Open Access
Add to BibSonomy
Abstract
Ensuring uniform illuminance in waveguide-based augmented reality (AR) display devices is crucial for providing an immersive and comfortable visual experience. However, there is a lack of a straightforward and efficient design method available to achieve illuminance uniformity over the full field of view. To address this issue, we propose a novel design that utilizes random mask gratings (RMGs) as the folding grating and the out-coupling grating. Unlike traditional approaches that modify the grating structure, we control the diffraction efficiency distribution by adjusting the filling factor of the mask while keeping the grating structure unchanged in one RMG. The grating structures are designed and optimized based on rigorous coupled wave analysis and particle swarm optimization. The feasibility of our method is verified by the simulation results in Lighttools. In the FOV range of 20°×15°, the eyebox uniformities of all fields are greater than 0.78, which can provide a good visual experience for users.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Augmented reality (AR) technology has been attracting more and more attention since it was invented in the 1960s. We can see the virtual images and the real-world scene at the same time Through AR display devices. AR technology has been widely used in military, entertainment, medical treatment and education [1–3].
There are various approaches to realize AR [4], including half-mirror [5–7], freeform optical prism [8,9], retina scanning [10,11], geometrical waveguide [12,13] and grating waveguide [14–16]. Compared with other approaches, grating waveguide has the advantages of compactness and wide field of view (FOV). Also, grating waveguide based AR devices can provide large eyebox through exit pupil expansion (EPE), which is important for user experiences. However, the energy of undiffracted light will decrease in the EPE process, which can cause poor spatial illuminance uniformity within the eyebox. Recent years, numerous studies have been struggling to improve the eyebox uniformity of grating waveguide system. Liu et al. [17] proposed a symmetric binocular waveguide system with two projectors and two in-couplers at both side. Light beams from two projectors travel along the opposite direction in the waveguide, and the eyebox uniformity is greatly improved. Chen et al. [18] divided the out-coupling grating into multiple sub-regions, and each sub-region has different diffraction efficiency. However, the distance between adjacent replicated exit pupils varies with the propagation angle. If only the center field is considered when designing the diffraction efficiency distribution, the eyebox uniformities of other fields will not be satisfactory. Liu et al. [19] considered the eyebox uniformities of different fields when optimizing the diffraction efficiency distribution. However, the diffraction efficiency of each sub-region does not vary with the propagation angle, and the simulated and experimental results are not good enough. In order to realize eyebox uniformity over the full FOV, Yan et al. [20] used linked list method to calculate the required angular diffraction efficiency distribution of each sub-region. And the grating structure of each sub-region is designed and optimized. However, iterative computation is necessary when calculating the diffraction efficiency distribution, which causes low computing efficiency. Additionally, the grating structures of some sub-regions are very difficult to manufacture.
In this paper, we propose an innovative design for grating waveguide system aimed at improving the eyebox uniformity over the full FOV. Based on classic L-shaped gating waveguide model, we solve for the analytical solutions of the diffraction efficiency distributions that can satisfy the illuminance uniformity condition. In our design, we use random mask gratings (RMGs) as the folding grating and the out-coupling grating, and the required diffraction efficiency distributions can be realized. Unlike traditional approaches that modify the grating structure, we control the diffraction efficiency distribution by adjusting the filling factor of the mask while keeping the grating structure unchanged in one RMG. Thus, the design process could be greatly simplified compared with traditional method. The grating structures of the two RMGs are designed and optimized based on rigorous coupled wave analysis and particle swarm optimization. We build an L-shaped gating waveguide model that utilizes RMGs in Lighttools, and use Rsoft to generate the bidirectional scattering distribution functions of the grating structures. The simulation results show that our method is feasible. In the FOV range of 20°×15°, the eyebox uniformities of all fields are greater than 0.78, which can provide good visual experience for users.
2. Principle of random mask grating
The illumination uniformity of grating waveguide system can be divided into two parts: angular uniformity and spatial uniformity. Angular uniformity, also called image uniformity, refers to the brightness uniformity of the virtual image at one observation point within the eyebox. Spatial uniformity, also called eyebox uniformity, refers to the uniformity of illuminance at different point within the eyebox. Poor eyebox uniformity could lead to significant variations in the brightness of the virtual image as the viewer's eyeball rotates, which can cause poor user experience. The angular uniformity can be achieved through image preprocessing, which means the overall uniformity can be achieved as long as the eyebox uniformity is realized for the full FOV.
The energy of undiffracted light will decrease in the EPE process, which means the spatial uniformity will be poor if the diffraction efficiency is constant in one grating. The traditional solution is to divide the grating into multiple sub-regions. As shown in Fig. 1(a), the diffraction efficiency gradually increases along the EPE direction, so that the spatial uniformity can be improved. In this method, grating structures with different efficiencies are required, and the grating containing different grating structures is difficult to manufacture. The schematic of random mask grating (RMG) is shown in Fig. 1(b). The RMG is divided into numerous square cells. For each square cell, the grating structure exists or not is random. The grating structure is the same in one RMG. The equivalent efficiency distribution can be adjusted by the probability of existence of grating structure (PGS). If the PGS gradually increases along the EPE direction, the function of the RMG can be the same as that of a grating with multiple sub-regions.
Fig. 1. (a) Schematic of grating with multiple sub-regions. Light gray area for grating structure with low diffraction efficiency and dark gray area for grating structure with high diffraction efficiency. (b) Schematic of random mask grating. Black cells for areas with grating structure and white cells for areas without grating structure.
The classic L-shaped grating waveguide is shown in Fig. 2(a). The collimated incident light is coupled into the waveguide by the in-coupling grating. Then the light is redirected by the folding grating, and the EPE in the horizontal direction is realized. Finally, the light leaks out from the waveguide at the out-coupling grating, and the EPE in the vertical direction is realized. Light in the waveguide should meet the total internal reflection (TIR) condition of the waveguide, so that the light that can propagate in the waveguide losslessly. The TIR condition can be well described in the wave vector domain (k-domain) [21]. The TIR condition of the waveguide can be expressed as:
Fig. 2. Classical L-shaped grating waveguide system. (a) Schematic of waveguide layout. (b) K-domain analysis diagram.
The diffraction efficiency distribution of the folding grating determines the eyebox uniformity in the horizontal direction. For the folding grating, the wave vector range of each diffraction order is shown in Fig. 3(a). We can see that the zeroth order and the minus first order are in the annular region, and all other orders are outside the outer circle, which means only the zeroth reflective order and the minus first reflective order exist. If the materials of the folding grating are lossless, the relation of the diffraction efficiencies can be expressed as:
where ${R_0}$ and ${R_{ - 1}}$ are the diffraction efficiencies of the zeros reflective order and minus first reflective order, respectively.Fig. 3. Diffraction characteristic of folding grating. (a) K-domain analysis diagram. (b) Schematic of horizontal EPE in XZ view. (c) Multiple diffraction effect.
In order to realize eyebox uniformity for each field in the horizontal direction, the diffraction efficiency of the folding grating not only needs to vary with position, but also with the incident angle. The efficiency distribution of the minus first order can be expressed as a bivariate function ${R_{ - 1}}({x,\varphi } )$, where x represents the distance to the beginning of the folding grating and φ is the incident angle. The schematic of horizontal EPE is shown in Fig. 3(b). The distance between adjacent exit pupils varies with the incident angle. If the thickness of the waveguide is t, the distance of EPE can be expressed as:
The relation between the residual energy of the zeroth order ${I_{R0}}({x,\varphi } )$ and the efficiency distribution can be expressed as:
Because only two diffraction orders exist, the reduced energy of the zeroth order equals to the light energy of the minus first order. The uniformity condition in the horizontal direction can be expressed as:
If the horizontal length of the folding grating is ${L_{fold}}$, the input light energy is $I(\varphi )$, and the utilization rate of light energy is ${\eta _{fold}}$, we can get the boundary condition:
Based on the differential equations above, we can solve for the efficiency distribution that meets the uniformity condition:
For the folding grating, ${\eta _{fold}}$ should not be very high. High utilization rate means high diffraction efficiency at the end of the folding grating. Gratings with high diffraction efficiency are difficult to design and manufacture. In addition, high diffraction efficiency can also result in severe multiple diffraction effect [20]. As shown in Fig. 3(c), though the energy is mainly at the minus first order, most energy will diffract back to the zeroth order at next diffraction due to high diffraction efficiency. Thus, part of the energy will be wasted and can not reach the out-coupling grating. Then the energy received by the right part of the out-coupling grating and eyebox will be less than the expected value, and the eyebox uniformity will significantly decrease.
From the expression in Eq. (7), the efficiency distribution can be expressed as a product of two parts:
If we find a feasible value c and a grating structure with ${\eta _{ - 1}}(\varphi )$ equal to $A(\varphi )$, the efficiency distribution in Eq. (7) can be realized. We set the PGS of the RMG to $B(x )$, then the equivalent efficiency distribution equals to the required efficiency distribution.
The diffraction efficiency distribution of the out-coupling grating determines the eyebox uniformity in the vertical direction. The wave vector range of each diffraction order is shown in Fig. 4(a). The zeroth order and the minus second order are in the annular region, which means the zeroth reflective order and the minus second reflective order exist. The minus first order is in the inner circle, which means both reflective order and transmissive order exist. The schematic of vertical EPE is shown in Fig. 4(b). Among all diffraction orders, only the minus first reflective order can enter the human eye. And the energy of the minus second reflective order and the minus first transmissive order will be lost.
Fig. 4. Diffraction characteristic of out-coupling grating. (a) K-domain analysis diagram. (b) Schematic of vertical EPE in YZ view.
We use ${R_0}({y,\varphi } )$ and ${R_{ - 1}}({y,\varphi } )$ to represent the efficiency distributions of the zeroth reflective order and the minus first reflective order, respectively, where y is the distance to the beginning of the out-coupling grating and φ is the incident angle. The relation between the residual energy of the zeroth order ${I_{R0}}({y,\varphi } )$ and the efficiency distribution can be expressed as:
The eyebox uniformity condition in the vertical direction can be expressed as:
If the vertical length of the out-coupling grating is ${L_{out}}$, the input light energy is $I(\varphi )$, and the utilization rate of light energy is ${\eta _{out}}$, the boundary condition can be expressed as:
Because the condition in Eq. (2) can not be met for out-coupling grating, we can not solve for the efficiency distribution directly.
If we use RMG as the out-coupling grating, the differential equations can be simplified. We use ${\eta _0}(\varphi )$ and ${\eta _{ - 1}}(\varphi )$ to represent the efficiencies of the zeroth reflective order and the minus first reflective order, respectively. And the spatial distribution of the PGS is ${P_{out}}(y )$. The equivalent efficiency distributions of the out-coupling RMG can be expressed as:
Then Eq. (11) can be simplified as:
We can solve for the required equivalent efficiency distribution of the zeros order:
The efficiency ${\eta _0}(\varphi )$ and the PGS distribution can be expressed as:
The efficiency ${\eta _{ - 1}}(\varphi )$ does not affect the eyebox uniformity. However, ${\eta _{ - 1}}(\varphi )$ determines the out-coupling efficiency of the out-coupling RMG. The out-coupling efficiency can be expressed as:
Under the condition of eyebox uniformity, the higher ${\eta _{ - 1}}(\varphi )$, the higher the energy efficiency.
3. Grating structure design and optimization
As shown in Fig. 5, we design a layout of an L-shaped grating waveguide using RMGs. In our design, the wavelength is 532 nm. The waveguide material is HOYA-FD60W glass, with the refractive index of 1.817 at 532 nm. The thickness of the waveguide is 1 mm. The periods of in-coupling grating, the folding RMG and the out-coupling RMG are 440 nm, 311 nm and 440 nm, respectively. When the FOV is 20°×15°, the size of the eyebox is 16mm × 12 mm at an eye relief of 18 mm.
In our design, the horizontal length of the folding RMG is 30 mm. We divide the folding RMG evenly into 15 sub-regions along the horizontal direction. We set the PGS of the last sub-region to 1, and ${\eta _{fold}}$ to 0.7. We can get the PGS of each sub-region and diffraction efficiency of the grating structure ${\eta _{ - 1}}(\varphi )$ based on Eq. (7). The PGS of each sub-region is shown in Fig. 6(a). The vertical length of the out-coupling RMG is 18 mm, and we divide it into 9 equal sub-regions. We set the PGS of the last sub-region to 1, and ${\eta _{out}}$ to 0.75. And the PGS of each sub-region is shown in Fig. 6(b). The PGS value of each sub-region is larger than 0.3. Though higher ${\eta _{fold}}$ and ${\eta _{out}}$ can provide higher energy efficiency, the PGS values at the beginning of the RMGs will be very low if we increase ${\eta _{fold}}$ or ${\eta _{out}}$. If the PGS is too low, some areas in the eyebox may not receive any light, and the eyebox uniformity will be worse.
The grating structure of the folding RMG and out-coupling RMG is shown in Fig. 7. The grating structure is a trapezoid with two base angles less than 90°, which can be mass manufactured by nanoimprint technology [23]. A layer of TiO2 can make the diffraction efficiency curve smoother [24]. We choose nanoimprint polymer that refractive index is 1.76 at 532 nm. We use rigorous coupled wave analysis (RCWA) to calculate the diffraction efficiency of each order. The grating structure can be described by depth (H), TiO2 thickness (Ht) and shape parameters (L1, L2 and L3). We choose particle swarm optimization (PSO) to optimize the grating structure. The shape parameters are interdependent, and the constraint conditions are complex. So we define three new parameters to describe the shape of the grating structure:
And the constraint conditions are:
All possible grating shapes can be described by the constraint conditions.
For the folding RMG, only the efficiency of the minus first order needs to be considered. Here we set the objective function as:
For the out-coupling RMG, both eyebox uniformity and energy efficiency need to be considered. We set the objective function as:
We use the RCWA function of Rsoft software and Python to build the whole optimization module. The parameters of the optimized grating structures are shown in Table 1. The diffraction efficiencies of the optimized grating structures of folding RMG and out-coupling RMG are shown in Fig. 8(a) and Fig. 8(b), respectively. For the out-coupling RMG, though R0 is very close to the ideal efficiency, which means good eyebox uniformity, the energy efficiency is not high enough. Metagratings with higher design freedom could be a possible solution [25].
Fig. 8. Diffraction efficiencies of the optimized grating structures of for unpolarized light. (a) Folding RMG. (b) Out-coupling RMG.
Table 1. Optimized parameters of grating structures
The grating structure of the in-coupling grating is shown in Fig. 9(a). The sawtooth structure can provide high diffraction efficiency, and the efficiency can be further improved by coating a layer of sliver. The parameters of the in-coupling grating are shown in Table 1, and the diffraction efficiency is shown in Fig. 9(b). The average efficiency for unpolarized light is 0.747.
Fig. 9. (a) Grating structure of in-coupling grating. (b) Diffraction efficiency of in-coupling grating. TE for transverse electric mode and TM for transverse magnetic mode.
4. Simulation results
We set the size of the RMG cell to 0.2 mm. Based on the design above, we can get the layouts of the RMGs. The layouts of the folding RMG and the out-coupling RMG are shown in Fig. 10(a) and Fig. 10(b), respectively. In order to investigate the influence of random mask on imaging, we build a simple model in Zemax. As shown in Fig. 11(a), the imaging system uses a perfect lens with a diameter of 3 mm and a focal length of 23 mm to imitate the human eye. A random mask with PGS of 0.3 is added. The modulation transfer function (MTF) results of different pixel sizes are shown in Fig. 11(b). If the pixel size is 0.2 mm, the MTF is very close to the diffraction limit (without random mask) when the spatial frequency is lower than 40lp/mm, and the decline is not significant for higher spatial frequency. The MTF value is larger than 0.61 at 100lp/mm. A spatial frequency of 100lp/mm corresponds to a resolution of 1600 × 1200 when the FOV is 20°×15°. Though the random mask will affect the imaging quality, it is still acceptable for visual system.
Fig. 10. Layout of RMGs. (a) Folding RMG. (b) Out-coupling RMG. Black cells for areas with grating structure.
As shown in Fig. 12(a), we build the L-shaped waveguide in Lighttools software. We use Rsoft to generate the bidirectional scattering distribution functions of the grating structures. Though we use unpolarized diffraction efficiency for grating structure optimization, the polarization of the light is considered in the simulation. We use 9-point method to describe the eyebox uniformity. As shown in Fig. 12(b), we select 9 squares of 3mm × 3 mm that are evenly distributed in the eyebox.
Fig. 12. (a) L-shaped grating waveguide model built in Lighttools. (b) Schematic of 9-point method. Red squares for selected regions. From left to right and top to bottom, the 9 regions are numbered 1-9 in order.
We use ${I_i}({i = 1,2, \cdots 9} )$ to represent the average illuminance of each square region, and the expression of the spatial uniformity is:
The spatial illuminance distributions at different viewing angles are shown in Fig. 13, and the spatial uniformities are shown in Table 2. The expression of the normalized illuminance is:
Fig. 13. Normalized illuminance distributions at different viewing angles. (a) (−10°, 7.5°), (b) (0°, 7.5°), (c) (10°, 7.5°), (d) (−10°, 0°), (e) (0°, 0°), (f) (10°, 0°), (g) (−10°, −7.5°), (h) (0°, −7.5°) and (i) (10°, −7.5°).
Table 2. Normalized illuminance and eyebox uniformity at different viewing angles
It is shown that the spatial uniformities of the center field is greater than 0.84, and the uniformities of all fields are greater than 0.78, which can provide good visual experience for users. The simulation results indicates that high eyebox uniformity over the full FOV can be achieved by utilizing RMGs.
The 9-point method is not able to measure the whole eyebox. We use a square of 3mm × 3 mm as a convolution kernel and apply it to the spatial illuminance distribution of the eyebox. Then we can analyze the illuminance uniformity over the full eyebox. The normalized convolutional illuminance distribution of the center field is shown in Fig. 14. We use P5/P95 value to indicate the uniformity of each field. The results are shown in Table 3. The P5/P95 values of all fields are greater than 0.66.
Table 3. P5/P95 values of different fields
The overall energy efficiency of each field is shown in Table 4. The overall efficiency represents the energy received by the eyebox divided by the input energy. The multiple diffraction effect of the in-coupling grating can decrease the in-coupling efficiency, and the angular uniformity can also be affected [26]. The angular nonuniformity can be solved by adjusting the input image. The multiple diffraction effect of the folding grating can also influence the overall efficiency, as well as eyebox uniformity. As shown in Fig. 3(c), the directions of the zeros order and the minus first order are different. If we use a complex grating structure, it is possible to lower the efficiency of undesired diffraction, and the multiple diffraction effect can be suppressed.
Table 4. Overall energy efficiencies of different fields
5. Conclusion and discussion
For waveguide based AR display devices, the illuminance uniformity is crucial for optimal user experiences. Insufficient eyebox uniformity could lead to significant variations in the brightness of the virtual image as the viewer's eyeball rotates. However, there is no straightforward and efficient design method available to achieve illuminance uniformity over the full field of view.
In this paper, we propose a novel grating waveguide that utilizes random mask gratings as the folding grating and the out-coupling grating, which can achieve illuminance uniformity over the full field of view. We analyze the EPE process of L-shaped grating waveguide system and solve for the diffraction efficiency distributions of the gratings that satisfy the uniformity condition. The equivalent diffraction efficiency of RMG is controlled by the filling factor of the mask, and the grating structure is unchanged in one RMG. The grating structures of the two RMGs are designed and optimized based on rigorous coupled wave analysis and particle swarm optimization. The feasibility of our method is verified by the simulation results in Lighttools. In the FOV range of 20°×15°, the eyebox uniformities of all fields are greater than 0.78.
In our design, the FOV can be much larger if only the TIR condition is considered. However, it is not easy to realize larger FOV and eyebox uniformity at the same time. For each grating, the range of incident angle will be much larger, and the design of the grating structure will be very difficult. Also, the multiple diffraction effect of the folding grating will be much severer because the folding grating is longer and wider. The difficulties can be solved by optimizing the structure of each grating. However, trapezoid grating structure and PSO algorithm may not achieve this goal. More complex grating structures and optimization algorithm are required. This could be a meaningful work in the future.
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.
References
1. A. A. Cameron, “Optical waveguide technology and its application in head-mounted displays.” Head-and Helmet-Mounted Displays XVII; and Display Technologies and Applications for Defense, Security, and Avionics VI, Vol. 8383 (SPIE, 2012), 109–119.
2. T. Sielhorst, M. Feuerstein, and N. Navab, “Advanced medical displays: A literature review of augmented reality,” J. Disp. Technol. 4(4), 451–467 (2008). [CrossRef]
3. H. Kaufmann, K. Steinbügl, A. Dünser, et al., “General training of spatial abilities by geometry education in augmented reality,” Annual Review of CyberTherapy and Telemedicine: A Decade of VR 3, 65–76 (2005).
4. J. Xiong, E. Hsiang, Z. He, et al., “Augmented reality and virtual reality displays: emerging technologies and future perspectives,” Light: Sci. Appl. 10(1), 216 (2021). [CrossRef]
5. M. Antonio, J. Bayo-Monton, A. Lizondo, et al., “Evaluation of Google Glass technical limitations on their integration in medical systems,” Sensors 16(12), 2142 (2016). [CrossRef]
6. S. Ashok, A. Riser, and J. R. Rogers, “Design of an advanced helmet mounted display (AHMD),” Cockpit and Future Displays for Defense and Security, Vol. 5801 (International Society for Optics and Photonics, 2005), 304–315.
7. L. Wei, Y. Li, J. Jing, et al., “Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface,” Opt. Express 26(7), 8550–8565 (2018). [CrossRef]
8. D. Cheng, Y. Wang, H. Hua, et al., “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009). [CrossRef]
9. D. Cheng, Y. Wang, H. Hua, et al., “Design of a wide-angle, lightweight head-mounted display using free-form optics tiling,” Opt. Lett. 36(11), 2098–2100 (2011). [CrossRef]
10. J. Xiong, G. Tan, T. Zhan, et al., “Breaking the field-of-view limit in augmented reality with a scanning waveguide display,” OSA Continuum 3(10), 2730–2740 (2020). [CrossRef]
11. R. Gabai, G. Cahana, M. Yehiel, et al., “Enhanced 3D perception using Laser based scanning display,” Optical Architectures for Displays and Sensing in Augmented, Virtual, and Mixed Reality (AR, VR, MR) II, Vol. 11765 (International Society for Optics and Photonics, 2021).
12. J. Yang, P. Twardowski, P. Gérard, et al., “Design of a large field-of-view see-through near to eye display with two geometrical waveguides,” Opt. Lett. 41(23), 5426–5429 (2016). [CrossRef]
13. K. Zhao and J. Pan, “Optical design for a see-through head-mounted display with high visibility,” Opt. Express 24(5), 4749–4760 (2016). [CrossRef]
14. Y. Weng, Y. Zhang, W. Wang, et al., “High-efficiency and compact two-dimensional exit pupil expansion design for diffractive waveguide based on polarization volume grating,” Opt. Express 31(4), 6601–6614 (2023). [CrossRef]
15. J. Xiao, J. Liu, J. Han, et al., “Design of achromatic surface microstructure for near-eye display with diffractive waveguide,” Opt. Commun. 452, 411–416 (2019). [CrossRef]
16. Y. Zhang and F. Fang, “Development of planar diffractive waveguides in optical see-through head-mounted displays,” Precis. Eng. 60, 482–496 (2019). [CrossRef]
17. Z. Liu, Y. Pang, C. Pan, et al., “Design of a uniform-illumination binocular waveguide display with diffraction gratings and freeform optics,” Opt. Express 25(24), 30720–30731 (2017). [CrossRef]
18. C. Chen, Y. Cui, Y. Chen, et al., “Near-eye display with a triple-channel waveguide for metaverse,” Opt. Express 30(17), 31256–31266 (2022). [CrossRef]
19. A. Liu, Y. Zhang, Y. Weng, et al., “Diffraction efficiency distribution of output grating in holographic waveguide display system,” IEEE Photonics J. 10(4), 1–10 (2018). [CrossRef]
20. S. Yan, E. Zhang, J. Guo, et al., “Eyebox uniformity optimization over the full field of view for optical waveguide displays based on linked list processing,” Opt. Express 30(21), 38139–38151 (2022). [CrossRef]
21. J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 37(34), 8158–8159 (1998). [CrossRef]
22. Y. Wu, C. Pan, C. Lu, et al., “Hybrid waveguide based augmented reality display system with extra large field of view and 2D exit pupil expansion,” Opt. Express 31(20), 32799–32812 (2023). [CrossRef]
23. S. Steiner, M. Jotz, F. Bachhuber, et al., “Enabling the Metaverse through mass manufacturing of industry-standard optical waveguide combiners,” Optical Architectures for Displays and Sensing in Augmented, Virtual, and Mixed Reality (AR, VR, MR) IV. Vol. 12449 (SPIE, 2023), 24–42.
24. C. Pan, Z. Liu, Y. Pang, et al., “Design of a high-performance in-coupling grating using differential evolution algorithm for waveguide display,” Opt. Express 26(20), 26646–26662 (2018). [CrossRef]
25. Z. Liu, D. Wang, H. Gao, et al., “Metasurface-enabled augmented reality display: a review,” Adv. Photonics 5(03), 034001 (2023). [CrossRef]
26. J. Goodsell, P. Xiong, D. K. Nikolov, et al., “Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers,” Opt. Express 31(3), 4599–4614 (2023). [CrossRef]
