed above the waveguide substrate 201. In some embodiments, the slab waveguide layer 210 is disposed on the first surface 203 (i.e., the top surface) or the second surface 205 (i.e., the bottom surface) opposite to the first surface 203 of the waveguide substrate 201.

[0025] In the embodiment shown in the first configuration 401, the grating structures 208 are disposed in the slab waveguide layer 210. In the embodiments shown in the third configuration 403 and the fourth configuration 404, the grating structures 208 are disposed above the slab waveguide layer 210 and, in some embodiments, on the slab waveguide layer 210. The grating structures 208 have a grating RI n grat . The grating material 212 of the grating structures 208 results in the grating RI n grat . In the embodiment of the second configuration 402, the grating structures 208 of the input coupler 202 are disposed in the slab waveguide layer 210, and the grating structures 208 of the first grating 204 and the second grating 206 are disposed above the slab waveguide layer 210.

[0026] The slab waveguide layer 210 includes at least one slab depth d swg . The first grating 204 has a first slab depth d swg1 . The second grating 204 has a second slab depth d swg2 . The slab depth d swg corresponds to the first slab depth d swg1 or the second slab depth d swg2 . The slab depth d swg is from the lower surface 209 to the upper surface 211 of the slab waveguide layer 210. The first slab depth d swg1 of the first configuration 401 is from the lower surface 209 to the upper surface 211 between the grating structures 208 of the first grating 204. The second slab depth d swg2 of the first configuration 401 is from the lower surface 209 to the upper surface 211 between the grating structures 208 of the second grating 206. In other embodiments, the first slab depth d swg1is the thickness of the slab waveguide layer 210 below the first grating 204, i.e., the distance from the lower surface 209 to the upper surface 211. The second slab depth d swg2 is the thickness of the slab waveguide layer 210 below the second grating 206. The slab waveguide layer 210 has a slab refractive index (RI) n swg . The top plate 214 corresponds to the area between and above the grating structures 208. In some embodiments, the top plate 214 is air (refractive index of 1.0). In other embodiments, the top plate 214 is a coating 504, as Figure 4C shown. The top plate 214 has a top plate RI n 顶板 . The waveguide 200 has an n greater than n 顶板 and an n greater than n swg and an n greater than n sub and an n greater than n swg .

[0027] The waveguide substrate 201 can be formed of any suitable material, provided that the waveguide substrate 201 can sufficiently transmit light at a selected wavelength or wavelength range and can serve as a suitable support for the waveguide 100 described herein. Substrate selection can include substrates of any suitable material, including but not limited to amorphous dielectrics, non-amorphous dielectrics, crystalline dielectrics, silicon oxide, polymers, and combinations thereof. In some embodiments that can be combined with other embodiments described herein, the waveguide substrate 201 comprises glass, silicon (Si), silicon dioxide (SiO 2 ), germanium (Ge), silicon germanium (SiGe), indium phosphide (InP), gallium arsenide (GaAs), gallium nitride (GaN), fused silica, quartz, sapphire (Al 2 O 3 ), silicon carbide (SiC), lithium niobate (LiNbO 3 ), indium tin oxide (ITO), or combinations thereof. In other embodiments that can be combined with other embodiments described herein, the waveguide substrate 201 comprises high refractive index glass. The high refractive index glass comprises greater than 2 wt% of a lanthanide element (Ln), titanium (Ti), tantalum (Ta), or combinations thereof.

[0028] The slab waveguide layer 210 can comprise one or more of the following: silicon oxycarbide (SiOC), titanium dioxide (TiO 2 ), silicon dioxide (SiO 2 ), vanadium(IV) oxide (VO x ), aluminum oxide (Al 2 O 3 ), aluminum-doped zinc oxide (AZO), indium tin oxide (ITO), tin dioxide (SnO 2 ), zinc oxide (ZnO), tantalum pentoxide (Ta 2 O 5) Silicon nitride (Si 3 N 4 ) Zirconium dioxide (ZrO 2 ) Niobium oxide (Nb 2 O 5 ) Cadmium stannate (Cd 2 SnO 4 ) Titanium silicon oxide (TiSiO x ) or silicon carbonitride (SiCN). The grating material 212 may comprise one or more of the following: SiOC, TiO 2 , SiO 2 , VO x , Al 2 O 3 , AZO, ITO, SnO 2 , ZnO, Ta 2 O 5 , Si 3 N 4 , ZrO 2 , Nb 2 O 5 , Cd 2 SnO 4 , TiSiO x or SiCN. In some embodiments, the slab waveguide material of the slab waveguide layer 210 is the same as the grating material 212, resulting in the same n grat and n swg . In other embodiments, the slab waveguide material of the slab waveguide layer 210 is different from the grating material 212, resulting in different n grat and n swg .

[0029] Blue, green, and red channel light will propagate in both the waveguide substrate 201 and the slab waveguide layer 210 and will still experience resonance conditions because the light can be reflected from the top plate and substrate interface. The top plate RI n 顶板 , the slab refractive index RIn swg and the slab depth d swg , such as a first slab depth d swg1 and a second slab depth d swg2 , must be selected to reduce the diffraction efficiency ratio of blue channel light to red channel light.

[0030] When the following conditions are met, the resonance conditions for the substrate mode in the waveguide 200 will occur:

[0031] 2n swg k 0 cos(θ)d + φ sub + φ grating = 2πm

[0032] where n swg is the refractive index RI of the plate, n swg , k 0 is the wave number of light (2π / λ 0 ), d is the depth d of the plate, swg , θ is the propagation angle of light in the plate waveguide layer, φ sub is the phase accumulated upon reflection at the plate waveguide - substrate interface 213, and φ 光栅 is the phase accumulated upon reflection at the plate waveguide - top plate interface 213. The phases φ sub and φ 光栅 can be calculated using the Fresnel equations.

[0033] The change Δd in the plate depth d between the resonance peaks swg is determined by solving the above resonance condition according to the following formula:

[0034]

[0035] Δd depends on the wavelength (λ 0 ) and the propagation angle (θ). λ 0 corresponds to the wavelengths of blue channel light (wavelength from about 380 nm to about 495 nm), green channel light (wavelength from about 495 nm to about 590 nm), and red channel light (wavelength from about 590 nm to about 750 nm).

[0036] The diffraction efficiency of the waveguide 200 is modeled by optical simulation. The optical simulation includes rigorous coupled - wave analysis (RCWA), finite - difference time - domain (FDTD) method, finite element method (FEM), other simulation methods, and combinations thereof. The optimal refractive index RI n swg of the plate and the plate depth d swg are selected through modeling.

[0037] Figure 3 is a graph of the simulated diffraction efficiency of three waveguides. The simulated waveguide 100 does not include the plate waveguide layer 210. The diffraction efficiency ratio is the ratio of the minimum diffraction efficiency of blue channel light to the maximum diffraction efficiency of red channel light. The modeled waveguide 100 described herein has a diffraction efficiency DE 1 of 4.5:1.0 (the minimum diffraction efficiency of blue channel light is 18% compared to the maximum diffraction efficiency of red channel light of 4%). Wave 301A is the first model for the waveguide 200 at a wavelength λ 0Diffraction efficiency of the lower blue channel light. Wave 301B is the first model for waveguide 200 at a wavelength λ of 520 nm 0 Diffraction efficiency of the lower green channel light. Wave 301C is the first model for waveguide 200 at a wavelength λ of 620 nm 0 Diffraction efficiency of the lower red channel light. The first model of waveguide 200 has an n sub waveguide substrate 201 with an n of 2.0 and an n at 450 nm swg of 2.45, an n at 520 nm swg of 2.37, and an n at 620 nm swg of 2.31 for the amorphous TiO x plate - like waveguide layer 210. The first model of waveguide 200 has a diffraction efficiency DE at 50 nm 2 of 1.8:1.0. To improve the diffraction efficiency ratio, the second modeling of waveguide 200 is carried out.

[0038] Wave 302A is the second model for waveguide 200 at a wavelength λ of 450 nm 0 Diffraction efficiency of the lower blue channel light. Wave 302B is the first model for waveguide 200 at a wavelength λ of 520 nm 0 Diffraction efficiency of the lower green channel light. Wave 302C is the third model for waveguide 200 at a wavelength λ of 620 nm 0 Diffraction efficiency of the lower red channel light. The second model of waveguide 200 has an n sub waveguide substrate 201 with an n of 2.0 and an n at 450 nm swg of 2.73, an n at 520 nm swg of 2.61, and an n at 620 nm swg of 2.53 for the crystalline TiO x plate - like waveguide layer 210. The average n swg is 2.62. The second model of waveguide 200 has a diffraction efficiency DE at 35 nm 3 of 1.1:1.0. Thus, the second model of waveguide 200 includes an n of 2.0 sub , an average n of 2.62 swg and a plate - like depth d of 35 nm swg .

[0039] In some embodiments, the substrate RI n of the waveguide substrate at 620 nm sub is from 1.8 to 2.10. In other embodiments, the substrate RI n of the waveguide substrate at 620 nm sub is greater than 2.77. Table 1 shows based on a substrate RI n of 2.0 suband the corresponding slab RI n at 620 nm swg of the slab depth d swg for the optimal range.

[0040] <![CDATA[Plate-like RI n at 620 nm swg > <![CDATA[Optimal range of the plate-like depth d swg > 2.1 75nm - 110nm 2.2 55nm - 100nm 2.3 35nm - 85nm 2.4 30nm - 70nm 2.5 25nm - 60nm 2.6 15nm - 50nm

[0041] Table 1

[0042] Figures 4A to 4C is a cross-sectional view of the waveguide 200 according to different configurations. In the second configuration 402 as shown in Figure 4A , the grating structure 208 of the input coupler 202 is disposed in the slab waveguide layer 210, and the grating structures 208 of the first grating 204 and the second grating 206 are disposed above the slab waveguide layer 210. The grating material 212 of the grating structure 208 above the slab waveguide layer 210 has a grating RI n grat . In some embodiments, the slab waveguide layer 210 is the same as the grating material 212, resulting in the same n grat and n swg . In other embodiments, the slab waveguide layer 210 is different from the grating material 212, resulting in different n grat and n swg . The third configuration 403 as shown in Figure 4B and the fourth configuration 404 as shown in Figure 3 C include a grating structure 208 disposed above the slab waveguide layer 210 and, in some embodiments, disposed on the slab waveguide layer. The fourth configuration 404 of the waveguide 200 includes a second slab waveguide layer 410. The slab waveguide layer 210 and the second slab waveguide layer 410 are disposed on opposite sides of the waveguide substrate 201. The second slab waveguide layer 410 includes at least a third grating 407 disposed thereon. In some embodiments, a fourth grating 409 is disposed above the second slab waveguide layer 410.

[0043] Figures 5A to 5E is a cross-sectional view of the grating 500. The grating 500 may correspond to at least one of the input coupler 202, the first grating 204, or the second grating 206 of the waveguide 200. As shown in Figure 5A , the grating structure 208 is a blazed grating structure. As shown in Figure 5B , the grating structure 208 has sidewalls 502 that are parallel to each other and angled with respect to the first surface 203 of the waveguide substrate 201. As shown in Figure 5C , the grating structure 208 has sidewalls 502 that are parallel to each other and perpendicular to the first surface 203 of the waveguide substrate 201. The top plate 214 is a coating 504. As shown in Figure 5D , the grating structure 208 includes a first layer 506 of a first material and a second layer 508 of a second material. As shown in Figure 5E , the grating structure 208 has a two-dimensional periodicity.

[0044] Although the foregoing is directed to examples of the present disclosure, other and further examples of the present disclosure may be devised without departing from the basic scope thereof, and the scope of the present disclosure is determined by the appended claims.

Claims

1. A waveguide, the waveguide comprises: A waveguide substrate having a substrate refractive index (RI) n sub ; A plate-shaped waveguide layer, the plate-shaped waveguide layer is disposed above the waveguide substrate, and the plate-shaped waveguide layer has a plate-shaped RIn swg and a plate-shaped depth d swg , the plate-shaped depth d swg ranging from the lower surface to the upper surface of the plate-shaped waveguide layer; at least one grating, the at least one grating being defined by a plurality of grating structures, the grating structures being disposed in, on or above the plate-like waveguide layer; and A top plate, the top plate being between and above the grating structures, the top plate having a top plate RI n 顶板 and an interface with the slab waveguide layer, wherein the slab RI n swg is greater than the substrate RI n sub and the slab RI n swg is greater than the top plate RI n 顶板 .

2. The waveguide according to claim 1, wherein the plate-like waveguide layer is disposed on the waveguide substrate.

3. The waveguide according to claim 1, wherein the grating structure comprises a grating material different from the plate-like waveguide of the plate-like waveguide layer.

4. The waveguide according to claim 1, wherein the grating is an input coupler, a folded grating, or an output coupler.

5. The waveguide according to claim 1, wherein the plate-like depth d swg is from the lower surface to the upper surface of the plate-like waveguide layer between the grating structures provided in the plate-like waveguide layer.

6. The waveguide according to claim 1, wherein the waveguide substrate comprises glass, silicon (Si), silicon dioxide (SiO 2 ), germanium (Ge), silicon germanium (SiGe), indium phosphide (InP), gallium arsenide (GaAs), gallium nitride (GaN), fused silica, quartz, sapphire (Al 2 O 3 ), silicon carbide (SiC), lithium niobate (LiNbO 3 ), indium tin oxide (ITO), or a combination thereof.

7. The waveguide according to claim 1, wherein the plate-shaped waveguide layer comprises one or more of the following: silicon oxycarbide (SiOC), titanium dioxide (TiO 2 ), silicon dioxide (SiO 2 ), vanadium(IV) oxide (VO x ), aluminum oxide (Al 2 O 3 ), aluminum-doped zinc oxide (AZO), indium tin oxide (ITO), tin dioxide (SnO 2 ), zinc oxide (ZnO), tantalum pentoxide (Ta 2 O 5 ), silicon nitride (Si 3 N 4 ), zirconium dioxide (ZrO 2 ), niobium oxide (Nb 2 O 5 ), cadmium stannate (Cd 2 SnO 4 ), titanium silicon oxide (TiSiO x ) or silicon carbonitride (SiCN) materials.

8. The waveguide according to claim 1, wherein the substrate RI n at 620 nm sub is from 1.8 to 2.

10.

9. The waveguide according to claim 1, wherein the substrate RI n at 620 nm sub is greater than 2.

77.

10. The waveguide according to claim 1, wherein the plate-like RI n at 620 nm swg is from 1.8 to 2.

6.

11. The waveguide according to claim 1, wherein the plate-like depth d swg : When the plate-like RI n at 620 nm swg is 2.1, it is 75 nm to 110 nm; When the plate-like RI n at 620 nm swg is 2.2, it is 55 nm to 100 nm; When the plate-like RI n at 620 nm swg is 2.3, it is from 35 nm to 85 nm; When the plate-like RI n at 620 nm swg is 2.4, it is 30 nm to 70 nm; When the plate-like RI n at 620 nm swg is 2.5, it is from 25 nm to 60 nm; and When the plate-like RI n at 620 nm swg is 2.6, it is 15 nm to 50 nm.

12. The waveguide according to claim 1, wherein the diffraction efficiency ratio of the blue channel light of the waveguide to the diffraction efficiency of the red channel light is 1.1:1.

0.

13. The waveguide according to claim 1, wherein the grating structure is a blazed grating structure.

14. The waveguide according to claim 1, wherein the grating structure has sidewalls that are parallel to each other and angled with respect to the waveguide substrate.

15. The waveguide according to claim 1, wherein the grating structure has two-dimensional periodicity.

16. The waveguide according to claim 1, wherein the top plate is a coating.

17. The waveguide according to claim 1, wherein the waveguide has 2n swg k 0 cos(θ)d + φ sub + φ grating = the resonance condition of 2πm Wherein, k 0 is the wave number of light (2π / λ 0 ), d is the plate depth d swg , θ is the propagation angle of light in the plate waveguide layer, φ sub is the phase accumulated upon reflection at the interface, and φ 光栅 is the phase accumulated upon reflection at the interface.

18. The waveguide according to claim 17, wherein a change Δd in a plate depth d between resonance peaks swg is determined by solving the following equation: where λ 0 corresponds to the wavelength of blue channel light, green channel light, or red channel light.

19. A waveguide, the waveguide comprises: Waveguide substrate having a substrate refractive index (RI) n sub ; A plate-shaped waveguide layer, the plate-shaped waveguide layer is disposed above the waveguide substrate, and the plate-shaped waveguide layer has a plate-shaped RIn swg and a plate-shaped depth d swg , the plate-shaped depth d swg ranging from the lower surface to the upper surface of the plate-shaped waveguide layer; At least one grating, the at least one grating being defined by a plurality of grating structures disposed in, on, or above the slab waveguide layer; a top plate, the top plate being between and above the grating structures, the top plate having a top plate RI n 顶板 and an interface with the slab waveguide layer, wherein the slab RI n swg is greater than the substrate RI n sub and the slab RIn swg is greater than the top plate RI n 顶板 , and the slab depth d swg : When the plate-like RI n at 620 nm swg is 2.1, it is 75 nm to 110 nm; When the plate-like RI n at 620 nm swg is 2.2, it is 55 nm to 100 nm; When the plate-like RI n at 620 nm swg is 2.3, it is from 35 nm to 85 nm; When the plate-like RI n at 620 nm swg is 2.4, it is 30 nm to 70 nm; When the plate-like RI n at 620 nm swg is 2.5, it is from 25 nm to 60 nm; and When the plate-like Rl n at 620 nm swg is 2.6, it is from 15 nm to 50 nm.

20. A waveguide, the waveguide comprises: Waveguide substrate having a substrate refractive index (RI) n sub ; A plate-shaped waveguide layer, the plate-shaped waveguide layer is disposed above the waveguide substrate, and the plate-shaped waveguide layer has a plate-shaped RIn swg and a plate-shaped depth d swg ; A folded grating, the folded grating being defined by a grating structure provided in the plate-like waveguide layer, the plate-like depth d swg is from the lower surface to the upper surface of the plate-like waveguide layer between the grating structures; and The top plate, which is between and above the grating structures, and the top plate has a top plate RI n 顶板 and an interface with the slab waveguide layer, where the slab RI n swg is greater than the substrate RI n sub and the slab RI n swg is greater than the top plate RI n 顶板 .

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