Ding et al.

Light: Science & Applications (2024)13:185 Official journal of the CIOMP 2047-7538
https://doi.org/10.1038/s41377-024-01537-8 www.nature.com/lsa

ARTICLE Open Access

Breaking the in-coupling efficiency limit in

waveguide-based AR displays with polarization
volume gratings
Yuqiang Ding1, Yuchen Gu2, Qian Yang 1
, Zhiyong Yang1, Yuge Huang3, Yishi Weng2, Yuning Zhang2 ✉ and
Shin-Tson Wu 1 ✉

Abstract
Augmented reality (AR) displays, heralded as the next-generation platform for spatial computing, metaverse, and
digital twins, empower users to perceive digital images overlaid with real-world environment, fostering a deeper level
of human-digital interactions. With the rapid evolution of couplers, waveguide-based AR displays have streamlined the
entire system, boasting a slim form factor and high optical performance. However, challenges persist in the waveguide
combiner, including low optical efficiency and poor image uniformity, significantly hindering the long-term usage and
user experience. In this paper, we first analyze the root causes of the low optical efficiency and poor uniformity in
waveguide-based AR displays. We then discover and elucidate an anomalous polarization conversion phenomenon
inherent to polarization volume gratings (PVGs) when the incident light direction does not satisfy the Bragg condition.
This new property is effectively leveraged to circumvent the tradeoff between in-coupling efficiency and eyebox
uniformity. Through feasibility demonstration experiments, we measure the light leakage in multiple PVGs with varying
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thicknesses using a laser source and a liquid-crystal-on-silicon light engine. The experiment corroborates the
polarization conversion phenomenon, and the results align with simulation well. To explore the potential of such a
polarization conversion phenomenon further, we design and simulate a waveguide display with a 50° field of view.
Through achieving first-order polarization conversion in a PVG, the in-coupling efficiency and uniformity are improved
by 2 times and 2.3 times, respectively, compared to conventional couplers. This groundbreaking discovery holds
immense potential for revolutionizing next-generation waveguide-based AR displays, promising a higher efficiency
and superior image uniformity.

Introduction twins, and spatial computing. AR displays have enabled

After decades of device innovation and vibrant advances widespread applications in smart education and training,
in microdisplay technologies, ultra-compact imaging smart healthcare, navigation and wayfinding, gaming and
optics, and high-speed digital processors, augmented entertainment, and smart manufacturing, just to name
reality (AR) has evolved from a futuristic concept to a a few.
tangible and pervasive technology. By seamlessly blending Since its primitive conception in the 1990s, AR has
the projected virtual content with real-world scenes, AR made significant strides, particularly with the emergence
enhances our perception and interaction with environ- and development of waveguide-based AR displays. These
ment, opening exciting possibilities for metaverse, digital displays enable wearable systems to be lightweight and
have a slim form factor while maintaining high optical
performance. Furthermore, the rapid development of
Correspondence: Yuning Zhang (zyn@seu.edu.cn) or
Shin-Tson Wu (swu@creol.ucf.edu) couplers, including partial reflective mirrors, surface relief
1
College of Optics and Photonics, University of Central Florida, Orlando, FL gratings (SRGs), volume holographic gratings, polariza-
32816, USA
2 tion volume gratings (PVGs), metasurfaces, etc., has
Joint International Research Laboratory of Information Display and
Visualization, Southeast University, Nanjing 210096, China
Full list of author information is available at the end of the article

© The Author(s) 2024

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Ding et al. Light: Science & Applications (2024)13:185 Page 2 of 12

a Blue absorption in b Spatially limited bandwidth c Limited angular and spectral d Multiple interactions at in-coupler
high-index waveguides modulation capability bandwidth at high efficiency
k1
W Strong light leakage
Unoptimized SRG

Diffraction efficiency
Optimized SRG In-coupler
t θ
k2 Waveguide

In-coupler
Waveguide

Angle of incidence over grating

e LP-S

VHG VHG VHG VHG

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-coupler1 and geometric in-coupler. e Multiple
interaction processes between the incident beam and the intensity-type VHG in-coupler

dramatically improved the optical performance of AR couplers and out-couplers2. Specifically, the effective
displays over the past few decades1–5. pupil expansion process for a given field angle utilizes
While waveguide displays have dramatically reduced the only a small portion of the folding coupler and out-
form factor, the low efficiency of optical combiners, par- coupler. If these components fail to accurately control the
ticularly the diffractive waveguide combiners, remains a angular and spectral response spatially, any exit pupil
major concern6. In the era of modern wireless near-eye expansion beyond the effective area will lead to light
displays powered by batteries, such a low optical efficiency wasting.
imposes a significant challenge, ultimately limiting the The third major optical loss mechanism is the limited
continuous operation time. angular and spectral bandwidth of the couplers in the high
The low optical efficiency primarily stems from four diffraction efficiency region1,2. As the FoV increases, the
aspects, all related to the nonuniformity issues, such as coupler’s bandwidth may not be sufficient to maintain a
color nonuniformity, FoV nonuniformity, and eyebox good uniformity. To improve uniformity, lower efficiency
nonuniformity1,2,6. The first major optical loss originates couplers are often compromised to achieve a broader
from the absorption and scattering of a high-index bandwidth8–10, as illustrated in Fig. 1c. Importantly, a
waveguide substrate7, as shown in Fig. 1a. These sub- larger FoV exacerbates energy loss during this process.
strates are typically used in a full-color diffractive wave- For instance, during Photonics West 2024, Applied
guide display to enlarge its FoV. For instance, a 10 mm- Materials demonstrated two SRG-based full-color wave-
thick high-index waveguide substrate from AGC Inc. guide displays with different FoVs. The display with a 20°
exhibits a transmittance of about 95% in the blue spectral FoV has an efficiency of 4500 nits lm−1 (~10%), while the
region. Due to multiple total internal reflections, the display with a 30° FoV only achieves 1300 nits lm−1 (~3%).
effective propagation distance in a 1 mm-thick waveguide As depicted in Fig. 1d, the fourth major cause of low-
can be as large as 50 mm. As a result, about 23% of the efficiency results from multiple interactions at the in-
blue light is absorbed. Such a noticeable optical loss not couplers11,12. Significant light leakage occurs at the in-
only lowers the overall waveguide efficiency but also coupler to maintain a good eyebox uniformity, even when
degrades the color uniformity. To obtain a balanced white the in-coupler is a fully reflective mirror or a grating with
at exit pupil, say D65, we must increase the power of the 100% diffraction efficiency. For instance, when a tradi-
blue channel. However, with active development of tional diffractive grating, such as an SRG or intensity-type
waveguide materials, and fabrication and purification VHG, is used as an in-coupler, the waveguide combiner
processes, this absorption/scattering loss could be gra- experiences substantial optical loss due to multiple
dually mitigated, becoming less significant over time. interactions between the incident light and the in-coupler,
The second major source of optical loss occurs during especially at extreme FoV angles. This light leakage not
the pupil expansion process. As illustrated in Fig. 1b, a only deteriorates the uniformity across the entire FoV but
significant portion of light is wasted due to the spatially also reduces the ambient contrast ratio of the virtual
limited bandwidth modulation capability of the folding images. A larger FoV exacerbates this loss. It is also worth
Ding et al. Light: Science & Applications (2024)13:185 Page 3 of 12

noting that a similar process occurs in geometric wave- In this paper, we present the discovery of an anomalous
guide combiners; however, in this case, the second or polarization conversion phenomenon in the PVGs. This
multiple interactions merely alter the propagation direc- phenomenon offers an intuitive solution to the above-
tion, as illustrated by the red lines in Fig. 1d, leading to mentioned issue for achieving a high and uniform in-
stray light13. coupling efficiency throughout the entire FoV while main-
Light leakage at the in-coupler is a longstanding issue taining continuous eyebox functionality. To prove concept,
over the past few decades1,2,11,12,14, yet no good solution preliminary experiments are conducted to validate this
can completely overcome this tough problem because it is polarization conversion process. The experimental results
fundamentally unavoidable with conventional in-couplers, closely align with the Rigorous Coupled-Wave Analysis
including SRG, intensity-type VHG, and even metasurface (RCWA) simulation. Moreover, the in-coupling efficiency
devices. Recent studies12 have indicated that the second limit of a 50° FoV waveguide-based AR display system is
interaction mirrors the symmetric process of the first enhanced by two times with the first-order polarization
interaction, implying that almost all the light experiencing conversion in a PVG, compared to conventional couplers.
the second interaction will either be coupled out of the Concurrently, the uniformity throughout the FoV is also
waveguide or change its propagation direction if the dif- improved by 2.3 times. Furthermore, by combining an
fraction efficiency is 100%. As further examined in con- additional polarization compensation film at the in-coupler,
ventional couplers (Fig. 1e), the second interaction is nearly all light can be coupled into the waveguides.
essentially a reverse process of the first interaction. This is
primarily because conventional couplers are made of Results
isotropic materials, leading to no polarization change The PVG is a polarization-selective holographic optical
during the interaction process. element that records the polarization information of two
As depicted in Fig. 1d, if the size (W ) of the in-coupler is interfering beams comprising a right-handed circular
greater than the total internal reflection (TIR) propagation polarization (RCP) and a left-handed circular polarization
distance d ¼ 2t  tanðθÞ, where t represents the waveguide (LCP). As illustrated in Fig. 2a, PVG features a slanted
thickness and θ denotes the TIR angle inside the waveguide, cholesteric liquid crystal (CLC) structure, where the liquid
then the in-coupling light will interact with the in-coupling crystal (LC) directors rotate along the helical axis15–21.
grating two or more times. In practical terms, achieving a This CLC structure endows PVG with the polarization-
continuous eyebox necessitates that W > d. Otherwise, selective characteristic of CLC, as depicted in Fig. 2a. It
users may not perceive digital information in certain regions reflects the circular polarization state possessing the same
within the eyebox. Thus, even if the width of the in-coupler handedness as the helical twist of the CLC while trans-
can be reduced by increasing the collecting power of the mitting the opposite component. For example, it diffracts
collimation lenses or shrinking the emission cone of the LCP while permitting RCP to pass through. Additionally,
microdisplay panels, the TIR angle θ or waveguide thick- the first-order (R1 ) diffraction efficiency increases with the
ness t must be decreased accordingly to maintain a good CLC pitch number and then gradually saturates.
continuity throughout the eyebox. Consequently, efficiency However, here we discover an anomalous phenomenon
loss and poor uniformity throughout the FoV persist as that deviates from the abovementioned rule. As depicted
significant challenges. For example, in a single-color wave- in Fig. 2b, when the incident angle in the glass substrate
guide display with a 70° (45°(H) × 55°(V)) FoV in a substrate approaches the Bragg plane, the Bragg condition does not
with an index n = 2.0, over 70% of the incident light is lost hold. Consequently, the PVG functions as a waveplate
due to the multiple interactions at the in-coupling process instead of a grating, altering the polarization state of the
for extreme field angles, resulting in a 70% drop in FoV incident light. For instance, it converts RCP to LCP when
uniformity. To boost the FoV uniformity, the overall in- the half-wave condition is satisfied. More specifically,
coupling efficiency is compromised. For a full-color, from the perspective of the incident light direction, as
30°(24°(H) × 18°(V)) FoV waveguide display using a n = 2 shown in Fig. 2c, the PVG resembles a tilted twisted-
substrate, the in-coupling efficiency loss for the blue and nematic (TN) liquid crystal waveplate22 with a very long
red colors at extreme field angles exceeds 73% and 51.5%, pitch (P),
respectively, causing a drop in color uniformity of around
2Λb
45%. To balance both color uniformity and FoV uniformity, P¼
 ð1Þ
the overall efficiency is also compromised. The calculation sin π2  α  θin
method for these examples will be discussed in the fol-
lowing section. Therefore, finding a solution to circumvent where Λb and α represent the Bragg period and the
the tradeoff between in-coupling efficiency, uniformity slanted angle of the PVG, θin corresponds to the incident
throughout the FoV, and eyebox continuity is urgently angle in the waveguide substrate. To demonstrate the
needed. waveplate behavior, the 0th order transmission efficiency
Ding et al. Light: Science & Applications (2024)13:185 Page 4 of 12

a LCP LCP RCP b RCP

c
Glass RCP
b
/

b
/
Glass

α α
/x
/x LCP
Photoalignment Glass Glass
layer RCP

α
d 1 e 1
LCP
Transmission efficiency

Stokes parameter S3

0.8
0.5

0.6
0
f
LCP RCP
0.4
–0.5 PVG
0.2

0 –1
0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
PVG thickness (nm) PVG thickness (nm)

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 S3 of transmitted
light varying with the PVG thickness. The birefringence of PVG for simulation is 0.4 (ne ¼ 2:0; no ¼ 1:6); input and output media are both glass with
ng ¼1.7; horizontal period Λx and slanted angle α of the PVG are 407 nm and 23.3°; the incident angle θin and wavelength λ 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

and output polarization state are simulated using the propagate inside the waveguide while maintaining its pro-
RCWA model23,24. As shown in Fig. 2(d, e), nearly all the pagation direction. Consequently, the in-coupling efficiency
light transmits through the PVG without changing its and uniformity are significantly improved while maintaining
propagation direction, regardless of the PVG thickness. a desired eyebox continuity.
Additionally, the polarization state (represented by the However, TIR is accompanied by a non-trivial phase
Stokes parameter S3 ) of the transmitted light oscillates as shift as the Fresnel reflection coefficient acquires a non-
the PVG thickness increases. zero imaginary part25. Besides, different polarization
Due to these two superior polarization properties, states, e.g., s and p lights will be introduced a different
employing PVG as an in-coupler in waveguide displays can phase shift, which depends on the polarization of the
dramatically enhance the in-coupling efficiency and uni- incident wave as shown below:
formity throughout the FoV, while keeping a good eyebox pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
continuity (or uniformity), in comparison with all other tra- 1 n2 sin2 θin  1
δ s ¼ 2 tan ð2Þ
ditional in-couplers and metasurface couplers. Specifically, as n cos θin
illustrated in Fig. 2f, the incident LCP light is deflected into
the waveguide substrate during the first interaction and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!
retains its polarization state based on the selectivity rule of 1 n n2 sin2 θin  1
δ p ¼ 2 tan ð3Þ
PVG. After the first interaction, following TIR, the polar- cos θin
ization state of light becomes RCP (the 1st green arrow) due
to the reversed propagation direction. During the second where δ s and δ p represent the additional phase induced by
interaction with the in-coupler (PVG), the light undergoes TIR process, n is refractive index of glass substrate, and
polarization conversion without altering its propagation θin denotes the incident angle. This indicates that circular
direction, meaning the light turns to LCP if the PVG thick- polarization will no longer be pure after TIR because of
ness satisfies the half-wave condition. Subsequently, after the phase difference induced by s and p polarization
another TIR at the top boundary of the PVG, the light states. Therefore, the incident light during the second
becomes RCP, which is then transmitted through the PVG interaction in the above situation is not a pure circular
due to its polarization selectivity. Finally, the light can polarization state and the optimal thickness will shift.
Ding et al. Light: Science & Applications (2024)13:185 Page 5 of 12

a b c
tPVG = 2.85 Pm
1st Light leakage 2nd Light leakage
1st light leakage 2nd light leakage
(3.3%) (80.1%)
θ
θ

LCP RCP + TIR phase shift

1 1

0.8 0.8
Diffraction efficiency

Diffraction efficiency
0.6 0.6 d tPVG = 4.1 Pm
st
1 light leakage 2nd light leakage
0.4 0.4 (2.1%) (1.3%)

0.2 0.2
R+1 - RCWA R0 - RCWA
R+1 - Experiment R0 - Experiment
0 0
0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000
PVG thickness (nm) PVG thickness (nm)

Fig. 3 Experimental results of the anomalous polarization conversion in PVG. a +1st order (Rþ1 Þ diffraction efficiency changes with thickness
during the first interaction for the incident LCP light. b 0th order (R0 ) 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

To validate the concept, we conducted an experiment analysis. Additionally, the light leakage in two PVGs with
using a 532 nm laser source and PVGs with different thicknesses was captured by a camera, as shown
varying thicknesses. We employed reactive mesogen in Fig. 3c and d. The left and right beams represent light
RM257, which possesses a birefringence Δn = 0.162 at leakage at the first and second interactions, respectively. It
λ = 532 nm, to fabricate the PVGs with different thick- is evident that light leakage is strong when t PVG ¼
nesses. This was achieved by adjusting the concentra- 2:85 μm but much weaker at t PVG ¼ 4:1 μm.
tion and spin coating speed on a waveguide substrate While the polarization conversion phenomenon has been
with n = 1.57. While other liquid crystal materials are successfully demonstrated at normal incidence using a laser
also feasible, they may yield different half-wave condi- source, it is crucial to assess its angular performance. By
tions if they exhibit a different birefringence. The hor- varying the incident angle of the laser source, the angular
izontal period Λx was set at 411 nm. To accommodate a performance of the second interaction is investigated, as
central wavelength at 532 nm and normal incidence, the shown in Fig. 4a, which agrees well with the RCWA simu-
slanted angle α is approximately 27.83°, determined lation. Furthermore, an LCoS light engine with a diagonal
based on the following Bragg equation: FoV of 20° was employed to evaluate the angular perfor-
mance of the polarization conversion in PVG-based wave-
2neff Λb cosðθin þ αÞ ¼ λb ð4Þ guide displays. As Fig. 4b, c shows, the waveguide display
with a 4.1 µm-thick PVG exhibits a much higher efficiency
where neff represents the effective refractive index of the and better uniformity than that with a 2.85 µm-thick PVG.
RM257, Λb is the Bragg period, λb is the Bragg Although the polarization conversion phenomenon in a
wavelength, and θin is the incident angle. PVG has been well verified using a laser source and an
Furthermore, Fig. 3 illustrates the experimental results LCoS light engine, these experiments do not fully
of the diffraction response of PVG at various thicknesses. demonstrate its full potential due to the limited birefrin-
In Fig. 3a, it is evident that the first-order (R1 ) diffraction gence (Δn) and FoV. Therefore, in the following, we will
efficiency at normal incidence increases with the use a reactive mesogen with Δn ¼ 0:4 to thoroughly
increased PVG thickness (t PVG Þ. Simultaneously, using an analyze the potential of the polarization conversion phe-
out-coupling prism, the second interaction (R0 diffraction nomenon in waveguide-based AR displays with a large
order) at a large incidence angle, calculated using FoV of 50°.
sin1 ðλb =ðΛx  nÞÞ in the glass substrate, also depends It should be noted that, similar to a half-wave plate
on the PVG thickness, as depicted in Fig. 3b. This (HWP), the angular bandwidth of the polarization conver-
dependency agrees well with the RCWA simulation sion is inherently limited due to dispersion. Additionally,
results. Furthermore, the polarization state of the light multiple half-wave conditions exist, as depicted in
leakage during the second interaction remains consistent Figs. 2e and 5a. Importantly, as the order of the half-wave
(LCP). This phenomenon further supports our previous condition increases, the angular bandwidth narrows further,
Ding et al. Light: Science & Applications (2024)13:185 Page 6 of 12

tPVG = 2.85 Pm
a tPVG = 4.1 Pm b
1

0.8
Diffraction efficiency

0.6

0.4 tPVG = 4.1 Pm

c
0.2
R0 - RCWA

R0 - Experiment
0
–65 –60 –55 –50
Incident TIR angle (°)

Fig. 4 Experimental results of angular performance of the anomalous polarization conversion in PVG. a Angular response of 0th order (R0 )
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

a Diffraction order R0 b tPVG = 500 nm c tPVG = 2200 nm

1 –70 1 –70 1

–65 –65
0.8 0.8 0.8
Incident TIR angle (°)

Incident TIR angle (°)

Diffraction efficiency

–60 –60
0.6 0.6 0.6
–55 –55

0.4 –50 0.4 –50 0.4

–45 –45
0.2 0.2 0.2
–40 –40
0 0 0
0 1000 2000 3000 4000 5000 450 500 550 600 650 450 500 550 600 650
Thickness (nm) Incident wavelength (nm) Incident wavelength (nm)

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 (ne ¼ 2:0; no ¼ 1:6); input and output media are respectively glass (ng = 1.7Þ and
air; horizontal period ðΛx Þ and slanted angle (αÞ of the PVG are 407 nm and 23.3°; the incident angle ðθÞ and wavelength ðλÞ are −43° and 532 nm

as Fig. 5b, c depicts, making it impractical to cover the entire meticulously, including the display panel, collimation
TIR region within the waveguide. However, it is important lens, in-coupler, and out-coupler. For the light engine,
to note that the light loss typically increases as the TIR angle we assume that the in-coupler of the waveguide display
decreases, indicating that a significant light loss pre- (or exit pupil of the light engine) is a circle with a dia-
dominantly occurs on one side of the FoV. By satisfying the meter W = 3 mm, which depends on the design of the
limited half-wave condition around the minimum TIR collimation lens and the emission cone of the display
angles, a substantial improvement in in-coupling efficiency panel, as depicted in Fig. 6(a). In most waveguide-based
and uniformity can be achieved. displays, the emission cone is typically very small, around
Next, we further investigate the angular performance of ±15°. For our calculations, we employ an ideal lens as the
the first-order and second-order polarization conversions collimation lens. Therefore, the focal length of the colli-
in a PVG-based waveguide display with 50° [30° (H) × 40° mation lens (CL) can be calculated as follows:
(V)] diagonal FoV at λ = 532 nm. Both orders demon-
strate significant enhancements in in-coupling efficiency f ¼ W =ð2 tanð15°ÞÞ ¼ 5:598 mm ð5Þ
and uniformity throughout the entire FoV, surpassing the
theoretical in-coupling efficiency limit of conventional
diffractive in-couplers. Moreover, to achieve a diagonal FoV of 50° [30° (H) × 40°
Before conducting polarization raytracing, the system (V)], the panel size is set to 3 mm × 4.075 mm. Subse-
configuration and parameters must be designed quently, a waveguide substrate with thickness t = 0.55 mm
Ding et al. Light: Science & Applications (2024)13:185 Page 7 of 12

a c
W/2

W d

In-coupler
Exit pupil or Incident beam after 1st TIR
Microdisplay Projection lens In-coupler size

b d
–20 1

0.8
–10

Vertical FoV (°)

d
0.6
0
0.4

10
0.2

20 0
W –10 0 10
t
Horizontal FoV (°)

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

and index n = 1.7 is utilized for design and simulation. Table 1 Design parameters of light engine and
Furthermore, to ensure a continuous eyebox, we assume polarization volume gratings in waveguide displays
that the pupil is continuous at the maximum TIR angle Parameters Design value
θmax . This implies that each TIR propagation distance d at
the maximum TIR angle is equal to the in-coupler size W , FoV 50° (30° (H) × 40° (V))
as illustrated in Fig. 6b, c. Based on following equation: In-coupler size 3 mm
Working wavelength 532 nm
d ¼ 2t  tan θmax ¼ W ð6Þ
Panel Size 3 mm × 4.075 mm
the maximum TIR angle is around 70°. Therefore, the Focal length of CL 5.6 mm
minimum TIR angle θmin = 38° and the horizontal period Refractive index of waveguide 1.7
Λx ffi 407 nm of the in-coupler and out-coupler can be
Thickness of waveguide 0.55 mm
derived from the FoV = 50° [30° (H) × 40° (V)]. In
summary, all the parameters of this waveguide system Maximum TIR angle 70°
are listed in Table 1. Birefringence of PVG 0.4
Due to the multiple interactions between incident light Horizontal period of PVG 407 nm
and conventional in-couplers12, the theoretical in-coupling
Slanted angle of PVG 23°
efficiency limit can be calculated based on the overlapping
area (Ao Þ of the second interaction between the incident
beam and the in-coupler, as depicted in Fig. 6b, c. More
specifically, the theoretical in-coupling efficiency limit (E) of 100% since there is no second interaction between the
a certain field can be expressed by the following equation: incident light and the in-coupler. As indicated in Fig. 6d,
  the minimum efficiency of the 50° FoV waveguide display
Ao 2 d 2d pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is only around 36%, implying that only 36% of the in-
E ¼1 ¼ 1  cos1 þ W 2  d2
Ain π W πW 2 coupling efficiency can be utilized to maintain good
ð7Þ uniformity throughout the entire FoV.
To analyze how to improve the in-coupling efficiency
where Ain is the area of in-coupler size or the exit pupil and uniformity using PVG as an in-coupler, we conduct
area of light engine. For instance, for the left-top corner polarization ray-tracing simulations using OpticStudio
FoV, it has a maximum in-coupling efficiency limit of (Ansys Zemax). The RCWA model of PVG is compiled
Ding et al. Light: Science & Applications (2024)13:185 Page 8 of 12

a b
Detector
Display

Lens
Call Call Waveguide
Raytracing
DLL RCWA model
model Return Return

In-coupler Out-coupler

c –20 1 d –20 1 e –20 1 f –20 1

0.8 0.8 0.8 0.8

–10 –10 –10 –10

Vertical FoV (°)

Vertical FoV (°)

Vertical FoV (°)

Vertical FoV (°)

0.6 0.6 0.6 0.6
0 0 0 0
0.4 0.4 0.4 0.4

10 10 10 10
0.2 0.2 0.2 0.2

20 0 20 0 20 0 20 0
-10 0 10 -10 0 10 –10 0 10 –10 0 10
Horizontal FoV (°) Horizontal FoV (°) Horizontal FoV (°) Horizontal FoV (°)

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

into a dynamic-link library (DLL) file and linked to is adopted:

OpticStudio, operating in non-sequential mode. As shown
in Fig. 7a, during the ray tracing process in Zemax I min
U¼  100% ð8Þ
OpticStudio, if a ray hits the grating with a DLL, RCWA is I max
automatically called to solve the field response and pro-
vide return data. The mathematical construction process where I min and I max represent the minimum and
is detailed in our previous research26. To measure the in- maximum brightness through the whole FoV, respec-
coupling efficiency, an ideal grating is used as the out- tively. If the in-coupling efficiency of conventional
coupler to couple all the light out of the waveguide. At the couplers is also considered as 80%, then the in-coupling
same time, an ideal lens and detector are used to mimic efficiency and uniformity will be improved by ~2× and
the eye and detect the efficiency as shown in Fig. 7b. ~2.3×, respectively.
Additionally, an anti-reflection coating is applied to the Furthermore, by optimizing the thickness and slanted
waveguide substrate. To have a better understanding of angle of the in-coupler PVG to satisfy the second-order
the polarization conversion process, both first- and half-wave condition around the extreme field, the in-
second-order half-wave conditions in Fig. 5b, c are studied coupling efficiency and uniformity can be improved to
in the following. First, through optimizing the PVG 63.8% (1.77x enhancement) and 75.3% (2.09× enhance-
thickness and slanted angle to satisfy the first-order half- ment), respectively, at slanted angle of 23.3° and thickness
wave condition, the optimal efficiency and uniformity of of 2.41 μm.
the in-coupling process are achieved at 23° slanted angle
and 0.7 μm thickness. The angular response of such a Discussion
PVG is simulated by RCWA. As shown in Fig. 7c, the To further enhance the in-coupling efficiency and uni-
average diffraction efficiency is around 80%. Based on the formity, one straightforward approach is to utilize a
polarization raytracing, the minimum in-coupling effi- waveguide with a higher refractive index. However, it’s
ciency is improved from 36% to 61.3% (1.7× improve- worth noting that the in-coupling efficiency may decrease
ment), as shown in Fig. 6c. Besides, the uniformity within again as the FoV gets wider. Besides, such polarization
the entire FoV is improved from 36% to 85.9% (2.39× conversion in PVG can only address the efficiency issues
improvement) if the following definition of uniformity U caused by the second interaction between the incident
Ding et al. Light: Science & Applications (2024)13:185 Page 9 of 12

a Weak light
c
Diffraction order R0
leakage –70 1
In-coupler
–65
0.8

Incident TIR angle (°)

–60
Waveguide 0.6
–55
Polarization compensation film
–50 0.4
b
–45
0.2
–40
0
450 500 550 600 650
Incident wavelength (nm)

Fig. 8 Generalization of the polarization conversion in PVG-based waveguide displays. a Polarization compensation layer in the in-coupling
process1. b RGB lights propagating in a single waveguide. c Angular and spectral response of diffraction order R0 with an optimized two-layer PVG as
an in-coupler in a single waveguide for a full-color display

beam and the in-coupler. To further enhance the in- angles based on the following diffraction equation:
coupling efficiency affected by the third interaction, as
illustrated in Fig. 8a, an additional compensation layer can λ
nin sinðθin Þ þ ¼ nout sinðθout Þ ð9Þ
be incorporated at the in-coupler PVG. This would Λx
achieve polarization conversion over a wider angular
response1,11 and further overcome the third interaction, where nin and nout are the refractive indices of the input
resulting in nearly all light being coupled into the wave- and output media, λ represents the incident wavelength,
guide with an approximately threefold enhancement. and θin and θout are the incident and diffracted (TIR)
However, this approach may impose significant challenges angles, respectively. It is evident that the diffracted (TIR)
in terms of fabrication requirements for the waveguide angle increases with the increase in wavelength for the
display system. same incident angle. Following this principle, a two-layer
Besides, our results can be readily applied to various PVG27 with a birefringence Δn = 0.4 is meticulously
waveguide designs, including different pupil expansion optimized to satisfy the half-wave conditions for RGB
schemes and different numbers of waveguides1, for lights at varying TIR angles. Illustrated in Fig. 8c, the
example, 1D EPE, 2D EPE, full-color display in a single optimized angular and spectral response of the diffracted
waveguide, two waveguides, and three waveguides. R0 order is achieved with the first-layer thickness of
Additionally, utilizing a multi-layer PVG will not only 820 nm and the second-layer thickness of 900 nm. The
expand the angular and spectral responses but also designed slant angle for the two layers is 21.2° and 25.6°,
enhance the in-coupling efficiency by satisfying the half- respectively, with a horizontal period of approximately
wave conditions for different incident angles and wave- 412 nm, while the index of the waveguide substrate is 1.7.
lengths, especially for full-color displays in a single Consequently, the polarization conversion phenomenon
waveguide. Clearly, satisfying the half-wave condition for in the multi-layer PVG helps enhance the in-coupling
RGB lights in three separate waveguides is feasible efficiency and uniformity throughout the FoV for a full-
because each waveguide exclusively transmits a single color display.
color, requiring each in-coupler to meet the half-wave More importantly, the polarization properties will
condition for that specific color. It is feasible even when facilitate more efficient rolling k vector designs28 and
using LED-based light engines with a wide spectrum (e.g., laser-based waveguide designs1. In these two designs, the
40 nm full width at half maximum), because the spectral beams from different FoVs do not overlap at the in-
bandwidth at the first-order half-wave condition is suffi- coupler. This implies that the in-coupler at different
ciently wide, as Fig. 5b shows. However, achieving full- spatial positions can be locally modulated to adjust the
color display with a single waveguide necessitates simul- half-wave conditions for different incident angles. Such
taneous satisfaction of the half-wave conditions for RGB in-coupler could be easily fabricated with inkjet
lights, posing challenges for a single-layer PVG. Addi- printing29.
tionally, the half-wave condition must be met at different While the polarization conversion phenomenon in PVG
TIR angles for RGB lights due to the dispersion of the in- can significantly enhance the in-coupling efficiency and
coupler, as illustrated in Fig. 8b. Specifically, same inci- uniformity, its efficacy is heavily dependent on the
dent angles of RGB lights will be diffracted to various TIR polarized light sources. When the light source is
Ding et al. Light: Science & Applications (2024)13:185 Page 10 of 12

polarized, such as in a Liquid-Crystal-on-Silicon (LCOS) examine and discuss the impact of the surface roughness
panel, PVG with the novel polarization properties of the PVG on the polarization conversion process.
demonstrates substantial advantages over conventional Overall, this polarization conversion phenomenon serves
in-couplers. However, when using an unpolarized light as the first evidence to showcase the superiority of PVG
source like micro-LEDs, a single PVG with the novel in-coupler in waveguide-based AR displays compared to
polarization property may only achieve a comparable level other couplers. This advancement is expected to accel-
to traditional polarization-independent in-couplers due to erate the development of high-efficiency waveguide-based
the polarization selectivity of CLC. Nonetheless, this AR displays and contribute to the commercialization of
polarization selectivity can be leveraged to implement PVG technology.
polarization multiplexing in two waveguides30 utilizing
different circular polarization-dependent PVGs with an Material and methods
unpolarized light source. Consequently, PVG would still Materials
exhibit a superior in-coupling efficiency and uniformity in The photoalignment material used in our experiments
such scenarios. is Brilliant Yellow (BY) from Sinopharm Chemical
As the polarization conversion phenomenon is intri- Reagent Co., Ltd. BY powders were dissolved in dimethyl-
cately linked to the PVG thickness, careful consideration formamide with a weight concentration of 0.5%. The
of PVG surface roughness during the fabrication process mixed solution was filtered using a 0.2 μm Teflon syringe
is essential. In Fig. 3b, we find that there exists a window before spin-coating onto the glass substrate. The LC
where the polarization conversion is relatively insensitive mixture is composed of solvent toluene and precursor
to PVG thickness variations. However, as the LC bire- which contains LC monomer RM 257 purchased from
fringence increases, the polarization conversion becomes Jiangsu Hecheng Advanced Materials Co., Ltd., surfactant
increasingly dependent on the PVG thickness. Based on Zonyl 8857A from Dupont, and photo-initiator Irgcure
the reported surface roughness of PVG31, the variation of 184 from MACKLIN.
PVG thickness can be well controlled to be below 25 nm,
which barely affects the polarization conversion phe- Methods
nomenon. Besides, alternative fabrication methods, such Figure 9a depicts the fabrication process of PVGs.
as inkjet printing29 could potentially improve the PVG Initially, the photoalignment material was spin-coated
surface flatness. onto a clean glass substrate with hydrophilic treatment by
Moreover, the fabrication procedures and complexity plasma etching. Brilliant yellow (BY) was used as the
remain consistent with previous PVG iterations. There- photoalignment material and dissolved in N,N-Dime-
fore, implementing the polarization conversion phenom- thylformamide (DMF) at a concentration of 0.5 wt%.
enon incurs no additional cost, as it is inherent to PVG Subsequently, the sample with the photoalignment film
and was first identified in this study. However, compared underwent polarized interference exposure, as shown in
to mature fabrication techniques1,32,33 (e.g., nanoim- Fig. 9b. The expanded and collimated laser beam was split
printing lithography or ion beam etching) for SRGs, large- into two arms by a polarization beam splitter (PBS). Each
scale fabrication capability is imperative for future scal- beam was then converted to the opposite circular polar-
ability to enable widespread applications of PVG. ization using a quarter-wave plate (QWP), respectively. In
In conclusion, we have discovered and demonstrated an our experiment, a 460 nm laser was employed as the
anomalous polarization conversion phenomenon in recording beam, and the exposure angle was set at 34°.
PVGs. This new property effectively resolves the tradeoff RM257 was utilized to create uniform LC layers after
between in-coupling efficiency and uniformity throughout spin-coating. Finally, the PVGs were exposed to UV light
the eyebox and FoV. By studying the multiple half-wave for stabilization. In accordance with the predetermined
conditions in a PVG, we achieve a remarkable 2× specifications, PVGs were fabricated, and the structures
improvement in in-coupling efficiency and 2.3× are shown in Fig. 9c through a polarizing optical micro-
enhancement in uniformity across the FoV for a wave- scope (POM) and in Fig. 9d through a cross-section
guide display with 50° FoV, compared to conventional scanning electron microscope (SEM).
couplers. To further overcome the in-coupling efficiency The 0.7 mm-thick glass substrates were purchased from
limit affected by the third interaction and achieve an Luoyang Guluo Glass. The substrate was cleaned using
approximately threefold enhancement, an additional ethanol and then treated by vacuum plasma for 40 s
compensation layer can be incorporated at the in-coupler before the spin-coating of BY solutions. The humidity of
PVG. Moreover, we delve into the broad applicability of the environment for spin-coating was controlled to be
the polarization conversion process, emphasizing its under 40%. The BY layer on the glass substrate was
potential to be integrated into various waveguide display exposed to a 460 nm laser (Coherent, Genesis CX-460)
designs, especially full-color displays. Additionally, we with 1 W output power for 2 min. We preheated the LC
Ding et al. Light: Science & Applications (2024)13:185 Page 11 of 12

a Photo-alignment
b
PH CL PBS QWP1
solution Pattern exposure Laser
M1
LP
OL

M: Mirror QWP2
PH: Pinhole
OL: Objective lens LCP
CL: Collimating lens M2
UV (365 nm) LC mixture
QWP: Quarter-wave plate
RCP
PBS: Polarization beam splitter
LP: Linearly polarized light
RCP: Left-handedness circularly polarized light
LCP: Right-handedness circularly polarized light Sample

Heating
d
c
411 nm

1 Pm

1Pm

Fig. 9 Fabrication of PVG. a Fabrication flowchart of PVGs. b Exposure setup for PVGs. c Cross section SEM image and (d) POM image of a PVG with
a horizontal period of 411 nm

Table 2 Materials and coating speed for PVGs fabrication

Sample Solute Solvent Concentration Coating speed (rpm) Sample thickness (nm)

1 RM257 (95.06%) R5011 (2.09%) Irgcure 184(2.85%) Toluene 6 wt% 600 (30 s) 500
2 – – 12 wt.% 1500 (30 s) 720
3 – – 12 wt% 1000 (30 s) 960
4 – – 12 wt% 600 (30 s) 1200
5 – – 18 wt% 1500 (30 s) 1650
6 – – 38 wt% 3000 (30 s) 2850
7 – – 38 wt% 2500 (30 s) 3050
8 – – 38 wt% 2000 (30 s) 3300
9 – – 38 wt% 1000 (30 s) 4400

mixture on a hot plate stage at 70 °C before spin-coating multiple beams post-interaction with the PVG through a
because the viscosity decreases with increased tempera- power meter. To ensure the incident light to the PVG is
ture. Besides, we also put the LC substrates on top of the circularly polarized, a circular polarizer is inserted after
hot plate right after the spin-coating process for several the laser source. Additionally, to verify the measurement
seconds to obtain better alignment. Detailed recipes are accuracy, a reference point (surface reflection of glass
summarized in Table 2. The PVG thickness was mea- substrate) is established using a clean glass substrate
sured with a profiler from BRUKER. In Fig. 3, an out- without PVG.
coupling prism is used to measure the diffraction effi-
ciency (R0 ) at the second interaction with a laser source
Acknowledgements
featuring a small beam size. This deliberate choice facil- The UCF group is indebted to Meta Platforms Technologies for the financial
itates the clear differentiation and measurement of support and Dr. Lu Lu for useful discussion.
Ding et al. Light: Science & Applications (2024)13:185 Page 12 of 12

Author details 11. Levola, T. Method and optical system for coupling light into a waveguide.
1
College of Optics and Photonics, University of Central Florida, Orlando, FL (2005).
32816, USA. 2Joint International Research Laboratory of Information Display 12. Goodsell, J. et al. Metagrating meets the geometry-based efficiency limit for
and Visualization, Southeast University, Nanjing 210096, China. 3Meta Reality AR waveguide in-couplers. Opt. Express 31, 4599–4614 (2023).
Labs Research, 9845 Willows Road NE, Redmond, WA 98052, USA 13. Zhou, Y., Zhang, J. F. & Fang, F. Z. Stray light analysis and design optimization
of geometrical waveguide. Adv. Opt. Technol. 10, 71–79 (2021).
Author contributions 14. Lin, Y. Y. et al. Enhanced diffraction efficiency with angular selectivity by
Y.D. and Y.G. contributed equally to this work. Y.D. proposed the idea and inserting an optical interlayer into a diffractive waveguide for augmented
initiated the project. Y.D. and Y.G. mainly conducted the experiments and reality displays. Opt. Express 30, 31244–31255 (2022).
wrote the manuscript. Q.Y., Z.Y., and Y.H. helped with simulation and technical 15. Kobashi, J., Yoshida, H. & Ozaki, M. Planar optics with patterned chiral liquid
discussion. S.W. and Y.Z. supervised the project and edited the manuscript. crystals. Nat. Photonics 10, 389–392 (2016).
16. Weng, Y. S. et al. Polarization volume grating with high efficiency and large
Data availability diffraction angle. Opt. Express 24, 17746–17759 (2016).
All data needed to evaluate the conclusions in the paper are present in the 17. Lee, Y. H., He, Z. Q. & Wu, S. T. Optical properties of reflective liquid crystal
paper. Additional data related to this paper may be requested from the polarization volume gratings. J. Opt. Soc. Am. B 36, D9–D12 (2019).
authors. 18. Nys, I. et al. Tilted chiral liquid crystal gratings for efficient large-angle dif-
fraction. Adv. Opt. Mater. 7, 1901364 (2019).
19. Zheng, Z. G., Lu, Y. Q. & Li, Q. Photoprogrammable mesogenic soft helical
Conflict of interest
architectures: a promising avenue toward future chiro-optics. Adv. Mater. 32,
The authors declare no competing interests.
1905318 (2020).
20. Zhang, Y. X., Zheng, Z. G. & Li, Q. Multiple degrees-of-freedom programmable
soft-matter-photonics: configuration, manipulation, and advanced applica-
Received: 25 April 2024 Revised: 16 July 2024 Accepted: 16 July 2024 tions. Responsive Mater. 2, e20230029 (2024).
21. Feng, X. Y. et al. Closer look at transmissive polarization volume holograms:
geometry, physics, and experimental validation. Appl. Opt. 60, 580–592
(2021).
22. Schadt, M. & Helfrich, W. Voltage-dependent optical activity of a twisted
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