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Abstract
We proposed a single-layer color echelle grating combined optical waveguide structure for an augmented-reality display. In this structure, we used echelle gratings with super-wavelength periodic scale as in-coupling, relay, and out-coupling elements. The combined propagation of three light beams in the waveguide was realized by overlapping different high diffraction orders of the RGB three primary colors, and deflection of the beam direction between gratings was achieved by conical diffraction generated by the inclined grating. Using the vector diffraction theory, the structural parameters and tolerance ranges of the three types of gratings were optimized, rendering average diffraction efficiencies of the three primary colors of the in-coupling, relay, and out-coupling gratings greater than 74%, 21%, and 35%, respectively. As a result, we obtained dual-channel one-dimensional pupil dilation of the original image and a field-of-view angle of h18.9° × v36.87°.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Lightweight and small-sized augmented reality (AR) glasses have been a longtime significant goal pursued by developers. Considering the rapid development of the semiconductor industry, the processors and sensors of AR glasses have become highly integrated; hence, a lightweight optical waveguide constitutes the top priority. AR displays can be divided into two types: geometric and diffractive optical waveguides. A geometric optical waveguide mainly offers two solutions: mirror array and free-form prism. Lumus, an Israeli company, has committed to the optimization and iteration of a reflector-array optical waveguide. A geometric optical waveguide does not involve a micro-nanostructure and has the advantages of non-dispersion and high color uniformity. By plating different thicknesses of semitransparent and semi-reflective films on the mirror array, pupil expansion and uniform output brightness can be realized. However, given that each mirror surface needs to be glued with more than ten film layers, making the process cumbersome, even if each step of the production can realize a high yield, it is difficult to ensure the overall yield. Common problems include black stripes on the background, uneven brightness, and ghost images [1,2]. Free-form prisms can correct aberrations by combining lens groups with one or more free surfaces to achieve fair imaging quality, large field of view (FOV), and high efficiency. Researchers are also optimizing the system towards miniaturization, enabling a better compromise between size and image quality [3–6].
Diffraction optical waveguides have become the mainstream solution, mainly classified into volume holographic and surface relief grating (SRG) optical waveguides. Features of a volume holographic optical waveguide include low production cost and easy production [7,8], as represented by products from Diglens, Sony, and Nanchang Tripole Optoelectronics. However, its performance is limited by the materials, and the wavelength and angle selectivity are not conducive to a single-layer color display. In addition, due to the lack of surface relief structure, it cannot be used for mass production by embossing replication. The SRG structure has outstanding flexibility in design and processing and greater advantage in angular bandwidth, especially in mass production using nanoimprinting technology. Therefore, most AR research and development companies, such as Microsoft, Vuzix, and Magic Leap, are committed to the research and development of SRG optical waveguides. For SRGs [9], monochromatic waveguides can be easily realized, the coupling efficiency of elements can reach 0.7 [10,11], and the diagonal FOV can surpass 70° [12–16]. However, the color display is made possible by stacking triple- or double-layer waveguides [9,17,18,19]. Each grating layer only works at a specific wavelength; the diffraction bandwidths of red and blue light are increased by designing the structure of the diffraction element, and the transmission of green light is also facilitated, making a double-layer waveguide structure possible, such as those of Vuzix Blade and HoloLens2. However, the problem is that the diffraction efficiency of green light will be lower than those of the other two light colors. Moreover, the total thickness and volume of multilayer waveguides are larger than those of single-layer waveguides. For example, the double-layer structure from HoloLens2 weighs more than 566 g [20], and the weight of the three-layer waveguide structure from Magic Leap One is 316 g [21]. In addition, the increase in the number of waveguide layers significantly reduces the transmittance of ambient light, resulting in greater light energy loss of the source and more internal friction. Usually, multiple waveguides can lead to a coupling efficiency of less than 1% [22]. Katana, affiliated with Wave Optics, has achieved single-layer color using a two-dimensional grating structure, with a diagonal FOV of 28–30°. It holds 15, 74, and 26 nm diffraction bandwidths for the RGB tricolor with a thickness of 1.15 mm and a weight of only 7 g [23], making it the thinnest product in the industry. metasurface grating is a novel and effective solution. The ultra-fine structure can achieve super-strong control of RGB tricolor light [24,25,26,27]. Lee et al. [26] achieved full-color display by designing a series of nanorod arrays with different orientations on a single lens and a high FOV of 90°, but the volume of the optical path was too large to adapt to the human structure. Jiasheng Xiao et al. [28] designed a meta-grating composed of multiple sub-gratings, which could perform achromatic processing on RGB colors and had a single grating coupling efficiency of 0.47. Diyang Gu et al. [27] used the super surface grating as a coupling and decoupling element to achieve the color display of a single-layer waveguide. The overall coupling efficiency is between 0.1 and 0.2, significantly higher than that of a traditional multi-layer waveguide. However, they failed to consider the pupil expansion problem and address the complex processing and sensitivity to manufacturing tolerances. Zeyang Liu et al. [29] proposed using a blazed grating to couple color light in single-layer waveguide, with a coupling efficiency of 0.78 to 0.86, and using a rectangular grating to couple out, but the efficiency is less than 0.14. Similarly, pupil expansion was not considered, and implementing an optical waveguide with an inclination of 30° was challenging.
In summary, single-layer waveguide color display through a traditional SRG structure is the main development trend of AR glasses. This study focused on the structural design of a single-layer color optical waveguide and proposed to achieve color display of single-layer waveguides using the designed echelle gratings. All gratings used were echelle gratings with super wavelength spacing [30,31,32,33]. Previously, echelle gratings have mostly been used in dispersion spectrometers [34]. Their production process is mature, and the combination of nanoimprinting technology will be beneficial to the realization of batch and industrialization. For the first time, we proposed to use echelle gratings to achieve a single-layer color AR optical waveguide with high diffraction efficiency and color uniformity. In addition, a pupil expansion scheme similar to that of HoloLens2 [35] was adopted to segment and transmit the original image using dual channels, providing a favorable initial structure for improving the angle of view and offering the possibility for further performance optimization [36,37].
2. Overall layout and structure of waveguide
Figure 1 shows a schematic of the designed optical waveguide structure, mainly comprising the waveguide and grating group. The grating group included the in-coupling, relay, and out-coupling gratings. The in-coupling and relay gratings were reflective, whereas the out-coupling grating was transmissive. The three RGB beams were diffracted three times through the in-coupling, relay, and out-coupling gratings. Specifically, the color image source from the microdisplay was collimated by the lens and incident vertically onto the in-coupling grating, where the first diffraction occurred and was transmitted by total reflection in the waveguide before entering the relay gratings distributed diagonally downward to the left and right. After the second diffraction and total reflection, the beam entered the out-coupling grating. After the third diffraction, it left the waveguide and entered the human eye. A beam combining diffraction and transmission of the three primary colors was achieved by using the high diffraction orders of the three echelle gratings and overlapping the corresponding diffraction angles of the orders.
Figures 2 and 3 show the front and side views of the optical waveguide display designed for AR; the orientation and layout of each grating groove are given in the front view. The in-coupling grating comprised two symmetrical modules on the left and right. After the incident light was diffracted by the in-coupling grating, the light deviated from the x-axis by 30°. The transmission angle of RGB tricolor light in the waveguide was designed to be greater than the total reflection angle corresponding to the glass substrate material to ensure that the light beam was effectively bound in the waveguide without leakage. The images projected by the microdisplay often need to be expanded to be better observed by the human eye. Therefore, we designed four relay gratings. Two relay gratings with different structures were seamlessly connected to form a large relay area, and large symmetrical relay areas were added on the left and right sides. When the beam reached the first relay grating, the grating deflected the beam to the out-coupling grating by 120°, while the remaining beam maintained the original path and continued to transmit forward until it reached the second relay grating. The second relay grating deflected all the beams by 120° to the out-coupling grating, expanding the light twice. Similarly, the out-coupling grating also comprised two symmetrical gratings, which vertically coupled the light from the relay grating out of the waveguide and into a complete image for the human eye. After one-dimensional expansion, the size of the exit pupil was doubled. To conform to the ergonomic characteristics, the incident and outgoing light were separated on opposite sides of the waveguide. In addition, to make the AR optical waveguide system suitable for headwear as lightweight as ordinary glasses, the waveguide thickness was set to 2.5 mm.
3. Coupling element design and calculation of diffraction efficiency
3.1 Coupling grating design and optimization
As the in-coupling, relay, and out-coupling gratings are structurally symmetric in this paper, we designed, optimized, and illustrated only the right channel grating. The grating structure of the left channel was symmetric to that of the right one about the y-axis, as shown in Fig. 2. The coupling gratings were the core components of the entire system. Before designing the specific structure of the gratings, it was necessary to derive some of their basic parameters. A glass substrate with refractive index ng = 1.85 was selected as the transmission medium. For cases in which the beam is vertically incident on the grating, we have
where m is the diffraction order of the corresponding wavelength λ, d is the grating period, and θd is the diffraction angle. When the beam propagates in the waveguide, it also needs to meet the total reflection conditions, and the diffraction angle should beHere, we designed a diffraction angle, θd = 35°, greater than the minimum total reflection angle, θTIR = 32.5°. The waveguide thickness H = 2.5 mm, and the distance D of the primary total reflection of the light ray is
To avoid the reverse coupling of light, the widths of the coupled gratings should be less than D (3.5 mm), so the grating width was set to 3 mm. For RGB tricolor, the following grating equations apply:
The RGB wavelengths were set as λR = 740 nm, λG = 555 nm, and λB = 444 nm. The corresponding diffraction orders were mR = −3, mG = −4, and mB = −5, respectively, and the grating period d = 2.09 µm, i.e., 2–5 times the wavelength.
The ability of the blazed grating to concentrate light energy to a higher diffraction order has been well utilized in the design of the coupling element for our optical waveguide displays. As shown in Fig. 4, the in-coupling grating we designed was a reflection-blazed grating with a right-triangle side section. The lower surface was coated with a 120 nm thick Ag film. The structure was designed to effectively shine the light energy of RGB tricolor light with an incidence angle of 0° to high diffraction orders of mR = −3, mG = −4, and mB = −5. These orders correspond to the same diffraction angle θd. We used this diffraction angle for image transmission. To avoid stray light and dispersion, light at other diffraction orders not used for imaging was suppressed. For the case of vertical incidence to the reflection blazed grating, the blaze angle of the grating α and diffraction angle θd are related as follows [38]:
The diffracted light was effectively focused on θd. Therefore, the blaze angle of the grating was set to 17.5°. Theoretically, it is intuitive that when the duty cycle of the reflective grating is 1, the reflectivity is the highest and the most effective light energy can be used. Thus, we only considered the structure with a duty cycle of 1. To verify the structural performance of the in-coupling grating, we modeled it and calculated the RGB tricolor transmission efficiency of the grating under different structures. Specifically, we used DELTA software [39] to scan the in-coupling grating with the blaze angle α in the range of 15° to 20° and the grating groove depth h in the range of 0.5 to 1 µm. We then computed the diffraction efficiency of RGB tricolor light for different structures at diffraction orders of mR = −3, mG = −4, and mB = −5. The results are shown in Fig. 5. The diffraction efficiency obtained given the theoretical structure mentioned above (blaze angle = 17.5°, groove depth = 660 nm) was ηR = 0.80, ηG = 0.76, and ηB = 0.74. In addition, within the range of α from 17° to 18° and h from 0.65 to 1 µm, RGB tricolor light had a diffraction efficiency greater than 0.6 and a large range of manufacturing tolerance.
Fig. 4. Diagrams (a), (b), (c) show the distribution of the diffracted light at all orders after RGB
Tricolor light is diffracted by the in-coupling grating, where the diffraction angle θd = 35°. The grating structure and geometric parameters are as follows: w is the grating width, h is the groove depth, and α is the blaze angle of the grating.
Fig. 5. Diffraction efficiency of RGB trichromatic light at different diffraction orders (mR = −3, mG = −4, mB = −5) with in-coupling gratings of various flare angles α and groove depths h.
To better reflect the blaze ability of the in-coupling grating, we recorded the diffraction efficiency of RGB tricolor at lower diffraction orders such as m = 0, m = −1, m = −2, etc. (Table 1). We then used the diffraction angle θd and azimuth φ to represent the direction of the diffracted light. As shown in Fig. 4, θd is the angle between the diffracted ray and the normal of the grating, and φ is the angle between the projection of the diffracted ray on the plane $x^{\prime}oy^{\prime}$ and the positive direction of the x’-axis, both of which are 180° here.
Table 1. Spatial Distribution and Diffraction Efficiency of Diffraction Light of Different Orders of RGB Tricolor after the In-coupling Grating
In addition, the bandwidth to which the coupling grating could respond to adapt or match different light sources was a major concern. As shown in Fig. 6, we analyzed the diffraction efficiency of the in-coupling grating on all visible light wavelengths at the diffraction orders of m = −3, m = −4, and m = −5. At the diffraction order m = −3, red light corresponded to a 130 nm bandwidth with a diffraction efficiency greater than 0.6, while green light and blue light were effectively suppressed at this diffraction order. Similarly, at the diffraction order of m = −4, green light had a corresponding 77 nm bandwidth with a diffraction efficiency of more than 0.6, while red and blue light were effectively suppressed at this order. Blue light had a 44 nm bandwidth at the diffraction order of m = −5 with a diffraction efficiency of more than 0.6. The diffraction efficiency of red and green lights at this order was close to zero. Thus, the designed coupled grating provides high diffraction efficiency for RGB tricolor light and features a wide blaze bandwidth.
Fig. 6. Diffraction efficiency distribution curve of visible light wavelengths at diffraction orders m = −3, m = −4, m = −5.
3.2 Relay grating design and optimization
As the entrance pupil needs to be doubled, two relay gratings are required. As shown in Fig. 7(a), (b), and (c), the two relay gratings designed are rectangular reflection gratings. The diffracted light requirements of relay grating 1 were mainly focused on the two corresponding diffraction orders of extension light and deflection light. The corresponding diffraction order of extension light of RGB tricolor light was m = 0, and the corresponding diffraction orders of deflection light were m = 3 for red light, m = 4 for green light, and m = 5 for blue light. However, relay grating 2 requires that the diffracted light mainly focuses on the diffracted order corresponding to the deflected light, while the extended order is not required. When the light from the in-coupling grating was at the angle of incidence θin = 35°, azimuth φ = 30° incident to the relay grating, the i angle between the deflected light and the projection of the extended light on the grating plane $x^{\prime}oy^{\prime}$ was 120°, i.e., the relay grating can deflect the original light by 120°. To meet this requirement, the grating vectors of the in-coupling, relay, and out-coupling gratings need to satisfy certain physical relationships.
Fig. 7. (a), (b), (c) Diffraction light distribution, structure, and geometric parameters of the relay grating of RGB tricolor light at each diffraction order when it arrives at the relay grating after exiting from the in-coupling grating, where w is the grating width and h is the groove depth.
Figure 8 is a schematic of each grating vector. The grating vector represents the orientation of the grating. As shown in Fig. 8(a), $\overrightarrow {\textrm{k}_\textrm{1} } \textrm{,}\overrightarrow {\textrm{k}_\textrm{2} } \textrm{,}\overrightarrow {\textrm{k}_\textrm{3} } $ represent the in-coupling, relay, and out-coupling grating vectors of the left channel, respectively. The angle between $\overrightarrow {\textrm{k}_\textrm{1} }$ and $\overrightarrow {\textrm{k}_\textrm{2} }$ is β = 30°, and the angle between $\overrightarrow {\textrm{k}_\textrm{1} }$ and $\overrightarrow {\textrm{k}_\textrm{3} }$ is ${\gamma }^{\prime} = 120^\circ$. In Fig. 8(b), $\overrightarrow {{\textrm{k}_\textrm{1} }^{\prime} } ,\overrightarrow {{\textrm{k}_\textrm{2} }^{\prime} } ,\overrightarrow {{\textrm{k}_\textrm{3} }^{\prime} }$ represent the in-coupling, relay, and out-coupling grating vectors of the right channel, respectively. The angle between $\overrightarrow {{\textrm{k}_\textrm{1} }^{\prime} }$ and $\overrightarrow {{\textrm{k}_\textrm{2} }^{\prime} }$ is ${\beta }^{{\prime}} = 30^\circ$, and the angle between $\overrightarrow {{\textrm{k}_\textrm{1} }^{\prime} }$ and $\overrightarrow {\mathop {\textrm{k}_\textrm{3} }\nolimits^{\prime} }$ is ${\gamma }^{\prime} = 120^\circ$. In addition, the grating period of the relay grating is determined by the angle β between $\overrightarrow {\textrm{k}_\textrm{1} }$ and $\overrightarrow {\textrm{k}_\textrm{2} }$ and the grating period of the in-coupling grating $\mathop d\nolimits_{\textrm{in}}$.
Here, drelay = 1.2 µm.
Fig. 8. (a) Schematic of the grating vectors of the left channel, and (b) schematic of the grating vectors of the right channel.
To optimize the structure of the relay grating, we also calculated, with a grating period of 1.2 µm, its diffraction efficiencies in the directions of light deflection η1 and light propagation η2 at different groove depths h (0.5 to 5 µm) and different widths w (0.24 to 1.9 µm). The results are shown in Fig. 9, where (a), (b), and (c) present the distribution of the diffraction efficiency of RGB tricolor in the direction of light deflection under different structures, η1; (d), (e), and (f) exhibit the distribution of the diffraction efficiency of RGB tricolor in the direction of light extension under different structures, η2. To maintain the uniformity of image brightness after expansion as much as possible, for relay grating 1, it is not necessary to have an excessively high diffraction efficiency in the direction of light deflection, which is approximately 0.2–0.3. More light is required to be distributed in the direction of light expansion. For relay grating 2, it is necessary to have high diffraction efficiency of deflection, as the total efficiency of the deflected beam provided is the product of the extended diffraction efficiency of relay grating 1 and the deflected diffraction efficiency of relay grating 2.
Fig. 9. Diagrams (a), (b), and (c) show the diffraction efficiency distribution of RGB tricolor light of the relay grating in the direction of light deflection at different groove depths and widths, respectively; (d), (e), and (f) are the diffraction efficiency distribution diagrams of RGB tricolor light of the relay grating in the direction of light propagation at different slot depths and widths, respectively.
The structures of relay gratings 1 and 2 that met our requirements were selected from the above structures. The specific parameters are listed in Table 2. The diffraction efficiencies of the grating in the deflected and extended lights are also presented in Table 3. The total diffraction efficiency provided by the two relay gratings to the coupled gratings η was calculated as indicated in the table. The total diffraction efficiencies of RGB tricolor light ranged between 0.2 and 0.3. The differences in this diffraction efficiency were no more than 0.07; thus, a light spot with uniform brightness can be provided for the coupled grating. In addition, we listed the spatial distribution and diffraction efficiency of RGB tricolor light at all orders after passing through the relay grating.
Table 2. Structural Parameters of Relay Gratings 1 and 2 and Different Diffraction Efficiencies of RGB Tricolor Light
Table 3. Spatial Distribution and Diffraction Efficiency of RGB Tricolor Light at All Orders after Passing Through the Relay Grating
3.3 Design and optimization of out-coupling grating
Figure 10 shows the structure of the designed out-coupling grating. The out-coupling grating is a transmission grating with an inclined triangle side section. Its structure is designed to effectively couple the diffracted light from the relay grating vertically out of the waveguide before the final image is received by the human eye. In contrast to the virtual reality display, the out-coupling grating must have satisfactory transmittance to the ambient light to meet the requirements of the AR optical waveguide display to fuse virtual information in different actual situations.
Fig. 10. (a) (b) (c) Distribution of diffracted light at all orders of RGB tricolor light after the out-coupled grating, and structural and geometric parameters of the out-coupled grating: w is the grating width, h is the groove depth, and α is the blaze angle of the grating.
When the optical fiber is coupled in and out of the waveguide, the grating equation is satisfied:
With formulas (7) and (8), we can derive that dout = din; that is, the period of the out-coupling grating should be consistent with the period of the in-coupling grating, both of which are 2.09 µm. For the out-coupling grating, we explored the diffraction efficiency of the grating coupling RGB tricolor to the high diffraction orders of m = −3, m = −4, and m = −5 under different structural parameters. These diffraction orders have the same diffraction angle θd = 0°. Considering that the light can be best coupled out of the waveguide when the duty cycle of the grating is 1, we only considered the grating structure with this duty cycle. As the blaze angle of the grating α and the height h completely determine the shape of the grating, we scanned the blaze angle of the out-coupling grating α from 56° to 66° and the height h from 2 to 3 µm. The diffraction efficiency of RGB tricolor light emitted from the −3, −4, and −5 levels is shown in Fig. 11. The RGB tricolors all correspond to a wide range, in which the coupling efficiency is more than 0.3, considered the manufacturing tolerance range of the out-coupling grating. This efficiency is satisfactory, and the coupling efficiency of the rectangular gratings is often less than 0.05 because we used high diffraction orders for light transmission.
Fig. 11. Diagrams (a), (b), and (c) show the distribution of the efficiency of out-coupling gratings when the duty cycle is 1, at different flare angles α and groove depths h.
We selected the optimal structure from these models, which can balance the difference between the diffraction efficiencies of RGB tricolor; finally, the out-coupling grating was designed with the blaze angle α = 63° and groove depth h = 2.65 µm. The diffraction efficiency corresponding to RGB tricolor light was decent at ηR = 0.36, ηG = 0.35, and ηB = 0.36, and the difference between the diffraction efficiencies was no more than 0.01. In addition to diffraction efficiency, we also focused on the transmittance of ambient light. After simulation, the out-coupling grating had a transmittance of more than 0.9 for the visible light range from 400 to 780 nm. Similarly, in Table 4, we listed the distribution and diffraction efficiency of diffracted light at all orders of RGB tricolor after the out-coupling grating.
Table 4. Spatial Distribution and Diffraction Efficiency of RGB Tricolor Light at All Orders after the Out-coupling Grating
4. Optical waveguide pupil simulation and discussion
We simulated the overall structure of the optical waveguide using LightTools optical design software. The parameters of the grating, wavelength of the light source, and refractive index of the waveguide used in the simulation were consistent with those designed above. The volume of the entire waveguide was length × width × height = 26 mm × 15 mm × 2.5 mm. The thickness was comparable to that of ordinary lenses and the size was smaller than that of ordinary lenses, and thus it can be well integrated with glasses. Figure 12 shows the ray-tracing diagram and outgoing spot diagram of the simulated optical waveguide.
To simplify the design, the light source was set as RGB collimated parallel light, with no collimating lens group added. After the expansion of relay gratings 1 and 2 on the left and right sides, in Fig. 11(b), the size of the exit pupil area was 4 mm × 8 mm. Usually the distance between the glasses and the eyes is 12 mm, and thus the field angle was calculated as h18.9° × v36.87°.
Fig. 12. (a) Ray tracing diagram of the optical waveguide simulation in LightTools. (b) Radiation illuminance diagram of the outgoing spot of the optical waveguide.
In summary, we adopted a new grating layout to expand the exit pupil and successfully simulated the exit pupil expansion. Although only one dimension of expansion was conducted, we obtained detailed and specific structures of each grating and the direction of the grating vector, which is of guiding significance for the design of AR optical waveguides. Increasing the size of the image source and further optimizing the design of the coupled grating are the two ways to improve the angle of view, and the latter is also a problem we will study in the next step. In Table 5, we present the parameters of the in-coupling, relay, and out-coupling gratings and the diffraction efficiency of RGB tricolor light, along with the calculated coupling efficiency of the whole waveguide system. The exit pupil area near the coupled grating was pupil area 1, the exit pupil area far from the coupled grating was pupil area 2, and the final coupling efficiency was between 0.056 and 0.08. In previous studies of diffractive optical waveguides, the coupling efficiency of the waveguide after pupil expansion processing was usually less than 0.03. Here, it was doubled or even more, which improved the efficiency of the light source and reduced the electrical loss. In addition, the difference in the overall coupling efficiency of each color light did not exceed 0.024, ensuring that the input image did not produce significant color difference after waveguide expansion. In addition, the color balance can be achieved by adjusting the output power of each monochromatic light source.
Table 5. In-coupling, Relay, and Out-coupling Grating Parameters and Diffraction Efficiency of RGB Tricolor Light and Coupling Efficiency of the Entire Waveguide to RGB Tricolor Light
5. Conclusion
This study presents a single-layer color dual-channel optical waveguide structure for an AR imaging display using three types of echelle gratings with ultra-wavelength scale grating periods as in-coupling, relay, and out-coupling gratings. High diffraction orders of −3, −4, and −5 were generated by the inter-echelle gratings of periods 2.09 and 1.29 µm under normal-incidence illumination of the three primary colors at 740, 555, and 444 nm, resulting in beam splitting at the in-coupling end of the three primary colors beam in the optical waveguide, folding pupil dilation at the relay end, and beam combination at the out-coupling end. The secondary diffraction of the relay grating achieved pupil dilation of the beam, and the conical diffraction generated by its inclined reticle enabled the beam to be converted to the lower out-coupling grating. Further, the out-coupling grating with the inclined reticle ensured that the conical diffracted beam was perpendicular to the waveguide.
Based on the vector diffraction theory, the blaze angle (duty cycle), groove depth, and corresponding diffraction efficiency of three echelle gratings with small-blaze-angle triangular groove, rectangular groove, and large-blaze-angle triangular groove were calculated. The groove parameters and tolerance range corresponding to high diffraction efficiency were optimized to achieve average diffraction efficiencies of the three primary colors of reflection of the in-coupling, reflection relay, and transmission of out-coupling gratings greater than 74%, 24%, and 35%, respectively. Thus, we obtained the dual channel one-dimensional pupil expansion of the original image pair and achieved a field angle of view of h18.9° × v36.87°. The calculation results show that a grating combining high diffraction order, conical diffraction, and high diffraction efficiency is a solution for a single-layer color optical waveguide display device.
Funding
National Natural Science Foundation of China (61831015, 61901264); Basic and Applied Basic Research Foundation of Guangdong Province (2021A1515011933); Special Project for Research and Development in Key areas of Guangdong Province (2020B090921002); Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission (cstc2021jcyj-msxmX1136); Science and Technology Commission of Shanghai Municipality (19ZR1427200).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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