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Abstract
We propose a two-dimensional exit pupil expansion (2D-EPE) design of a diffractive waveguide (DW) based on polarization volume grating (PVG). The designed waveguide structure and pupil expansion principle are introduced in this paper. The light propagation behavior and available field of view (FoV) of the proposed waveguide are investigated by simulations. In addition, the waveguide sample based on the proposed design is prepared, and an imaging system based on a monochromatic MicroLED projector is built for AR imaging experiments. The experimental results show that the prepared waveguide system can achieve a clear AR display with a diagonal FoV of 30° and obtain an exit pupil magnification of nearly 20 times compared to the entrance pupil size. The optical imaging efficiency was measured to be 3.85%, and the backward light leakage rate was as low as 8.7%. This work further enhances the feasibility and practicality of the PVG-waveguide technology and provides a promising candidate for AR-DW applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Diffractive waveguides (DW) are currently receiving increasing attention as an optical solution for augmented reality (AR) display. With thinness and expandable exit pupil characteristics, the DW solution can effectively reduce the system volume and increase the size of the eye box, which shows great potential in various AR application scenarios, such as head-up displays (HUDs) and near-eye displays (NEDs) [1,2].
As one of the most significant features and advantages, exit pupil expansion of the DW system can be categorized into two schemes in the implementations: one-dimensional and two-dimensional exit pupil expansions (1D-EPE and 2D-EPE). The basic structure and the light propagation principle of a 1D-EPE DW are shown in Fig. 1. Such a waveguide structure has two coupling gratings whose grating vectors in the waveguide plane are parallel and equal in magnitudes, performing as the in and out-couplers, respectively. The in-coupling grating diffracts light from the air with diffractive angles larger than that of the total internal reflection (TIR) in the waveguide medium. The light is trapped and propagated with low loss in the waveguide medium under the TIR condition. Eventually, the propagating light will be diffracted by the out-coupling grating and coupled out of the waveguide medium again. By adjusting the local distribution of diffraction efficiency, it is possible to make the out-coupling grating diffract only part of the light energy, and the rest of the light can continue propagating along the waveguide. With continuous propagations and repetitive diffractions, the light is continuously duplicated and coupled out of the waveguide at the out-coupling area to achieve an expanded exit pupil. Due to the single direction of the grating vector in the waveguide plane, such a waveguide scheme can only achieve the exit pupil expansion in one dimension. In the non-expanding direction (y-direction in Fig. 1), the exit pupil size will decrease rapidly with increasing propagation distance (see the dashed frame in Fig. 1(b)). As a result, a 1D-EPE waveguide usually requires an elongated entrance pupil whose size along the non-expanded direction is much larger than that of the expanded direction to obtain a sufficient output eye box size, which significantly increases the volume, weight, and the design difficulty of an imaging projector.
Fig. 1. The basic structure and the light propagation of a 1D-EPE DW. (a) The lateral view. (b) The perspective view. The black dashed frame indicates the change in pupil size during propagation.
In contrast, a 2D-EPE system enables the exit pupil expansion in the entire waveguide plane. A typical “L-shaped” 2D-EPE structure is shown in Fig. 2(a) [3,4]. An additional steering grating is included in the waveguide system, which can deflect the propagating light in the waveguide plane (xy-plane). Due to the existence of the steering grating, the grating vectors of the in and out-coupling grating can no longer be parallel in the waveguide plane, which means the replication and expansion of light can be conducted along two different directions in sequence.
Fig. 2. The basic structure and the light propagation of a 2D-EPE DW. (a) The “L-shaped” scheme. (b) The 2D out-coupling grating scheme. The upper right corner shows the k-vector diagram, and the red arrow indicates the grating vectors of the coupling grating in the waveguide
In the basic “L-shaped” structure, all three coupling gratings can be one-dimensional (1D) gratings, and light will pass through the three gratings in sequence to achieve a 2D expansion. In contrast, another type of 2D-EPE structure uses a 2D crossed grating to combine the function of steering and out-coupling gratings. As shown in Fig. 2(b), such a crossed grating contains two primitive vectors ${\textrm{u}_\textrm{1}}$ and ${\textrm{u}_\textrm{2}}$, which can steer the propagating light and simultaneously expand the exit pupil in different directions. Compared to the ‘L-shaped’ scheme, such a structure has some apparent advantages, such as smaller waveguide size, less diffractive interactions loss, and better fabrication tolerance, which is beneficial for both high imaging quality and low fabrication cost [5].
However, the current waveguide devices employing the above two 2D-EPE schemes generally have problems with low light efficiency and serious backward light leakage (also known as the “bright eyes” problem [6]). Improving the diffraction performance of coupling gratings is a direct way to solve the above issues. In most current implementations, surface relief gratings (SRGs) are applied as waveguide coupling gratings. Theoretically, an SRG-based waveguide has a high degree of design freedom. It can achieve desired diffractive efficiency and output uniformity by controlling the morphology of the grating units, such as height, duty cycle, slanted angle, etc. However, due to the current preparation processes and cost limitations, realizing the optimal morphology with mass production for SRG-couplers is challenging [6], which means current SRG-couplers difficult to achieve efficient single-order diffraction while suppressing unwanted diffractive orders.
Polarization volume grating (PVG) was proposed in 2016 as a new type of grating element [7,8]. As a volume grating, PVG can achieve a high diffraction efficiency for single diffraction order (−1st or +1st) in the Bragg domain (operating bandwidth) without complex surface morphology modulation. Compared to conventional volume holographic gratings (VHG) [9–11], PVG has a much greater refractive index modulation contrast, which allows for wider angular and wavelength bandwidth. In addition, PVG introduces a unique polarization selectivity, providing a new design dimension and freedom for applications. As a liquid crystal grating, PVG also has potential dynamic modulation properties, and the diffraction performance can be further enhanced by superposition and local period control methods [12]. Therefore, the potential of PVG as a waveguide coupler has been widely recognized [13,14]. For AR applications, the PVG-waveguide solution is expected to facilitate improved optical efficiency and suppress optical leakage while providing acceptable FoV and color performance for DW systems.
In recent years, researchers have conducted comprehensive research on PVG in various aspects, such as physical models [15–18], simulation methods [19–21], multiplexing technology [22,23], fabrication processes [24–26], optimization methods [27,28], etc. In 2018, we prepared the first PVG-waveguide prototype system with 1D-EPE function to achieve a full-color AR imaging, which validated the feasibility of the PVG waveguide scheme for AR applications [29]. To further enhance the practicability and performance of PVG-waveguide, a 2D-EPE design for PVG-waveguide is proposed in this paper. Such a PVG-based waveguide design is not only size-compact but also expected to feature higher optical efficiency, lower backward light leakage, high transmittance, and large exit pupil size. A prototype with the proposed design also has been demonstrated in this paper. The experiment results confirm the feasibility of the design and further advance the development of PVG waveguide technology in AR applications.
2. Structure and multiplexed design of polarization volume grating
In the proposed 2D-EPE waveguide design, PVGs are applied as the coupling gratings. The physical structure and diffraction properties of PVG have been extensively studied, and the simplified model is illustrated in Fig. 3(a) [15,19]. Different from the traditional volume grating, the periodic refractive index modulation in a PVG is anisotropic. As the host material, liquid crystal molecules rotate periodically in the three-dimensional space of the grating. The periodicity along the grating plane (${{d}_{p}}\; in$ xy-plane) is determined by the pattern of the alignment layer, while in the direction perpendicular to the grating plane, periodic helical rotation is generated by the chiral doping. Under the combined effect of the alignment anchoring force and the chiral twisting force, the helix axis will be tilted to reach the minimized elastic energy in LC material [16,17]. When the grating reaches a sufficient thickness, efficient volume grating diffraction can be achieved, and the Bragg condition can be expressed as:
Fig. 3. (a) The simplified structure of the PVG. (b) Polarization selectivity characteristics of a PVG. (c-e) Schematic diagram of the PVG multiplexing design, including (c) the realization of efficient diffraction for unpolarized image sources and further extension of (d) wavelength and (e) angular operating bandwidth. Wherein the LCP is right-handed circular polarization, RCP is left-handed circular polarization, and NP indicates non-polarization.
Figure 3(b) introduces the polarization selectivity of a PVG. Only the circularly polarized incidence with the same helix handedness as the PVG will be diffracted (right-handed, as an example in the figure). PVG layers with different handedness can be composited to allow efficient diffraction for non-polarized incident light, as shown in Fig. 3(c) [23]. Such a multiplexing design is essential to ensure the optical efficiency of a waveguide system using non-polarized imaging sources such as micro-OLED, micro-LED, or DLP projectors. Based on the same principle and preparation process, the angular and wavelength bandwidth of the PVG can also be adjusted or further expanded by compounding multilayers of PVG with different chiral doping concentrations, as shown in Fig. 3(d-e). It should be noted that for AR waveguide applications, the composite PVG layers used in the same waveguide layer should have the same period ${{d}_{p}}$ in the waveguide plane to ensure the same diffraction dispersion and avoid ghosting in AR imaging.
The PVG-coupler multiplexing design illustrated in Fig. 3(b-e) can effectively improve the diffraction performance of the PVG, which will benefit the display performance of the waveguide system in terms of efficiency and FoV. Based on these PVG enhancement methods and preparation processes, we proposed a PVG waveguide multiplexing design in this paper to achieve 2D-EPE functionality and further enhance the performance and applicability of PVG waveguide technology.
3. 2D-EPE PVG waveguide design
The structure of the proposed PVG-based 2D-EPE waveguide is illustrated in Fig. 4(a). Four PVGs are placed on the inner surface of two waveguide substrates. The two substrates are filled with the optical adhesive with the same refractive index as the substrates to form a waveguide piece. In this design, two PVGs with opposite chiral handedness (left- and right-handedness) combine into an in-coupler ${\mathbf{G}_{i}}$. The two in-coupling PVGs have the same periodicity (grating vector) but can diffract left-handed and right-handed circularly polarized light, respectively. The out-couplers combined by two PVGs (${G_{o1}}$ and ${G_{o2}}$) with opposite chiral handedness, and their grating vector are mirror-symmetrical with respect to the y-axis. It is worth noting that both in- and out-coupling gratings contain two PVG components with different chiral handedness (as shown in Fig. 4(a)), which makes the waveguide structure can couple the non-polarized light with high efficiency [23]. Since the non-polarized light can be decomposed into two orthogonal circularly polarized lights with equal intensity but random phase difference, the two PVG components of the in-coupling PVGs will be able to diffract the left- and right-handedness circularly polarized light components, separately. The resulting diffracted light will be coupled into the waveguide and remain unpolarized state for propagation. When the propagating non-polarized light reaches the out-coupling grating, the two orthogonally polarized components of the light will again be diffracted by the two out-coupling PVGs with different chiral handedness respectively, and eventually coupled out of the waveguide.
Fig. 4. (a) The structure of the proposed PVG-based 2D-EPE waveguide. “Left” and “Right” denote the different PVGs with left and right chiral handedness respectively. (b) The shape of the designed waveguide and the designed grating vector components of the PVG couplers in the waveguide plane.
The components of the grating vector in the waveguide plane (xy-plane) for designed PVG-couplers are shown in Fig. 4(b), which satisfies the following relation:
In Eq. (2), the ${\mathbf{G}_{{ip}}}$, ${\mathbf{G}_{{op1}}}$ and ${\mathbf{G}_{{op2}}}$ are the projected grating vector components in waveguide plane of the in- and out-coupling PVGs. Vector of in-coupling PVG (${\mathbf{G}_{{ip}}}$) is parallel to the + y, and vectors of two out-coupling PVGs (${\mathbf{G}_{op1}}$ and ${\mathbf{G}_{{op2}}}$) are +60 and −60 degrees from the -y-direction, respectively. The vector magnitudes of the three grating vectors are equal, and the sum of grating vectors in the waveguide plane is designed to 0 to eliminate the diffraction dispersion. As a result, the grating vectors in the waveguide plane can be determined by the equation of
The light propagation and the principle of pupil expansion for the proposed waveguide structure can be analyzed in the k-vectors diagram [6], which is shown in Fig. 5. The four rectangles indicate the range of light vectors in FoV after each diffraction, and the four points ${{\boldsymbol k}_{ip}}$, ${{\boldsymbol k}_{1p}}$, ${{\boldsymbol k}_{2p}}$ and ${{\boldsymbol k}_{3p}}$ represent the light vectors of the central FoV during the propagation. The gray ring represents the TIR region, and light vectors in this region can propagate in the waveguide medium under the TIR condition.
Fig. 5. The k-diagram of the proposed 2D-EPE waveguide system. The gray ring represents the TIR region. The colored arrows represent the projection of the grating vector components of the in and out-coupling PVGs in the waveguide plane.
As the propagation paths illustrated in Fig. 5, after being diffracted by the in-coupling PVG, the light vector acquires the momentum ${\mathbf{G}_{{ip}}}$ in the y-direction and is trapped in the waveguide medium with TIR propagation. The light vector will then obtain two different grating momentum ${\mathbf{G}_{{op1}}}$ and ${\mathbf{G}_{{op2}}}$ at the out-coupling PVGs, and deflect in the + x and -x-directions, respectively. Eventually, the light vector in both propagation directions will be diffracted again by the other grating component, restored to the original incident state, and coupled out of the waveguide medium.
To present a clearer picture of the steering and replication process of light rays within the waveguide system, we simulated the light propagation based on the ray-tracing method, and the results are shown in Fig. 6. For clarity of illustration, only the case of normal incidence is included. It can be seen that the light from the in-coupling PVG, which initially propagates in the + y-direction, is deflected in the + x and -x-directions at the out-coupling PVGs, respectively, while continuously splitting, replicating, and is eventually coupled out of the waveguide at different spatial locations.
Fig. 6. The propagation behavior of light in the proposed waveguide structure. (a) top view, (b) perspective view, and (c) lateral view. For clarity, only the case of normal incidence is included.
From the lateral view of the waveguide propagation (Fig. 6(c)), interactions between the propagating light and the two out-coupling PVGs are demonstrated. The propagating light from the in-coupling PVG is first diffracted by one of the out-coupling grating components (${\mathbf{G}_{{o2}}}$ as an example), deflected in the -x-direction and maintained TIR propagation in the waveguide. After a TIR bounce, the deflected light will be diffracted again by the ${\mathbf{G}_{{o1}}}$ from the downside, and leave the waveguide medium at the same angle as that of the incidence.
The proposed waveguide structure enables efficient 2D-EPE light propagation, which depends on the efficient single-order diffraction characteristics of the PVG couplers. As shown in Fig. 6, the propagating light is only split into two rays of transmitted-0th and reflected-1st orders after diffracted by the out-coupling PVGs. In addition, the out-coupled light leaves the waveguide only from one side of the waveguide. For AR-waveguide application, such diffraction characteristics avoid stray light and efficiency degradation caused by unwanted diffractive orders and can suppress the backward light leakage (leave toward the -z-direction only in Fig. 6).
4. PVG-couplers design
In contrast to a thin grating, PVG has not only a grating vector component in the grating plane (xy-plane) but also in the direction perpendicular to the grating surface (z-direction). When the diffracted momentum from these two orthogonal grating vectors is resonantly matched, efficient Bragg single-order diffraction can be achieved.
The workflow and the desired diffraction features of the in and out-coupling PVGs in the proposed waveguide system are shown in Fig. 7. The periodicity of PVGs on the grating plane is first determined by Eq. (3), wherein the diffraction angle ${\theta _o}$ should satisfy the TIR condition of the waveguide medium, which can be expressed as:
The periodicity perpendicular to the grating surface can be obtained based on the principle of vector conservation between the diffracted light and the grating vector in the z-direction. As a result, the grating vector for the in-coupling PVG can be determined by the equation of
For two out-coupling PVGs, each PVG needs to perform two functions. The first is to deflect the propagating light from the in-coupling grating in the xy-plane. The second is to couple the deflected light from the other out-coupling PVG out of the waveguide. As shown in Fig. 7(b-e), ${\boldsymbol{k}_{\boldsymbol{1}}}$ is the diffracted light vector from the in-coupling PVG with diffractive angle ${\theta _o}$, ${\boldsymbol{k}_{\boldsymbol{2}}}$ and ${\boldsymbol{k}_{\boldsymbol{3}}}$ are the diffracted light vector deflected by the out-coupling PVGs, which have the same elevation angle as that of ${\boldsymbol{k}_{\boldsymbol{1}}}$. The ${\boldsymbol{k}_{\boldsymbol{2}}}^\prime$ and ${\boldsymbol{k}_{\boldsymbol{3}}}^\prime$ are the light vectors of deflected light after an odd number of TIRs bounces, which are opposite to the ${\boldsymbol{k}_{\boldsymbol{2}}}$ and ${\boldsymbol{k}_{\boldsymbol{3}}}$ in the z-direction.
Fig. 7. The workflow and the desired diffraction features of the in and out-coupling PVGs in the proposed waveguide system.
Take one of the out-coupling PVGs (out-coupling PVG1) as an example. Such a PVG-coupler is designed to have high-efficient diffraction for both the ${\boldsymbol{k}_{\boldsymbol{1}}}$ (propagating light from in-PVG) and ${\boldsymbol{k}_{\boldsymbol{3}}}^\prime$ (deflected light by out-coupling PVG2). This requires that the out-coupling PVG1 contains two different longitudinal grating vectors to generate two Bragg regimes for different angles of incidence. Such diffraction properties can be achieved by stacking two PVGs layers with different longitudinal periods (${d_{\boldsymbol{z}}}$ and ${d^{\prime}_{\boldsymbol{z}}}$ in Fig. 8). In fabrication, the longitudinal periods of the two PVG layers are adjusted by the concentration of the chiral dopant, respectively. The bottom PVG layer can be served as the alignment layer of the top layer, and the period in the grating plane (xy-plane) of the two PVGs can be automatically consistent to ensure the same diffraction dispersion.
Fig. 8. Schematic diagram of stacked PVG for out-coupling PVGs, which makes the out-coupling PVGs have both functions of deflecting and out-coupling for propagating light.
As a result, the longitudinal grating vectors of the out-coupling PVGs illustrated in Fig. 7 can be determined by
Due to the relationship of $|\mathbf{G} |\mathrm{\ =\ 2\pi /d}$, the period length d can be obtained from the calculated grating vector G, and the structure parameters of all PVG-couplers can be determined.
To verify the feasibility of the proposed waveguide structure, we designed and prepared a waveguide sample to realize an AR-waveguide display by using a green MicroLED imaging projector with a central wavelength of 528 nm. The designed structure parameters for the in and out-coupling PVGs are listed in Table 1. Wherein the ${{d}_{p}}$ is the horizontal period (in xy-plane), the ${{d}_{z}}$ indicates the longitudinal periods along the z-direction, the $\mathrm{\Lambda}$ is the corresponding Bragg period, and $\varphi $ is the tilt angle of the grating vectors.
Table 1. The structure parameters of PVG-couplers used in simulations and experiments
The refractive index of the waveguide is 1.57, which is consistent with the average refractive index neff of PVG material (ne = 1.687, no = 1.508) we used in experiments. Based on such a configuration, the diffraction angle ${\theta _o}$ for normal incident light at 528 nm is designed to be 55.4° in the waveguide.
An electromagnetic model is built by using the commercial software COMSOL to simulate the angular bandwidth of in and out-coupling PVGs. Also, the variation of possible FoV in the k-vector diagram (see Fig. 5) is investigated. In the simulation, a uniform intensity distribution covering a 40° diagonal FoV (4:3) is used as the incident light of in-coupling PVG to simulate the input from the projector, as shown in Fig. 9(a). As a result, the output intensity distribution from the out-coupling PVGs is demonstrated in Fig. 9(b). After undergoing multiple diffractions in the process described in Fig. 7. The output FoV from the out-coupling PVGs is compressed to about 30° due to the operating bandwidth of the gratings. Therefore, a MicroLED monochrome projector with 30° diagonal FoV is prepared as an imaging source for the prototype.
Fig. 9. The variation of FoV in the k-vector diagram, (a) A uniform intensity distribution covering a 40° diagonal FoV (4:3) is used as the incident light of in-coupling PVG to simulate the input from the projector and (b) The intensity distribution of the output from the out-coupling PVG after multiple diffractions during waveguide propagation.
5. Waveguide sample preparation
The fabrication processes of the PVG-couplers are shown in Fig. 10. Two optical flat glasses with a refractive index of 1.57 and thickness of 0.7 mm were used as waveguide substrates. The solution of azo-dye brilliant yellow [30] (0.5 wt.% BY in DMF) is coated on the pre-cleaned substrate through the slit to generate a photo-alignment (PA) layer. The sample with the PA layer was then subjected to polarized interference exposure. In our experiment, a 457 nm laser was used as the recording light. Two opposite-handed circularly polarized beams are overlapped on the sample with an angle of 68° to generate the required polarized interference patterns with a horizontal period of 408.62 nm in the PA layer. The orientation of the interference pattern and grating vector in the waveguide plane can be adjusted to meet the requirement of in and out-coupling PVGs (Eq. (3)) by employing a rotary stage. The intensity of each path beam for interference is equal, and the exposure dosage is 1 J/cm2.
Fig. 10. The fabrication processes of the PVG-couplers. PA: photo-alignment, CLCRM: cholesteric liquid crystal reactive monomer, LCP: left-handed circular polarization, and RCP: right-handed circular polarization.
The cholesteric liquid crystal reactive monomer (CLCRM) solution was then coated onto the PA layer. Under the combined anchoring force from the PA layer and twist force from the chiral dopant, the liquid crystal molecules will self-assemble into the desired PVG structures. A fixed PVG polymer film will be generated after the UV curing. The cured PVG film can be used as a new PA layer and provide the surface anchoring force for the CLCRM molecules which is coated on it. For out-coupling PVG, two layers of CLCRM solutions with different chiral doping concentrations will be sequentially coated to achieve the deflection and out-coupling of the propagating light at the same time.
In this work, the reactive mesogen RM257 (ne = 1.687, no = 1.508) with chiral dopant R5011 (right-handed)/S5011 (left-handed) and Irgacure 651 have been used as the CLCRM precursor and photo-initiator, respectively. The propylene glycol methyl ether acetate (PGMEA) has been employed as a solvent to dissolve all the solute materials after oscillation [31] with the proportion of 1:5. The mass fractions of each solute material for proposed PVG-couplers are listed in Table 2.
Table 2. The mass fraction of materials for PVG-couplers (wt. %)
The fabrication process of the waveguide is shown in Fig. 11. PVG couplers with opposite handedness will be fabricated on the two waveguide substrates, respectively. The optical adhesive (Norland 61) is used as the filler to bond the two substrates into one waveguide sheet (thickness of 1.4 mm). The 10 µm silica micro-spheres are evenly scattered on the waveguide edges as spacers. After compression and UV curing, a waveguide piece with uniform thickness can be prepared.
6. Results and discussions
The appearance of the prepared waveguide is shown in Fig. 12(a). The size of the in-coupling PVG is a $\mathrm{6\ \times 6\;\ m}{\textrm{m}^2}$, while the size of the out-coupling PVG is about $\mathrm{25\ \times 24\;\ m}{\textrm{m}^2}$. Figure 12(b) shows the photograph of light propagation and output of the prepared waveguide when a laser beam incident vertically into the in-coupling PVG. The area enclosed in the red dashed line in Fig. 12(b) is the projection of the output light on a black receiving plate. It can be seen that after passing through the waveguide, the single laser beam is duplicated in the waveguide plane, and expanded into a two-dimensional lattice output, which can preliminary demonstrate the 2D-EPE function of the prepared waveguide. Figure 12(c) presents the appearance of the MicroLED projector prepared for the AR imaging experiment. Such a projector utilizes a 0.13” green MicroLED display (JBD AMµLED) with a resolution of 640$\mathrm{\ \times }$480. The designed exit pupil diameter of the projector is 6 mm, and the diagonal FoV is 30°.
Fig. 12. (a) The appearance of the prepared waveguide. (b) The photograph of light propagation and output of the prepared waveguide when a laser beam incident vertically into the in-coupling PVG. The area enclosed in the red dashed line is the projection of the output light on a black receiving plate. (c) The appearance of the MicroLED projector prepared for the AR imaging experiment.
The photographs of the imaging test system and the AR imaging results are shown in Fig. 13. Figure 13(a) and (b) demonstrate the output difference between the 1D-EPE and the 2D-EPE PVG-waveguide captured from a distance of 100 mm. As shown in Fig. 13(a), since the 1D-EPE waveguide extends the exit pupil only in one dimension, the exit pupil behaves as a thin strip when the entrance pupil diameter is 6 mm. In contrast, for the prepared 2D-EPE waveguide, the exit pupil is extended in two dimensions at the out-coupling area (see Fig. 13(b)), achieving a pupil magnification of about 20 times. When the eye relief is 18 mm, an eye box size of 18.2 mm × 17.3 mm can be obtained.
Fig. 13. The output difference between the (a) 1D-EPE and the (b) 2D-EPE PVG-waveguide with the same imaging projector (entrance pupil diameter is 6 mm). Photos were taken at a distance of 100 mm from the waveguides. (c) Photograph of the AR imaging result, captured at a distance of 18 mm from the waveguide.
The AR imaging result is shown in Fig. 13(c). A camera was placed in front of the out-coupler with an eye-relief of 18 mm, and a green virtual image with a 30° diagonal FoV (4:3) merged into the real scene was captured.
The optical efficiency of the proposed system was initially evaluated by the luminance meter (Konica Minolta CS-200). The waveguide input luminance of a full-size green test image from the MicroLED projector was measured as 32086 nit (cd/m2), and the output luminance in the center of the out-coupling area was 1235.2 nit, which corresponds to the optical imaging efficiency of 3.85%. If the incident energy of the waveguide is evaluated by the luminous flux (lm), the corresponding value for our MicroLED imaging engine is 2.8 lm, and the calculated optical efficiency is about 441 nit/lm [6].
The backward light leakage was also measured on the opposite side at the same position of the waveguide, with a measured value of 118.1 cd/m2. The ratio of forward luminance to backward luminance is about 10.5:1, corresponding to a light leakage rate of about 8.7%. Meanwhile, we measured the brightness of the light from a D65 source passing through the out-coupling PVG and obtained a transmission of 68%, indicating a low scattering and acceptable transmission of the prepared waveguide for ambient light.
This work preliminarily validates the feasibility of the proposed 2D-EPE design. Further optimization work, such as FoV and exit pupil uniformity enhancement, are not included in this paper. However, some existing optimization methods with outstanding ideas for PVG or SRG-based waveguides can also be applied to this design, such as using the compensator layer to control the polarization state variation during the light propagation [27] or adding a polarization management layer (PML) in the out-coupling region to adjust the local diffraction efficiency [32], which can improve the output uniformity. Also, the FoV of the waveguide system can be further expanded by methods such as PVG multilayer strategies [22,23] or waveguide multi-channel structure [33,34], etc. In addition, schemes such as multi-color waveguide stacking commonly used in diffractive waveguide technology can also be applied to the proposed 2D-EPE PVG waveguide structure in the future to achieve the full-color AR display [29,35].
7. Conclusions
In summary, we have proposed a 2D-EPE scheme for PVG-waveguide. The structure of the designed waveguide was introduced in detail. The light propagation behavior and available FoV of the proposed waveguide scheme were investigated. In addition, a 2D-EPE PVG-waveguide sample was prepared, and an AR imaging system based on a monochrome MicroLED display was built to validate the feasibility of the prepared waveguide. The results show that the built AR imaging system with the prepared waveguide can achieve a pupil magnification of nearly 20 times. A clear virtual image display with a 30° diagonal FoV and optical imaging efficiency of 3.85% was achieved. The backward light leakage rate was calculated as low as 8.7%. In addition, the ambient light transmission in the out-coupling area was measured as 68%. This work further enhances the feasibility of PVG for diffractive waveguide technology and provides a new technical path and promising candidates for AR applications.
Funding
National Natural Science Foundation of China (62105060); Fundamental Research Funds for the Central Universities (2242021K1G005); Basic Research Program of Jiangsu Province (BK20212006).
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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