Design of waveguide with double layer diffractive optical elements for augmented reality displays

Abstract

We investigated a diffraction optical waveguide structure with a double layer coupling configuration. This double layer-coupled diffraction optical waveguide structure modulates light information through wavefront modulation for propagation within the optical waveguide and then reproduces the light information through further wavefront modulation, thus achieving optical information transmission. Analysis indicates that the theoretical maximum field of view can reach 90° × 90°. With an actual field of view set to 53° × 53°, an entrance pupil size of 3.2 × 3.2 mm², an eye relief of 10 mm, and 50 pupil expansion, the system’s total energy transmission efficiency is 37%, with field of view uniformity at 91% and uniformity within the eye movement range reaching 97%.

Introduction

Theoretically, diffraction optical waveguides can support the transmission of information over large field of view angles. Additionally, the lightweight design of the optical waveguide structure makes it suitable for integration into eyeglass-shaped products. By utilizing multiple total internal reflections within the waveguide, pupil expansion is achieved, providing users with a larger eye movement range. These characteristics make it a significant research focus in the field of augmented reality displays^{1,2,3,4,5,6,7,8,9,10,11,12}.

However, diffraction optical waveguides still face several challenges. The first issue is the limitation of the waveguide’s field of view (FOV)^13,14,15,16. The primary cause of this limitation is the refractive index of the waveguide material, which restricts the expansion of the FOV. Theoretically, this constraint limits the maximum allowable FOV. Various scholars have proposed solutions to address this issue: Microsoft and DigiLens have developed multiple pupil expansion schemes that can increase the allowable FOV⁹; Chao Ping Chen proposed a three-layer waveguide angle splitting and combining scheme, theoretically increasing the FOV limit to 90° in x-direction. The second issue is the inability to achieve high brightness uniformity across a large FOV^17,18, which practically limits the expansion of the AR diffraction waveguide’s FOV. The main reason is that the grating structure cannot ensure high diffraction efficiency for the large angular bandwidth corresponding to a large FOV. As a result, after multiple grating couplings within the waveguide, the transmission efficiency at the edge of the FOV significantly decreases, causing a noticeable drop in brightness at the FOV edges. Yinyue Lin proposed adding an optical element layer to improve the diffraction efficiency at the edge of the FOV¹⁸. However, this method still fails to provide high uniformity for larger FOVs. Most current products compensate for the imaging brightness by increasing the brightness of the edge FOV information, but further improvement is still needed. The third issue is improving uniformity within the eye movement range^19,20,21. Ideally, the coupling energy emitted at various pupil expansion positions should be as uniform as possible to minimize the observation differences at different positions within the eye movement range. Ao Liu optimized the coupling and emission gratings in different regions, achieving a coefficient of variation of 0.2897 for a 30° FOV²⁰. Shufeng Yan used optimization algorithms to achieve a pupil expansion uniformity of 61.7% with FOV as 15° × 15°²¹. However, these methods face significantly reduced applicability when dealing with more complex design requirements for larger FOVs.

To address the aforementioned issues, we introduce a double layer-coupled diffraction optical waveguide combiner. This design can provide a larger field of view (FOV) while ensuring high brightness uniformity across the FOV and high uniformity in pupil expansion.

Design theory

Double layer diffractive waveguide

Fig. 1

The double layer coupling waveguide imaging system consists of a cross-section.

Fig. 2

Light shaping process of in-coupling and out-coupling double layer DOEs.

Figure 1 depicts a cross-sectional view of our waveguide system that is capable of collimating and reconstructing the field of view (FOV). This is achieved by two double layer diffractive optical elements for in-coupling and out-coupling. The imaging process involves the source, in-coupling DOE, out-coupling DOE, and the eye. The in-coupling DOE modifies the wavefront phase of the input field to a plane wave, resulting in FOV collimation and diffraction. And the plane wave propagation in the waveguide with the angle which is satisfied the total reflection at the interface of waveguide and air. The wavefront phase of the out-coupled beam from the waveguide is then modified back to its original wavefront phase, achieving diffraction and FOV reconstruction. Figure 2 illustrates the light shaping process of each layer of double layer coupling DOEs. In the system, we have chosen a slanted grating structure as one layer for both the in-coupling and outcoupling double layer DOEs to provide high efficiency of diffraction.

In actually, surface light source is modeling as two-dimensional point source array to provide the light information. The field at the plane before in-coupling DOE is calculated in k-domain by the following process: performing a Fourier transform to k-domain, applying the propagation operator and executing an inverse Fourier transform back to x-domain. This modeling is appropriate for micro-display panels such as OLEDs. We have also selected a lanthanum dense flint glass N-LASF44 (Schott) as the material for the waveguide. This glass has a refractive index of ${\text{n}}_{\text{wg}}$ = 1.8006/1.8083/1.8163 at 633/546/486 nm, which corresponds to a critical angle ${\theta}_{\text{c}}$ of 33.73°/33.57°/33.40°. To make sure we can accommodate longer wavelengths, it would be safer to use a slightly larger angle, such as 34.0°, as the common critical angle ${\theta}_{\text{c}}$.

Limitation of FOV

Fig. 3

K-space diagram of double layer coupled waveguide. To avoid the excess notations, both abscissa and ordinate shall be divided by the free-space wavenumber ${\text{k}}_{\text{0}}\text{=}{2{\pi}}/{\lambda}$.

Figure 3 illustrates the change in field of view (FOV) as it transitions from air to a waveguide, represented in wave vector space or k-space. To simplify the notation, both the x-axis and y-axis values are divided by the free-space wavenumber ${\text{k}}_{\text{0}}$, which is equal to $\text{2}{\pi}/{\lambda}$. The input FOV is located within the innermost circle with a radius of ${\text{R}}_{\text{air}}\text{=}{\text{n}}_{\text{air}}\left({\text{k}}_{\text{0}}\right)\text{=}\text{1}\left({\text{k}}_{\text{0}}\right)$, while the outermost circle with a radius of ${\text{R}}_{\text{wg}}\text{=}{\text{n}}_{\text{wg}}\left({\text{k}}_{\text{0}}\right)$ represents the waveguide FOV.

In the bilayer-coupled diffraction optical waveguide, optical information is modulated into a planar wavefront before entering the waveguide, where the light propagates as a planar wave. It satisfies the condition that diffraction orders can propagate through total internal reflection within the waveguide, expressed by the equation:

$$\begin{array}{c}{\kappa}_{\text{wg}}\text{=}\frac{{2{\pi}}}{\lambda}{\text{n}}_{\text{wg}}\text{s}\text{i}\text{n}\left({\theta}_{\text{wg}}\right)\text{=}\frac{\pi}{\text{d}}{\epsilon}\left[\frac{{2{\pi}}}{\lambda}\text{,}\frac{{2{\pi}}}{\lambda}{\text{n}}_{\text{wg}}\right]\end{array}$$

(1)

Here, $\lambda$ is the wavelength of the light, ${\text{n}}_{\text{wg}}$ is the refractive index of the waveguide material, ${\theta}_{\text{wg}}$ is the angle of propagation within the waveguide, and $\text{d}$ is the grating period.

In this context, optical information appears as a point in the k-domain (wave vector domain), indicating that the field of view (FOV) of the optical information is no longer restricted by the refractive index of the waveguide material or the grating period $\text{d}$. Theoretically, the FOV is limited only by the propagation characteristics of light in air. Therefore, within the aforementioned range $\text{d}{\epsilon}\text{[}{\lambda}/{\text{n}}_{\text{wg}}\text{,}{\lambda}{]}$, a maximum FOV of 90° × 90° (diagonal 180°) can be achieved.

Pupil duplication

Fig. 4

Pupil duplication through a succession of TIRs at an angle ${\theta}_{\text{wg}}$.

Exit pupil extension could increase the size of eyebox, which is benefit for the users with different distance between the pupil of eyes or keep the imaging to eyes when the eyes moving. To achieve exit pupil extension, each exit pupil out-couples a small part of energy of the beam, the residual part will incident the next exit pupil for out-coupling.

Figure 4 depicts the process by which an input entrance pupil, with a diameter ${\text{D}}_{\text{p}}$ that matches the length of the in-coupling grating ${\text{W}}_{\text{in}}$, is replicated through a series of Total Internal Reflections (TIRs) at an angle ${{\theta}}_{\text{wg}}$. The number of replicated pupils, denoted as $\text{N}$, is equal to the number of TIRs involved in the process. This relationship can be expressed as:

$$\begin{array}{c}{\text{W}}_{\text{out}}\text{=}\text{2}\text{D}\text{tan}{\theta}_{\text{wg}}\cdot\text{(}\text{N}-\text{1}\text{)}\text{+}{\text{D}}_{\text{p}}\end{array}$$

(2)

The Eq. 2 provides calculates the number of pupils $\text{N}$ based on the length of the out-coupling grating (${\text{W}}_{\text{out}}$), the thickness of the waveguide ($\text{D}$) and the angle in the waveguide (${\theta}_{\text{wg}}$) and the diameter of in-coupling DOE (${\text{D}}_{\text{p}}$). This equation is valid when the angle of incidence in the waveguide (${\theta}_{\text{wg}}$) is greater than the critical angle (${{\theta}}_{\text{c}}$) of 34.0°, ensuring total internal reflection (TIR) occurs.

The design requirement for pupil duplication mandates no overlap between adjacent pupils, as each pupil couples only one beam, illustrated in Fig. 4. The design requirement for pupil duplication mandates no overlap between adjacent pupils, as each pupil couples only one beam, illustrated in Fig. 4. The diameter of the in-coupling diffractive optical element (DOE), denoted as “${\text{D}}_{\text{p}}$,” should not exceed the distance between adjacent pupils, defined as ${\text{d}}_{\text{p}}=\text{2D}\text{tan}{{\theta}}_{\text{wg}}$. The size of the aperture, “${\text{D}}_{\text{p}}$,” significantly influences the optical flux that can be coupled into the waveguide. A larger aperture enables greater energy coupling and transmission through the waveguide. Additionally, optical elements in the system face diffraction issues stemming from their aperture sizes, which can spread the spectrum in the k-domain. This results in a rectangular function addition in the x-domain and convolution with a sinc function in the k-domain, leading to space-frequency spread. A larger aperture minimizes this spread, described by the sinc(k/a) function, where “a” represents the aperture diameter. Thus, it is requisite for the optical diameter to be sufficiently large to mitigate diffraction effects. Consequently, set the pupil diameter “${\text{D}}_{\text{p}}$” equal to the distance between adjacent pupils “${\text{d}}_{\text{p}}$.”

From the result in Fig. 5, the angle of TIR ${\theta}_{\text{wg}}$ ranges from 34.0° to 45.0°, and the number of pupils $\text{N}$ ranges from 8 to 12. ${\text{W}}_{\text{out}}$ is between 21.58 mm and 48 mm. As the result, the angle of TIR ${{\theta}}_{\text{wg}}$ =38.2° and the number of pupils $\text{N}$=10 is selected with the size of out-coupling grating ${\text{W}}_{\text{out}}$ as 32.0 mm.

Fig. 5

Out-coupling grating size at angle of TIR under different number of exit pupil extension from 1 to 15 with the thickness of waveguide as D = 2.0 mm.

Intensity, uniformity and coefficient of variation

During the in-coupling process, the intensity of beam in waveguide could calculated by:

$$\begin{array}{c}{\text{I}}^{\text{wg}}\text{=}{\eta}_{\text{in-coupling}}\left(\text{T,}\text{0}\right){\text{I}}_{\text{0}}\end{array}$$

(3)

Where ${\text{I}}_{\text{0}}$ is the intensity of incident beam of waveguide and ${\eta}_{\text{in-coupling}}\left(\text{T,}\text{0}\right)$ is the transmission efficiency of in-coupling DOE.

During the TIR process, the intensity of beam keeps ${\text{I}}^{\text{wg}}$ and for the 1st exit pupil,

$$\begin{array}{c}{\text{I}}_{\text{1}}^{\text{inc}}\text{=}{\text{I}}^{\text{wg}}\end{array}$$

(4)

During the out-coupling process, the reflection and transmission intensity for the i-th exit pupil shall be given by:

$$\begin{array}{c}{\text{I}}_{\text{i}}^{\text{res}}={\text{I}}_{\text{i}}^{\text{ref}}={\text{I}}_{\text{i}}^{\text{inc}}{\eta}_{\text{i}}\left(\text{R,}\text{0}\right)\\\:{\text{I}}_{\text{i}}^{\text{out}}={\text{I}}_{\text{i}}^{\text{trans}}={\text{I}}_{\text{i}}^{\text{inc}}{\eta}_{\text{i}}\left(\text{T,}{-1}\right)\end{array}$$

(5)

With ${{\eta}}_{\text{i}}\left(\text{R,}\text{0}\right)$ is the 0th order reflection diffraction efficiency of i-th out-coupling DOE and ${\eta}_{\text{i}}\left(\text{T,}{-1}\right)$ is the (-1) th order transmission diffraction efficiency of i-th out-coupling DOE. ${\text{I}}_{\text{i}}^{\text{res}}$ and ${\text{I}}_{\text{i}}^{\text{out}}$ represent the residual intensity which will propagate in the waveguide and the out-coupling part which is coupled leave the waveguide respectively.

Thus, for incident of i-th pupil ${\text{I}}_{\text{i}}^{\text{inc}}$ in the waveguide shall be given by:

$$\begin{array}{c}{\text{I}}_{\text{i}}^{\text{inc}}\text{=}{\text{I}}_{\text{0}}^{\text{inc}}\prod_{\text{j=}\text{1}}^{{i-}\text{1}}{\eta}_{\text{j}}\left(\text{R,0}\right)\end{array}$$

(6)

with ${\eta}_{\text{0}}\left(\text{R,}\text{0}\right)\text{=}\text{1}$.

Above all, the intensity of all 10 pupils ${\text{I}}_{\text{i}}^{\text{out}}\text{(}\text{i}\text{=1}{,}\text{...}{,}\text{10)}$ are calculated:

$$\begin{array}{c}{\text{I}}_{\text{i}}^{\text{out}}\text{=}{\text{I}}_{\text{0}}{\eta}_{\text{in-coupling}}\left(\text{T,}\text{0}\right)\left(\prod_{\text{j=}\text{1}}^{\text{i-}\text{1}}{\eta}_{\text{j}}\left(\text{R,}\text{0}\right)\right){\eta}_{\text{i}}\left(\text{T,}{-1}\right)\end{array}$$

(7)

Uniformity is a measure of how evenly the irradiance or intensity is distributed across the pupils. It is calculated as

$$\begin{array}{c}\text{U}\text{=}\text{1}-\frac{{\text{I}}_{\text{max}}-{\text{I}}_{\text{min}}}{{\text{I}}_{\text{max}}+{\text{I}}_{\text{min}}}\text{=}\frac{\text{2}{\text{I}}_{\text{min}}}{{\text{I}}_{\text{max}}+{\text{I}}_{\text{min}}}\end{array}$$

(8)

where ${\text{I}}_{\text{min}}$ and ${\text{I}}_{\text{max}}$ represent the minimum and maximum intensities of the area, respectively.

The uniform depends on the efficiency of different ${\eta}_{\text{in-coupling}}\left(\text{T,}\text{0}\right)$ of in-coupling DOE, ${\eta}_{\text{j}}\left(\text{R,}\text{0}\right)$ and ${\eta}_{\text{i}}\left(\text{T,}\text{-1}\right)$ of out-coupling DOEs. By the design of DOEs, the high uniformity of out pupil could be provided. The ideal design target could be express as:

$$\begin{array}{c}{\eta}_{\text{system}}\text{=}{\eta}_{\text{in-coupling}}\text{(}\text{T}\text{,}\text{0}\text{)}\left(\prod_{\text{j=}\text{1}}^{\text{i-}\text{1}}{\eta}_{\text{j}}\left(\text{R,}\text{0}\right)\right){\eta}_{\text{i}}\left(\text{T,}{-1}\right)\text{=}\text{const}\end{array}$$

(9)

In the actual results, high uniformity of system $\:{U}_{\text{s}\text{y}\text{s}\text{t}\text{e}\text{m}}$ is achieve by decrease the difference between the maximum and minimum of ${\eta}_{\text{system}}$. Consider the energy utilization of system, the average efficiency ${\bar{{\eta}}}_{\text{system}}$ should be as large as possible. Thus, increasing the average efficiency of system ${\bar{{\eta}}}_{\text{system}}$ and decreasing the efficiency range of system ${\triangle}{\eta}\text{=}{\eta}_{\text{max}}{-}{\eta}_{\text{min}}$ is the design and optimization target for double layer coupling AR waveguide system.

Results and discussion

Diffractive optical elements in waveguide

The in-coupling double layer Diffractive Optical Element (DOE) includes the in-coupling DOE, illustrated in Fig. 6(a), along with the in-coupling slanted grating, whose structure appears in Fig. 7(a) and parameters are provided in Table 1.. For the out-coupling double layer DOEs, each comprises an out-coupling DOE, as depicted in Fig. 6, combined with a grating whose structure is shown in Fig. 7, with corresponding parameters listed in Table 1. as O1-O10. Ten sub-DOEs for out-coupling facilitate one-dimensional pupil expansion, enhancing horizontal eye movement range. Furthermore, a slanted turning grating—composed of five sub-grating structures with varying depths and parameters detailed in Table 1. as F1-F5—has been incorporated into the optical waveguide, enabling two-dimensional pupil expansion and increasing vertical eye movement range.

In total, there are 50 out-coupling double layer DOEs in the waveguide, organized in 5 rows and 10 columns, resulting in effective exit pupil extension. Each double layer DOE, positioned at the i-th column and j-th row, consists of the out-coupling DOE and grating structured as outlined in Table 1. as Oi grating.

Table 1. Structure, diffraction efficiency of working orders (WO) of gratings and working efficiency $\:\left(\prod\:_{\text{j=1}}^{\text{i-1}}{\eta}_{\text{j}}\left(\text{WO1}\right)\right){\eta}_{\text{i}}\left(\text{WO2}\right)$ of double layer coupled waveguide combiner.

Fig. 6

Structure and efficiency of wavefront phase modulation layer of double layer coupled waveguide combiner. (a) In-coupling DOE height profile. (b) Out-coupling DOE height profile.

Fig. 7

Structure of grating layer of double layer coupled waveguide combiner. (a) In-coupling grating structure with $\text{d}$=473.12 nm, ${\theta}_{\text{slant,in}}$=28.2$\:^\circ\:$, $\:{\text{h}}_{\text{in}}$=650 nm. (b) Out-coupling grating structure with $\text{d}$=473.12 nm, ${\theta}_{\text{slant,out}}\in\:$ [0$\:^\circ\:$, 50$\:^\circ\:$], $\:{\text{h}}_{\text{out}}=$ 670 nm. (c) Fold coupling grating structure with $\:\text{d}$=332.43 nm, ${\theta}_{\text{slant,fold}}=$25$\:^\circ\:$, $\:{\text{h}}_{\text{fold}}\in\:$ [50 nm, 400 nm].

Define the amplitude of the incident field for the in-coupling and out-coupling diffractive optical elements (DOEs) as 1 V/m. In DOE design and analysis, the operational phase modulation order is + 1, with the corresponding field illustrated in Fig. 8-(a) and Fig. 9-(a) in units of V/m. Additional field orders generated by the in-coupling and out-coupling DOEs are presented in Fig. 8-(b), (c), (d), and (e), as well as Fig. 9-(b), (c), (d), and (e). The analysis reveals that the fields at these other orders are significantly smaller than the operational order. From the data in Figs. 8 and 9, the maximum values for the − 1 order, 0 order, + 2 order, and + 3 order of the in-coupling DOE are 9.5212 × 10⁻⁵ V/m, 1.6897 × 10⁻⁴ V/m, 1.6901 × 10⁻⁴ V/m, and 9.5206 × 10⁻⁵ V/m respectively. The maximum values for these same orders in the out-coupling DOE are 1.0462 × 10⁻⁴ V/m, 1.8569 × 10⁻⁴ V/m, 1.8577 × 10⁻⁴ V/m, and 1.0465 × 10⁻⁴ V/m respectively. A further analysis of the higher order results is depicted in Fig. 10, which shows the maximum field values at various diffraction orders on a logarithmic scale. This indicates that the energy contribution from other diffraction orders is minimal and can be disregarded in the imaging process.

Fig. 8

Filed generated by in-coupling phase modulation DOE at different diffraction orders with unit as V/m (a) + 1 order (working order) (b) -1 order (c) 0 order (d) + 2 order (e) + 3 order.

Fig. 9

Filed generated by out-coupling phase modulation DOE at different diffraction orders with unit as V/m (a) + 1 order (working order) (b) -1 order (c) 0 order (d) + 2 order (e) + 3 order.

Fig. 10

Field generated by phase modulation DOE at different diffraction orders with log scale. (a) in-coupling phase modulation (b) out-coupling phase modulation.

Waveguide simulation

Fig. 11

The optical setup for simulation. The propagation process involves the source, in-coupling DOE, fold grating and out-coupling DOE.

The optical setup for our simulation is shown in Fig. 11, where the sub-gratings of fold grating are labeled as F1 to F5 and the sub-gratings of out-coupling DOEs are labeled as O1 to O10. The thickness $\text{D}$ of waveguide as 2.00 mm. The FOV is 53°×53° with diagonal FOV as 70°. The width ${\text{W}}_{\text{in}}$ of in-coupling DOE shall match the size of input pupil as a square with a diameter ${\text{D}}_{\text{p}}$ of 3.2 mm. The width ${\text{W}}_{\text{fold}}$ of fold grating is 16 mm, with each sub-grating being 3.2 mm with the position as (0, 11.2 mm) relative to in-coupling DOE. The width ${\text{W}}_{\text{out}}$ of out-coupling grating is 32 mm, with each sub-grating being 3.2 mm across. The exit pupil size is 32.0 mm × 16.0 mm with the position as (27.2 mm, 11.2 mm) relative to in-coupling DOE. Hence, if the eye relief is 10 mm, eye box will be 20.45 × 4.45 mm².

The field tracing result is shown in Fig. 12. (During the field tracing process, Fourier modal method and free space propagation operator are employed to calculate the electromagnetic field captured by the detector at different position.) The input intensity $\:{\text{I}}_{\text{0}}$ of double layer waveguide is normalized to be 1 V²/m². The radiant flux ${\Phi}_{\text{e}}\text{(}{\lambda}\text{)}$ and the luminous flux ${\Phi}_{\text{v}}\left({\lambda}\right)$ is related by

$$\begin{array}{c}{\Phi}_{\text{v}}\left({\lambda}\right)\text{=}{\text{K}}_{\text{m}}\cdot\text{V}\left({\lambda}\right)\cdot{\Phi}_{\text{e}}\left({\lambda}\right)\end{array}$$

(10)

with ${\text{K}}_{\text{m}}$=683.002 (lm/W²) is luminous efficacy and $\text{V}\text{(}{\lambda}\text{)}$ is luminous coefficient. The luminous intensity of source is 4.248$\:\times\:$10⁻¹⁰ cd with pixel size as 6 ${\upmu\:}$m$\:\times\:$6 ${\upmu\:}$m and the luminous is 11.80 cd/m². The It shows the field before and behind the in-coupling DOE and out-coupling DOE in x-domain and k-domain. The field is collimated and reconstructed process could be found from the phase in x-domain or amplitude in k-domain. The diffraction efficiency of double layer DOEs could be calculated from the amplitude in x-domain. The average diffraction efficiency of grating layer is selected for the calculation in Fig. 12. The field behind out-coupling DOEs is shown in Fig. 12. The luminance at detector are ${\text{L}}_{\text{v}\text{,min}}$ =0.0851 cd/m² and ${\text{L}}_{\text{v,max}}$=0.0891 cd/m² respectively.

By analyzing the 50 pupil out-coupled field shown as Fig. 13, the single pupil transmittance — the ratio of $\bar{\text{I}}$ to $\:{\text{I}}_{\text{0}}$ — and exit pupil extension out-coupling efficiency uniformity (EPE uniformity) are 0.7435% and 97.68%, respectively. Considering a total of 50 exit pupils extended, the transmittance of the optical waveguide is 37.17%.

Fig. 12

Field tracing result of double layer waveguide system at different plane. 1st and 2nd rows are amplitude and phase of field in x-domain, respectively. 3rd row is amplitude in of field in k-domain.

Fig. 13

Footprints and intensities of duplicated pupils of field.

Fig. 14

Simulation of imaging by a measurement lens. (a) Optical system diagram with imaging process (b) Field tracing result at back focal plane of measurement lens with focal length as 200 mm.

The imaging optical setup modeling for simulation is shown in Fig. 14(a). By analysis of the imaging results of lenses with focal length as 200 mm. It shows the larger image size with larger focal length. The field tracing result in imaging plane is shown in Fig. 14(b). From the result of field tracing, FOV could be calculated by the ratio of image size and focal length of inserted lens as 53° × 53° which is same as the in-coupling optical information. The luminance at detector are ${\text{L}}_{\text{v,min}}$=0.6633 cd/m² and ${\text{L}}_{\text{v,max}}$=0.7865 cd/m². Therefore, the FOV imaging efficiency uniformity, which is the luminance uniformity at detector, is 91.50% calculated by Eq. 8.

Experiment validation

Fig. 15

SEM results of double layer diffractive optical element (a) DOE layer (b) grating.

Fig. 16

(a) Diagram of optical waveguide combiner image system (b) Optical system in laboratory (c) Image result of double layer coupled diffractive waveguide by camera.

Actually, both of in-coupling and out-coupling double layer DOE consists of the binary diffractive optical element and rectangular grating. By the MEMS technology, diffractive optical elements above are fabricated with the test results of SEM shown in Fig. 15. However, due to the poor electrical conductivity of the material, phenomena such as electron accumulation occurred in the SEM results, which reduced the observation quality. The diagram of double layer coupled diffractive waveguide is shown in Fig. 16-(a) & (b). The image result taking by camera is shown in Fig. 16-(c). By analysis the imaging results, the uniformity of FOV reaches 88.96% and the uniformity within the eye movement range is 95.23%.

Comparison

Fig. 17

Comparison between double layer waveguide combiner and original waveguide combiner.

From the results, it is evident that the bilayer-coupled diffraction optical waveguide demonstrates several advantages: it theoretically supports a larger field of view (FOV) range as 90° × 90° (diagonal 180°), with simulation results indicating that under a large FOV of 53° × 53°, both the brightness uniformity of the FOV and the uniformity within the eye movement range exceed 90%. The field-of-view (FOV) uniformity, indicating the consistency of images at the detector, registers at 91.50%. In contrast, the uniformity throughout the eye movement range, referring to the energy uniformity post-out-coupling of diffractive optical elements (DOEs), achieves 97.68%. The out-coupling area measures 32.0 mm horizontally, while the eyebox extends 20.45 mm in the same direction, with an eye relief of 10 mm.

Figure 17 presents a radar chart comparing the bilayer-coupled diffraction optical waveguide with existing optical waveguides design in multiple aspects. The data for the origin AR waveguide, specifically the Microsoft HoloLens 2, is derived from the analysis of the test results presented by Kaul Kuttag²². and the data from three other designs referenced in articles^18,20,21, are examined utilizing Eq. 8.

When addressing the design complexity for a field of view (FOV) of 53° × 53°, the in-coupling grating must effectively manage diffraction efficiency across all air incident angles. Similarly, out-coupling gratings require a balance of diffraction efficiency for all angles within the waveguide while considering varying exit pupils. This paper introduces a double layer waveguide design that simplifies the process. The in-coupling grating layer only needs to account for a single incident angle, while the out-coupling grating primarily focuses on optimizing efficiency for different exit pupils with that same angle. This innovation notably reduces the spectrum range involved in grating design and optimization. Consequently, the optical design presents less complexity compared to the original waveguide, resulting from the diminished grating design spectrum while maintaining the same FOV.

Given the complexities of actual manufacturing processes, the structure can be produced without particularly sophisticated techniques. The initial waveguide design utilizes slanted grating-type surface relief grating, which can be created via lithography and etching for in-coupling, turn coupling, and out-coupling. The double-coupled waveguide integrates Fresnel-type diffractive optical elements and surface relief grating for both in-coupling and out-coupling, maintaining consistency for turn coupling. Both the Fresnel-type diffractive optical elements and surface relief grating can be manufactured using lithography and etching technology, eliminating the need for additional complicated fabrication steps. Hence, the fabrication difficulty slightly increases compared to the original waveguide, as the two types of diffractive optical elements require production.

Conclusion

In a nutshell, a double layer coupled waveguide has been proposed. Several key performance indicators have been numerically evaluated. FOV is 70°, exit pupil area is 32$\:\times\:$16 mm², eyebox area is 20.45 × 4.45 mm² with eye relief as 10 mm, waveguide combiner transmittance is 37%, eye box uniformity is 97.68%, FOV imaging efficiency uniformity is 91.50%.

This paper proposes a method for optical information transmission using a bilayer-coupled diffraction optical waveguide with wavefront modulation, which theoretically increases the field of view (FOV) range of the optical waveguide to 90° × 90° (diagonal 180°). Based on this proposed method, we designed a double layer coupled diffractive waveguide combiner for a large FOV and analyzed its optical information transmission efficiency and imaging performance without the addition of light source compensation. The results indicate that the efficiency uniformity within the FOV as 70° is improved to over 90%, and the pupil expansion uniformity of the bilayer-coupled diffraction optical waveguide is also increased to over 90%.