After decades of device innovation and vibrant advances in microdisplay technologies, ultra-compact imaging optics, and high-speed digital processors, augmented reality (AR) has evolved from a futuristic concept to a tangible and pervasive technology. By seamlessly blending the projected virtual content with real-world scenes, AR enhances our perception and interaction with environment, opening exciting possibilities for metaverse, digital twins, and spatial computing. AR displays have enabled widespread applications in smart education and training, smart healthcare, navigation and wayfinding, gaming and entertainment, and smart manufacturing, just to name a few.

Since its primitive conception in the 1990s, AR has made significant strides, particularly with the emergence and development of waveguide-based AR displays. These displays enable wearable systems to be lightweight and have a slim form factor while maintaining high optical performance. Furthermore, the rapid development of couplers, including partial reflective mirrors, surface relief gratings (SRGs), volume holographic gratings, polarization volume gratings (PVGs), metasurfaces, etc., has dramatically improved the optical performance of AR displays over the past few decades

While waveguide displays have dramatically reduced the form factor, the low efficiency of optical combiners, particularly the diffractive waveguide combiners, remains a major concern

The low optical efficiency primarily stems from four aspects, all related to the nonuniformity issues, such as color nonuniformity, FoV nonuniformity, and eyebox nonuniformity

Fig 1  Mechanisms of light loss in a waveguide-based AR display.

a Blue light absorption during propagation in a high-index waveguide substrate. b Effective pupil expansion process for a certain field angle in a traditional 2D exit pupil expansion (EPE). c Angular response for unoptimized and optimized SRGs. d Light loss due to multiple interactions at the diffractive in-coupler

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1 and geometric in-coupler. e Multiple interaction processes between the incident beam and the intensity-type VHG in-coupler

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The second major source of optical loss occurs during the pupil expansion process. As illustrated in Fig. 1b, a significant portion of light is wasted due to the spatially limited bandwidth modulation capability of the folding couplers and out-couplers

The third major optical loss mechanism is the limited angular and spectral bandwidth of the couplers in the high diffraction efficiency region

As depicted in Fig. 1d, the fourth major cause of low-efficiency results from multiple interactions at the in-couplers

Light leakage at the in-coupler is a longstanding issue over the past few decades

As depicted in Fig. 1d, if the size ($$W$$) of the in-coupler is greater than the total internal reflection (TIR) propagation distance $$d=2t\ast \tan \left(\theta \right)$$, where t represents the waveguide thickness and $$\theta$$ denotes the TIR angle inside the waveguide, then the in-coupling light will interact with the in-coupling grating two or more times. In practical terms, achieving a continuous eyebox necessitates that $$W$$ > $$d$$. Otherwise, users may not perceive digital information in certain regions within the eyebox. Thus, even if the width of the in-coupler can be reduced by increasing the collecting power of the collimation lenses or shrinking the emission cone of the microdisplay panels, the TIR angle $$\theta$$ or waveguide thickness $$t$$ must be decreased accordingly to maintain a good continuity throughout the eyebox. Consequently, efficiency loss and poor uniformity throughout the FoV persist as significant challenges. For example, in a single-color waveguide display with a $${70}^{\circ }$$ (45°(H) × 55°(V)) FoV in a substrate with an index n = 2.0, over 70% of the incident light is lost due to the multiple interactions at the in-coupling process for extreme field angles, resulting in a 70% drop in FoV uniformity. To boost the FoV uniformity, the overall in-coupling efficiency is compromised. For a full-color, 30°(24°(H) × 18°(V)) FoV waveguide display using a n = 2 substrate, the in-coupling efficiency loss for the blue and red colors at extreme field angles exceeds 73% and 51.5%, respectively, causing a drop in color uniformity of around 45%. To balance both color uniformity and FoV uniformity, the overall efficiency is also compromised. The calculation method for these examples will be discussed in the following section. Therefore, finding a solution to circumvent the tradeoff between in-coupling efficiency, uniformity throughout the FoV, and eyebox continuity is urgently needed.

In this paper, we present the discovery of an anomalous polarization conversion phenomenon in the PVGs. This phenomenon offers an intuitive solution to the abovementioned issue for achieving a high and uniform in-coupling efficiency throughout the entire FoV while maintaining continuous eyebox functionality. To prove concept, preliminary experiments are conducted to validate this polarization conversion process. The experimental results closely align with the Rigorous Coupled-Wave Analysis (RCWA) simulation. Moreover, the in-coupling efficiency limit of a 50° FoV waveguide-based AR display system is enhanced by two times with the first-order polarization conversion in a PVG, compared to conventional couplers. Concurrently, the uniformity throughout the FoV is also improved by 2.3 times. Furthermore, by combining an additional polarization compensation film at the in-coupler, nearly all light can be coupled into the waveguides.

The PVG is a polarization-selective holographic optical element that records the polarization information of two interfering beams comprising a right-handed circular polarization (RCP) and a left-handed circular polarization (LCP). As illustrated in Fig. 2a, PVG features a slanted cholesteric liquid crystal (CLC) structure, where the liquid crystal (LC) directors rotate along the helical axis

Fig 2  Working principles of PVG as in-coupler in waveguide displays.

a Slanted structure of PVG, which reflects LCP and transmits RCP. b PVG functions as a tilted twisted-nematic (TN) LC waveplate when the incident angle of light approaches the Bragg plane. c PVG functions as a tilted TN LC waveplate from the perspective of incident angle by rotating PVG. d 0th order transmission efficiency and (e) Stokes parameter $$S_3$$ of transmitted light varying with the PVG thickness. The birefringence of PVG for simulation is 0.4 ($$n_e=2.0,n_o=1.6$$); input and output media are both glass with $$n_g=$$1.7; horizontal period $${\mathrm{\Lambda }}_x$$ and slanted angle $$\alpha$$ of the PVG are 407 nm and 23.3°; the incident angle $${\theta }_{in}$$ and wavelength $$\lambda$$ are −45° and 532 nm. f Schematic of polarization conversion during the interaction between incident light and PVG without considering phase shift induced by Fresnel reflection

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However, here we discover an anomalous phenomenon that deviates from the abovementioned rule. As depicted in Fig. 2b, when the incident angle in the glass substrate approaches the Bragg plane, the Bragg condition does not hold. Consequently, the PVG functions as a waveplate instead of a grating, altering the polarization state of the incident light. For instance, it converts RCP to LCP when the half-wave condition is satisfied. More specifically, from the perspective of the incident light direction, as shown in Fig. 2c, the PVG resembles a tilted twisted-nematic (TN) liquid crystal waveplate

where $${\mathrm{\Lambda }}_b$$ and $$\alpha$$ represent the Bragg period and the slanted angle of the PVG, $${\theta }_{in}$$ corresponds to the incident angle in the waveguide substrate. To demonstrate the waveplate behavior, the 0th order transmission efficiency and output polarization state are simulated using the RCWA model

Due to these two superior polarization properties, employing PVG as an in-coupler in waveguide displays can dramatically enhance the in-coupling efficiency and uniformity throughout the FoV, while keeping a good eyebox continuity (or uniformity), in comparison with all other traditional in-couplers and metasurface couplers. Specifically, as illustrated in Fig. 2f, the incident LCP light is deflected into the waveguide substrate during the first interaction and retains its polarization state based on the selectivity rule of PVG. After the first interaction, following TIR, the polarization state of light becomes RCP (the 1st green arrow) due to the reversed propagation direction. During the second interaction with the in-coupler (PVG), the light undergoes polarization conversion without altering its propagation direction, meaning the light turns to LCP if the PVG thickness satisfies the half-wave condition. Subsequently, after another TIR at the top boundary of the PVG, the light becomes RCP, which is then transmitted through the PVG due to its polarization selectivity. Finally, the light can propagate inside the waveguide while maintaining its propagation direction. Consequently, the in-coupling efficiency and uniformity are significantly improved while maintaining a desired eyebox continuity.

However, TIR is accompanied by a non-trivial phase shift as the Fresnel reflection coefficient acquires a non-zero imaginary part

where $${\delta }_s$$ and $${\delta }_p$$ represent the additional phase induced by TIR process, $$n$$ is refractive index of glass substrate, and $${\theta }_{in}$$ denotes the incident angle. This indicates that circular polarization will no longer be pure after TIR because of the phase difference induced by $$s$$ and $$p$$ polarization states. Therefore, the incident light during the second interaction in the above situation is not a pure circular polarization state and the optimal thickness will shift.

To validate the concept, we conducted an experiment using a 532 nm laser source and PVGs with varying thicknesses. We employed reactive mesogen RM257, which possesses a birefringence $$\Delta n$$ = 0.162 at $$\lambda$$ = 532 nm, to fabricate the PVGs with different thicknesses. This was achieved by adjusting the concentration and spin coating speed on a waveguide substrate with n = 1.57. While other liquid crystal materials are also feasible, they may yield different half-wave conditions if they exhibit a different birefringence. The horizontal period $${\mathrm{\Lambda }}_x$$ was set at 411 nm. To accommodate a central wavelength at 532 nm and normal incidence, the slanted angle $$\alpha$$ is approximately 27.83°, determined based on the following Bragg equation:

where $$n_{eff}$$ represents the effective refractive index of the RM257, $${\mathrm{\Lambda }}_b$$ is the Bragg period, $${\lambda }_b$$ is the Bragg wavelength, and $${\theta }_{in}$$ is the incident angle.

Furthermore, Fig. 3 illustrates the experimental results of the diffraction response of PVG at various thicknesses. In Fig. 3a, it is evident that the first-order ($$R_1$$) diffraction efficiency at normal incidence increases with the increased PVG thickness ($$t_{PVG})$$. Simultaneously, using an out-coupling prism, the second interaction (R₀ diffraction order) at a large incidence angle, calculated using $$-{\sin }^{-1}({\lambda }_b/{(\mathrm{\Lambda }}_x\ast n))$$ in the glass substrate, also depends on the PVG thickness, as depicted in Fig. 3b. This dependency agrees well with the RCWA simulation results. Furthermore, the polarization state of the light leakage during the second interaction remains consistent (LCP). This phenomenon further supports our previous analysis. Additionally, the light leakage in two PVGs with different thicknesses was captured by a camera, as shown in Fig. 3c and d. The left and right beams represent light leakage at the first and second interactions, respectively. It is evident that light leakage is strong when $$t_{PVG}=2.85\mu \mathrm{m}$$ but much weaker at $$t_{PVG}=4.1\mu \mathrm{m}$$.

Fig 3  Experimental results of the anomalous polarization conversion in PVG.

a +1st order ($$R_{+1})$$ diffraction efficiency changes with thickness during the first interaction for the incident LCP light. b 0th order ($$R_0$$) diffraction efficiency changes with thickness during the second interaction for the incident RCP light with an extra TIR phase shift. c Light leakage at the PVG as in-coupler for the thickness of 2.85 µm and (d) 4.1 µm

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While the polarization conversion phenomenon has been successfully demonstrated at normal incidence using a laser source, it is crucial to assess its angular performance. By varying the incident angle of the laser source, the angular performance of the second interaction is investigated, as shown in Fig. 4a, which agrees well with the RCWA simulation. Furthermore, an LCoS light engine with a diagonal FoV of 20° was employed to evaluate the angular performance of the polarization conversion in PVG-based waveguide displays. As Fig. 4b, c shows, the waveguide display with a 4.1 µm-thick PVG exhibits a much higher efficiency and better uniformity than that with a 2.85 µm-thick PVG.

Fig 4  Experimental results of angular performance of the anomalous polarization conversion in PVG.

a Angular response of 0th order ($$R_0$$) diffraction efficiency during the second interaction for the incident RCP light with an extra TIR phase shift. Images of 20° FoV captured in a PVG-based waveguide display with the PVG thickness of (b) 2.85 µm and (c) 4.1 µm

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Although the polarization conversion phenomenon in a PVG has been well verified using a laser source and an LCoS light engine, these experiments do not fully demonstrate its full potential due to the limited birefringence ($$\mathrm{\Delta }n$$) and FoV. Therefore, in the following, we will use a reactive mesogen with $$\mathrm{\Delta }n=0.4$$ to thoroughly analyze the potential of the polarization conversion phenomenon in waveguide-based AR displays with a large FoV of 50°.

It should be noted that, similar to a half-wave plate (HWP), the angular bandwidth of the polarization conversion is inherently limited due to dispersion. Additionally, multiple half-wave conditions exist, as depicted in Figs. 2e and 5a. Importantly, as the order of the half-wave condition increases, the angular bandwidth narrows further, as Fig. 5b, c depicts, making it impractical to cover the entire TIR region within the waveguide. However, it is important to note that the light loss typically increases as the TIR angle decreases, indicating that a significant light loss predominantly occurs on one side of the FoV. By satisfying the limited half-wave condition around the minimum TIR angles, a substantial improvement in in-coupling efficiency and uniformity can be achieved.

Fig 5  Response of multiple half-wave polarization conversion in PVG.

a Reflected 0th order diffraction efficiency varying with the PVG thickness. Spectral and angular response of reflected 0th order at PVG thickness of (b) 500 nm (first-order half-wave condition) and (c) 2200 nm (second-order half-wave condition). The birefringence of PVG for simulation is 0.4 ($$n_e=2.0,n_o=1.6$$); input and output media are respectively glass (n_g = 1.7$$)$$ and air; horizontal period $$\left({\mathrm{\Lambda }}_x\right)$$ and slanted angle ($$\alpha )$$ of the PVG are 407 nm and 23.3°; the incident angle $$(\theta )$$ and wavelength $$(\lambda )$$ are −43° and 532 nm

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Next, we further investigate the angular performance of the first-order and second-order polarization conversions in a PVG-based waveguide display with 50° [30° (H) × 40° (V)] diagonal FoV at λ = 532 nm. Both orders demonstrate significant enhancements in in-coupling efficiency and uniformity throughout the entire FoV, surpassing the theoretical in-coupling efficiency limit of conventional diffractive in-couplers.

Before conducting polarization raytracing, the system configuration and parameters must be designed meticulously, including the display panel, collimation lens, in-coupler, and out-coupler. For the light engine, we assume that the in-coupler of the waveguide display (or exit pupil of the light engine) is a circle with a diameter $$W$$= 3 mm, which depends on the design of the collimation lens and the emission cone of the display panel, as depicted in Fig. 6(a). In most waveguide-based displays, the emission cone is typically very small, around ±15°. For our calculations, we employ an ideal lens as the collimation lens. Therefore, the focal length of the collimation lens (CL) can be calculated as follows:

Fig 6  Design of light engine and waveguide combiner.

a Light engine of waveguide displays. b Schematic of light propagation inside a waveguide around in-coupler region. c Cross section of the second interaction between in-coupler and one beam for a certain FoV. $$W$$ represents the diameter of the in-coupler or exit pupil size of light engine, t indicates the thickness of waveguide and $$d$$ represents the TIR propagation distance. d Theoretical in-coupling efficiency limit for the design with a FoV of 50° (30° (H) × 40° (V)) in Table 1

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Moreover, to achieve a diagonal FoV of 50° [30° (H) × 40° (V)], the panel size is set to 3 mm × 4.075 mm. Subsequently, a waveguide substrate with thickness $$t$$ = 0.55 mm and index $$n$$ = 1.7 is utilized for design and simulation. Furthermore, to ensure a continuous eyebox, we assume that the pupil is continuous at the maximum TIR angle $${\theta }_{max}$$. This implies that each TIR propagation distance $$d$$ at the maximum TIR angle is equal to the in-coupler size $$W$$, as illustrated in Fig. 6b, c. Based on following equation:

the maximum TIR angle is around 70°. Therefore, the minimum TIR angle $${\theta }_{min}$$ = 38° and the horizontal period $${\mathrm{\Lambda }}_x\cong 407\mathrm{n}\mathrm{m}$$ of the in-coupler and out-coupler can be derived from the FoV = 50° [30° (H) × 40° (V)]. In summary, all the parameters of this waveguide system are listed in Table 1.

Table 1  Design parameters of light engine and polarization volume gratings in waveguide displays

Parameters	Design value
FoV	50° (30° (H) × 40° (V))
In-coupler size	3 mm
Working wavelength	532 nm
Panel Size	3 mm × 4.075 mm
Focal length of CL	5.6 mm
Refractive index of waveguide	1.7
Thickness of waveguide	0.55 mm
Maximum TIR angle	70°
Birefringence of PVG	0.4
Horizontal period of PVG	407 nm
Slanted angle of PVG	23°

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Due to the multiple interactions between incident light and conventional in-couplers

where $$A_{in}$$ is the area of in-coupler size or the exit pupil area of light engine. For instance, for the left-top corner FoV, it has a maximum in-coupling efficiency limit of 100% since there is no second interaction between the incident light and the in-coupler. As indicated in Fig. 6d, the minimum efficiency of the 50° FoV waveguide display is only around 36%, implying that only 36% of the in-coupling efficiency can be utilized to maintain good uniformity throughout the entire FoV.

To analyze how to improve the in-coupling efficiency and uniformity using PVG as an in-coupler, we conduct polarization ray-tracing simulations using OpticStudio (Ansys Zemax). The RCWA model of PVG is compiled into a dynamic-link library (DLL) file and linked to OpticStudio, operating in non-sequential mode. As shown in Fig. 7a, during the ray tracing process in Zemax OpticStudio, if a ray hits the grating with a DLL, RCWA is automatically called to solve the field response and provide return data. The mathematical construction process is detailed in our previous research

Fig 7  Polarization raytracing results of PVG as an in-coupler in waveguide displays.

a Dynamics workflow between RCWA and Raytracing. b Shaded configuration of a waveguide display with a low-efficiency out-coupling grating. c Angular response of PVG with birefringence of 0.4 at slanted angle of 23° and thickness of 0.7 µm. d Improved in-coupling efficiency with optimized PVG by achieving the first-order half-wave condition. e Angular response of PVG with birefringence of 0.4 at slanted angle of 23.3° and thickness of 2.41 µm. f Improved in-coupling efficiency with optimized PVG by achieving the second-order half-wave condition

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where $$I_{min}$$ and $$I_{max}$$ represent the minimum and maximum brightness through the whole FoV, respectively. If the in-coupling efficiency of conventional couplers is also considered as 80%, then the in-coupling efficiency and uniformity will be improved by ~2× and ~2.3×, respectively.

Furthermore, by optimizing the thickness and slanted angle of the in-coupler PVG to satisfy the second-order half-wave condition around the extreme field, the in-coupling efficiency and uniformity can be improved to 63.8% (1.77x enhancement) and 75.3% (2.09× enhancement), respectively, at slanted angle of 23.3° and thickness of 2.41 μm.

To further enhance the in-coupling efficiency and uniformity, one straightforward approach is to utilize a waveguide with a higher refractive index. However, it's worth noting that the in-coupling efficiency may decrease again as the FoV gets wider. Besides, such polarization conversion in PVG can only address the efficiency issues caused by the second interaction between the incident beam and the in-coupler. To further enhance the in-coupling efficiency affected by the third interaction, as illustrated in Fig. 8a, an additional compensation layer can be incorporated at the in-coupler PVG. This would achieve polarization conversion over a wider angular response

Fig 8  Generalization of the polarization conversion in PVG-based waveguide displays.

a Polarization compensation layer in the in-coupling process

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1. b RGB lights propagating in a single waveguide. c Angular and spectral response of diffraction order $$R_0$$ with an optimized two-layer PVG as an in-coupler in a single waveguide for a full-color display

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Besides, our results can be readily applied to various waveguide designs, including different pupil expansion schemes and different numbers of waveguides

where $$n_{in}$$ and $$n_{out}$$ are the refractive indices of the input and output media, $$\lambda$$ represents the incident wavelength, and $${\theta }_{in}$$ and $${\theta }_{out}$$ are the incident and diffracted (TIR) angles, respectively. It is evident that the diffracted (TIR) angle increases with the increase in wavelength for the same incident angle. Following this principle, a two-layer PVG

More importantly, the polarization properties will facilitate more efficient rolling k vector designs

While the polarization conversion phenomenon in PVG can significantly enhance the in-coupling efficiency and uniformity, its efficacy is heavily dependent on the polarized light sources. When the light source is polarized, such as in a Liquid-Crystal-on-Silicon (LCOS) panel, PVG with the novel polarization properties demonstrates substantial advantages over conventional in-couplers. However, when using an unpolarized light source like micro-LEDs, a single PVG with the novel polarization property may only achieve a comparable level to traditional polarization-independent in-couplers due to the polarization selectivity of CLC. Nonetheless, this polarization selectivity can be leveraged to implement polarization multiplexing in two waveguides

As the polarization conversion phenomenon is intricately linked to the PVG thickness, careful consideration of PVG surface roughness during the fabrication process is essential. In Fig. 3b, we find that there exists a window where the polarization conversion is relatively insensitive to PVG thickness variations. However, as the LC birefringence increases, the polarization conversion becomes increasingly dependent on the PVG thickness. Based on the reported surface roughness of PVG

Moreover, the fabrication procedures and complexity remain consistent with previous PVG iterations. Therefore, implementing the polarization conversion phenomenon incurs no additional cost, as it is inherent to PVG and was first identified in this study. However, compared to mature fabrication techniques

In conclusion, we have discovered and demonstrated an anomalous polarization conversion phenomenon in PVGs. This new property effectively resolves the tradeoff between in-coupling efficiency and uniformity throughout the eyebox and FoV. By studying the multiple half-wave conditions in a PVG, we achieve a remarkable 2× improvement in in-coupling efficiency and 2.3× enhancement in uniformity across the FoV for a waveguide display with 50° FoV, compared to conventional couplers. To further overcome the in-coupling efficiency limit affected by the third interaction and achieve an approximately threefold enhancement, an additional compensation layer can be incorporated at the in-coupler PVG. Moreover, we delve into the broad applicability of the polarization conversion process, emphasizing its potential to be integrated into various waveguide display designs, especially full-color displays. Additionally, we examine and discuss the impact of the surface roughness of the PVG on the polarization conversion process. Overall, this polarization conversion phenomenon serves as the first evidence to showcase the superiority of PVG in-coupler in waveguide-based AR displays compared to other couplers. This advancement is expected to accelerate the development of high-efficiency waveguide-based AR displays and contribute to the commercialization of PVG technology.

The UCF group is indebted to Meta Platforms Technologies for the financial support and Dr. Lu Lu for useful discussion.

Y.D. and Y.G. contributed equally to this work. Y.D. proposed the idea and initiated the project. Y.D. and Y.G. mainly conducted the experiments and wrote the manuscript. Q.Y., Z.Y., and Y.H. helped with simulation and technical discussion. S.W. and Y.Z. supervised the project and edited the manuscript.

All data needed to evaluate the conclusions in the paper are present in the paper. Additional data related to this paper may be requested from the authors.

The authors declare no competing interests.