Exit Pupil Expansion Based on Polarization Volume Grating

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Article Exit Pupil Expansion Based on Polarization Volume Grating

Jingyi Cui and Yuning Zhang *

Joint International Research Laboratory of Information Display and Visualization, School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China; [email protected] * Correspondence: [email protected]

Abstract: In this paper, we demonstrate a waveguide display structure which can realize a large field of view on a two-dimensional plane and a larger exit pupil size at the same time. This waveguide structure has three polarization volume gratings as its coupling elements. We use Zemax to simulate the effect of monochromatic and full-color two-dimensional exit pupil expansion and actually prepared a monochromatic waveguide with a two-dimensional exit pupil expansion structure. For the red, green, and blue light beams, it can achieve a large diffraction angle and can achieve diffraction efficiency of more than 70%. The waveguide structure shown can have an angle of view of 35◦ in the horizontal direction and 20◦ in the vertical direction, and an exit pupil of 18 mm long and 17 mm wide was achieved at the same time. As measured, the overall optical efficiency was measured as high as 118.3 cd/m2 per lumen with a transparency of 72% for ambient light.

Keywords: polarization volume grating; exit pupil expansion; augmented reality

1. Introduction In order to achieve high-quality waveguide AR applications, wearable devices must Citation: Cui, J.; Zhang, Y. Exit Pupil have a sufﬁciently large exit pupil [1–3]. These systems require a larger exit pupil size to Expansion Based on Polarization allow the eyes to scan across the entire ﬁeld of view, and provide some additional tolerance Volume Grating. Crystals 2021, 11, 333. in the position of the exit pupil of the head-mounted or helmet-mounted display relative https://doi.org/10.3390/ to the viewer’s eye pupil. In this way, the wearer can observe the image information of a cryst11040333 micro source projected in a wide spatial range. This requires a compact high-performance

Academic Editors: Yun-Han Lee, imaging system with a large exit pupil size to accommodate eye movements. At the present Guanjun Tan and Yishi Weng moment, there are mainly three solutions for exit pupil expansion. They are micro-lens arrays exit pupil expanders, diffractive free space exit pupil expanders, and waveguide Received: 8 December 2020 holographic exit pupil expanders [4–7]. Micro-lens arrays expand the exit pupil when the Accepted: 24 March 2021 field produced by the first array of lenses overlaps the input NA of adjacent lenses in the Published: 25 March 2021 second array. It is important to have a 100% fill factor in order to gather as much previous light as possible from the micro-display [8–10]. Diffractive free space exit pupil expanders Publisher’s Note: MDPI stays neutral expand the exit pupil through two beam expanders, one PG-PC module, and one polarized with regard to jurisdictional claims in beam splitter cube [11,12]. In fact, with the above methods by using traditional visual published maps and institutional affil- system optical components, although the compact size design can be simplified to a certain iations. extent, this solution is difficult to provide a large field of view while providing solutions for large exit pupil due to the limitation of the Lagrangian invariant. The Lagrange invariant, axiomatically stated and applied to the pupils, can be written as follows [13],

· · = 0 · 0 · 0 Copyright: © 2021 by the authors. n ypupil θ n ypupil θ (1) Licensee MDPI, Basel, Switzerland. where θ represents the semi-ﬁeld of view at the entrance pupil, y is the radius of the This article is an open access article pupil pupil in object space, n is the refractive index in the object space, θ0 is the chief ray angle at distributed under the terms and 0 0 conditions of the Creative Commons the exit pupil, ypupil is the radius of the exit pupil, and n is the refractive index in the image Attribution (CC BY) license (https:// space. It can be seen from Equation (1), for a ﬁxed value of the Lagrange invariant, that creativecommons.org/licenses/by/ the FOV in image space is inversely proportional to the exit pupil height. A disadvantage 4.0/). of a small exit pupil is that vignetting and, in the worst case, 100% vignetting may occur,

Crystals 2021, 11, 333. https://doi.org/10.3390/cryst11040333 https://www.mdpi.com/journal/crystals Crystals 2021, 11, x FOR PEER REVIEW 2 of 12

𝑛⋅𝑦 ⋅𝜃=𝑛 ⋅𝑦 ⋅𝜃 (1)

where 𝜃 represents the semi-field of view at the entrance pupil, 𝑦 is the radius of the pupil in object space, 𝑛 is the refractive index in the object space, 𝜃 is the chief ray angle at the exit pupil, 𝑦 is the radius of the exit pupil, and 𝑛 is the refractive index in the image space. It can be seen from Equation (1), for a fixed value of the Lagrange Crystals 2021, 11, 333 invariant, that the FOV in image space is inversely proportional to the exit pupil height.2 of 11 A disadvantage of a small exit pupil is that vignetting and, in the worst case, 100% vignetting may occur, as eyes naturally move within the display, resulting in a blackout of the image.as eyes Both naturally the beam-splitting move within prism the display, and the resulting free-form in optical a blackout coupling of the scheme image. can Both be regardedthe beam-splitting as the off-axis prism deformation and the free-form of the opticalconventional coupling visual scheme system, can so be regardedthey are all as limitedthe off-axis by the deformation above condition. of the conventional visual system, so they are all limited by the aboveFortunately, condition. this limitation can be broken through by the third method using optical waveguideFortunately, imaging this technology limitation which can be relies broken on the through replication by the and third expansion method of using the wave- opti- guidecal waveguide transmission imaging process, technology and the whichtwo parameters relies on theof the replication size of the and pupil expansion and the of field the ofwaveguide view are independent transmission of process, each other, and the whic twoh is parameters convenient of for the design size of and the pupiloptimization and the [14].field Therefore, of view are optical independent waveguide of each imaging other, tec whichhnology is convenient is more suitable for design for achieving and optimiza- exit pupiltion [ 14expansion.]. Therefore, optical waveguide imaging technology is more suitable for achieving exit pupilTaking expansion. the reflective diffraction waveguide as an example (the coupling element uses a reflectiveTaking diffraction the reflective grating), diffraction it can waveguide be seen in as Figure an example 1 that (the as couplingthe beam element propagates uses withina reflective the waveguide, diffraction grating), a portion it canof the be light seen inenergy Figure is1 diffractedthat as the and beam derivable propagates each within time afterthe waveguide, entering the a in-coupling portion of the element, light energy and the is diffractedremaining andlight derivable energy continues each time to after be transmittedentering the in in-coupling the waveguide element, in total and internal the remaining reflection light until energy it again continues enters the to out-cou- be trans- plingmitted element in the waveguideand re-coupling in total occurs. internal In this reflection way, the until input it again beam enters will thebe continuously out-coupling copiedelement and and coupled re-coupling out on occurs. the outcoupling In this way, theelement, input ultimately beam will beachieving continuously an extended copied expansion.and coupled out on the outcoupling element, ultimately achieving an extended expansion.

FigureFigure 1. 1. OpticalOptical waveguide waveguide one-dimensional one-dimensional exit exit pupil pupil expansion expansion schematic. schematic.

AsAs shown shown in in Figure Figure 11,, only exit pupilpupil one-dimensionalone-dimensional expansionexpansion cancan bebe realized.realized. InIn fact,fact, a a two-dimensional two-dimensional expansion expansion structure structure can can be be designed designed to to obtain obtain a a larger larger exit exit pupil pupil size.size. Compared Compared with with the the one-dimensional one-dimensional wave waveguideguide dilation dilation structure, structure, two-dimensional two-dimensional exitexit pupil pupil expansion expansion requires requires only only one one more more coupling coupling steering steering element element to function to function as one- as dimensionalone-dimensional expansion expansion in the in other the other direction direction and andplane plane steering steering for fortransmitting transmitting light light in thein thewaveguide. waveguide. Nokia Nokia Research Research scientist scientist Tapani Tapani Levolas Levolas summarized summarized two possible two possible two- dimensionaltwo-dimensional expansion expansion structures structures for diffracti for diffractiveve waveguide waveguide coupling coupling elements elements in his pain perhis [15]. paper Both [15 ].structures Both structures showed showed in that pa inper that have paper three have coupling three coupling elements elements as in-cou- as pling,in-coupling, intermediate intermediate coupling, coupling, and out-coupling, and out-coupling, respectively. respectively. The difference The difference between between the twothe twostructures structures is mainly is mainly reflected reﬂected in the in numb the numberer of times of timesthe beam the beamis coupled is coupled at the inter- at the mediateintermediate coupling. coupling. The three The three coupling coupling elements elements in the in thestructure structure where where the thelight light beam beam is even-numberedis even-numbered coupled coupled at atthe the intermediate intermediate co couplingupling concentrate concentrate in in a asingle single direction, direction, whichwhich does does not not satisfy satisfy the the "glasses" "glasses" shape shape re requirement,quirement, as as the the other other structure structure where where the lightlight beam beam is is odd-numbered odd-numbered coupled coupled at at the intermediate coupling does. Therefore, Therefore, the the odd-numberedodd-numbered structure structure is is selected selected as as the the expansion expansion method described herein. According to previous researches, polarization volume holographic gratings (PVG) can not only achieve high-efﬁciency single-order diffraction under Bragg conditions, but also have a larger wavelength bandwidth and angular bandwidth and show polarization sensitivity similar to Pancharatnam–Berry (PB) phase gratings [16–19]. Therefore, compared to traditional volume holographic gratings [20–22] and surface relief gratings [23–25], polarization volume holographic gratings are more suitable as the coupling element of the holographic waveguide system, and it is an extremely excellent solution to realize the holographic optical waveguide display technology. However, the current application of PVG is still focused on achieving a one-dimensional exit pupil, which has a small exit pupil size. Therefore, expanding the size of the exit pupil from one-dimensional (linear Crystals 2021, 11, x FOR PEER REVIEW 3 of 12

According to previous researches, polarization volume holographic gratings (PVG) can not only achieve high-efficiency single-order diffraction under Bragg conditions, but also have a larger wavelength bandwidth and angular bandwidth and show polarization sensitivity similar to Pancharatnam–Berry (PB) phase gratings [16–19]. Therefore, compared to traditional volume holographic gratings [20–22] and surface relief gratings [23– 25], polarization volume holographic gratings are more suitable as the coupling element of the holographic waveguide system, and it is an extremely excellent solution to realize Crystals 2021, 11, 333 the holographic optical waveguide display technology. However, the current application3 of 11 of PVG is still focused on achieving a one-dimensional exit pupil, which has a small exit pupil size. Therefore, expanding the size of the exit pupil from one-dimensional (linear structure)structure) to to two-dimensional two-dimensional (planar(planar structure)structure) isis a a feasible feasible way way to to expand expand the the scope scope of of thethe exit exit pupil. pupil. ThisThis paperpaper brieﬂybriefly reviews reviews the the structure structure of of PVG PVG and and the the calculation calculation method method of of each each gratinggrating in in the the two-dimensional two-dimensional pupil pupil expansion expansio structure,n structure, and and then then uses uses Zemax Zemax to establish to estab- alish tracing a tracing model model and and obtain obtain the the simulation simulation imaging imaging results. results. Finally, Finally, a a monochromatic monochromatic waveguidewaveguide structure structure with with a a two-dimensional two-dimensional pupil pupil expansion expansion effect effect is is actually actually prepared. prepared.

2.2. MaterialsMaterials andand MethodsMethods UnlikeUnlike conventional conventional volume volume holographic holographic grating grating which which utilizes utilizes the the periodic periodic variation varia- oftion the of refractive the refractive index index of an ofisotropic an isotropic medium medium to produceto produce a Bragga Bragg effect effect [26 [26],], the the PVG PVG mediummedium is is anisotropic, anisotropic, and and its its periodic periodic refractive refractive index index modulation modulation is produced is produced by periodic by peri- rotationodic rotation of the of molecular the molecular optical optical axis in axis the medium.in the medium. In terms In of terms diffraction of diffraction characteristics, charac- PVGteristics, can producePVG can high-efﬁciencyproduce high-efficiency single-stage single-stage Bragg diffraction Bragg diffraction as volume as volume holographic holo- gratinggraphic does, grating thus does, ensuring thus opticalensuring coupling optical efﬁciencycoupling andefficiency image and transmission image transmission quality of thequality waveguide of the waveguide system. As ansystem. advantage, As an theadvantage, response the bandwidth response of bandwidth PVG is much of PVG larger is thanmuch the larger response than bandwidththe response of bandwidth traditional of volume traditional holographic volume grating holographic [27]. Thegrating narrow [27]. waveguideThe narrow FOV waveguide caused FOV by the caused small by response the small bandwidth response bandwidth is the main is problem the main faced problem by thefaced current by the waveguide current waveguide coupling technologycoupling tec basedhnology on volumebased on holographic volume holographic gratings. Thegrat- proposalings. The of proposal PVG is conducive of PVG is toconducive the solution to the to thissolution pain pointto this problem. pain point On problem. the other On hand, the PVGother also hand, exhibits PVG Pancharatnam–Berryalso exhibits Pancharatnam (PB) phase–Berry polarization (PB) phase response polarization characteristics response notcharacteristics found in volume not found holographic in volume grating holographic [28]. This grating feature [28]. guarantees This feature the guarantees see-through the abilitysee-through of the waveguideability of the system waveguide under system large FOV under (wide large response FOV (wide bandwidth) response andbandwidth) adds a newand designadds a dimensionnew design to dimension the waveguide to the coupling waveguide component. coupling The component. optimization The space optimiza- and applicationtion space and method application of the waveguide method of coupling the waveguide element coupling are expanded element by are using expanded PVG. The by basicusing grating PVG. The structure basic grating of PVG structure is shown inof FigurePVG is2 shown. in Figure 2.

FigureFigure 2. 2.The The grating grating structure structure of of polarization polarization volume volume holographic holographic gratings gratings (PVG). (PVG). PVG PVG has has a period a period of Λ in x–y plane and a period of Λin z-axis direction. Periodical refractive index planes of Λx in x–y plane and a period of Λz in z-axis direction. Periodical refractive index planes have a have a period of Λ. period of ΛB.

ΛB depicted in Figure2 means the period of periodical refractive index planes, which should be calculated by the Bragg equation after determining the center wavelength. The structure of two-dimension exit pupil expansion is more complicated than one- dimension because of the extra intermediate grating so that the light can be expanded into both horizontal and vertical directions, further expanding the exit pupil size. Therefore, we need to introduce the calculation method in detail before we simulate the structure. Taking the structure in Figure3 as an example, PVG1, PVG2, and PVG3 represent the in-coupling, intermediate, and out-coupling grating, respectively. The angle between incidence and the normal of PVG1 surface is θ0, and the angle between incidence and the grating vector of PVG1 is φ0. The angle between the light diffracted from PVG1 and the normal of PVG1 is Crystals 2021, 11, x FOR PEER REVIEW 4 of 12

Λ depicted in Figure 2 means the period of periodical refractive index planes, which should be calculated by the Bragg equation after determining the center wavelength. The structure of two-dimension exit pupil expansion is more complicated than one- dimension because of the extra intermediate grating so that the light can be expanded into both horizontal and vertical directions, further expanding the exit pupil size. Therefore, we need to introduce the calculation method in detail before we simulate the structure. Taking the structure in Figure 3 as an example, PVG1, PVG2, and PVG3 represent the in- Crystals 2021, 11, 333 coupling, intermediate, and out-coupling grating, respectively. The angle between4 ofinci- 11 dence and the normal of PVG1 surface is 𝜃, and the angle between incidence and the grating vector of PVG1 is 𝜙. The angle between the light diffracted from PVG1 and the normal of PVG1 is 𝜃 , and the angle with the grating vector of PVG1 is 𝜙 , recording the θ , and the angle with the grating vector of PVG1 is φ , recording the direction as (θ , φ ). 1direction as (𝜃 ,𝜙 ). Similarly, the direction of the light1 diffracted from PVG2 and1 PVG31 Similarly, the direction of the light diffracted from PVG2 and PVG3 can be recorded as can be recorded as (𝜃,𝜙) and (𝜃,𝜙), respectively. The angles are depicted in Figure 3, (θ2, φ2) and (θ3, φ3), respectively. The angles are depicted in Figure3, which shows the left viewwhich and shows front the view left of view the waveguide. and front view of the waveguide.

FigureFigure 3. 3.Schematic Schematic diagram diagram of of two-dimensional two-dimensiona exitl exit pupil pupil expansion expansion structure. structure.

ForFor the the in-coupling in-coupling grating grating PVG1, PVG1, we we decompose decompose the the incident incident light light and and ﬁrst-order first-order diffracteddiffracted light light in in the the direction direction of of the the grating grating vector vector and and the the direction direction perpendicular perpendicular to to thethe grating grating vector vector according according to to the the grating grating formula, formula, and and we we can can obtain obtain ( θ(𝜃0, ,𝜙φ0)) and and ( θ(𝜃1,φ,𝜙1)) satisfyingsatisfying the the following following formula, formula,

𝑠𝑖𝑛 𝜃 𝑠𝑖𝑛 𝜙 =𝑛𝑠𝑖𝑛𝜃 𝑠𝑖𝑛 𝜙 sin θ sin φ = n sin θ sin φ 0 0 1 1 𝜆,, (2)(2) n sin𝑛𝑠𝑖𝑛𝜃θ cos𝑐𝑜𝑠φ − 𝜙 sin−𝑠𝑖𝑛𝜃θ cos𝑐𝑜𝑠φ = 𝜙 λ= 1 1 0 0 d 𝑑 wherewhere n is the n averageis the average refractive refractive index index of the of glass the glass substrate, substrate,λ is the λ is wavelength the wavelength of the of incidentthe incident light light in vacuum, in vacuum, and dand is thed is period the period of the of surface the surface grating grating of PVG1 of PVG1 (d is (d actually is actu- equalally equal to Λx into Figure𝛬 in 2Figure). In this 2). paper, In this we paper, set the we surface set the period surface of theperiod in- andof the out-coupling in- and out- gratingscoupling as gratings the same as value the dsameto make value the 𝑑 model to make structure the model simpler. structure Then, thesimpler. surface Then, period the (writtensurface asperiodd0) of (written the intermediate as𝑑) of gratingthe intermediate PVG2 must grating satisfy PVG2 the relationship must satisfy (Equation the relation- (3)) toship make (Equation sure that (3)) a combinationto make sure ofthat the a threecombination surface of grating the three vectors surface has grating substantially vectors zerohas magnitude,substantially which zero magnitude, can allow light which to becan coupled allow light out ofto thebe coupled waveguide out inof thethe samewave- orientationguide in the as same it was orientation input. Advantageously, as it was input. allAdvantageously, wavelengths can all wavelengths experience the can same, expe- facilitatingrience the asame, color facilitating display. a color display. d d0 = , (3) 2 cos ρ where ρ represents half of the angle between the normal of PVG1 and the normal of PVG3, as shown in Figure3. Decomposing the incident light and diffracted light of PVG2 in the direction of its grating vector and the direction perpendicular to the grating vector, it can be obtained that (θ1, φ1) and (θ2, φ2) satisfy the following formula, ( sin θ1 sin (φ1 + ρ) = n sin θ2 sin φ2 2λ cos ρ (4) n sin θ2 cos (π − φ2) − n sin θ1 cos (φ1 + ρ) = − d Crystals 2021, 11, 333 5 of 11

Similarly, for the out-coupling grating PVG3, we can also get the (θ3, φ3) by the following formula, sin θ2 sin (φ2 − ρ) = sin θ3 sin φ3 λ (5) sin θ3 cos φ3 − n sin θ2 cos (φ2 − ρ) = d It still needs to be considered the period of the grating vector of the three coupled gratings in the z-direction (Λz) when using PVGs as the coupling elements, which can be written as Equations (6)–(8). Through the calculation, the periods in the z-axis direction of the three PVGs can be obtained. 2π 2π Λz = → = r (6) → 2 → → 2 k k iz k k Ki k − k k ix + k iy k

→ → d , i = 1, 3 k k + k k= (7) ix iy d0 , i = 2 → 2π k Ki k= (8) ΛB → → → where k ix, k iy, and k iz represent the component of the grating vector in the x, y, and z-axis, and i = 1, 2, 3 represents the in-coupling grating, the intermediate grating, and → the out-coupling grating, respectively; Ki represents the volume grating vector; ΛB is the grating period shown in Figure2. We can design the needed PVGs through the calculation of horizontal grating period length (Λx) and vertical grating period length (Λz) by the equations above after determining the value of ρ. Therefore, we need to determine a proper value of ρ. Figure4a represents the variation curve of the total efﬁciency of the emitted light with ρ. It can be seen from the curve that (1) when ρ is small, the total energy utilization rate of the system is generally lower; (2) the total energy utilization rate curve of the outgoing light has two peaks, appearing at ρ = 50◦ and ρ = 60◦, respectively, and the energy utilization rate will be slightly higher when ρ = 50◦. In this paper, three PVGs (in-coupling, intermediate coupling, and out-coupling, respectively) whose center wavelength is at 550 nm are presented in Crystals 2021, 11, x FOR PEER REVIEW 6 of 12 simulations and experiments, and the incident light is normal to the waveguide substrate. The propagation angle in the waveguide is set as 60◦ and ρ is set as 50◦ in order to get the highest energy utilization rate.

ρ Figure 4. ((aa)The) The variation variation curve curve of of the the total total efficiency efﬁciency of ofthe the emitted emitted light light with with ρ;;( (b)) ray ray tracing tracing diagram diagram of of a a two- two- dimensional expansion ho holographiclographic waveguide.

AsThe described ray-tracing above, diagram the light in Zemax stream is shownis coupled in Figure into the4. Inwaveguide this simulation from model,the in-cou- the plinghorizontal grating, grating then periodpropagates length in Λthex is wave set asguide 371 nmand for reaches the in-coupling the intermediate, (or out-coupling), which ex- tendsand 288.5 the horizontal nm for the FOV. intermediate After that, coupling the light grating. propagates along the x-axis and reaches the out-coupling and is diffracted out the waveguide, which extends the vertical FOV. Figure 5 shows the micro-image source image used in the simulation and the one- dimensional pupil expansion effect of red, green, and blue as a comparison with two- dimensional pupil expansion.

Crystals 2021, 11, x FOR PEER REVIEW 6 of 12

Crystals 2021, 11, 333 6 of 11 Figure 4. (a)The variation curve of the total efficiency of the emitted light with ρ ; (b) ray tracing diagram of a two- dimensional expansion holographic waveguide.

As describedAs described above, above, the the light light stream stream is is coupledcoupled into into the the waveguide waveguide from from the in-cou- the in- couplingpling grating, grating, then then propagates propagates inin thethe waveguidewaveguide and and reaches reaches the the intermediate, intermediate, which which ex- extendstends the horizontalthe horizontal FOV. FOV. After After that, that, the the light light propagates along along the the x-axisx-axis and and reaches reaches the out-coupling and is diffracted out the waveguide, which extends the vertical FOV. the out-coupling and is diffracted out the waveguide, which extends the vertical FOV. Figure 5 shows the micro-image source image used in the simulation and the one- Figure5 shows the micro-image source image used in the simulation and the one- dimensional pupil expansion effect of red, green, and blue as a comparison with two- dimensionaldimensional pupil pupil expansion expansion. effect of red, green, and blue as a comparison with two- dimensional pupil expansion.

Crystals 2021, 11, x FOR PEER REVIEW 7 of 12

FigureFigure 5. ( a5.) ( Thea)The micro-image micro-image source image; image; (b ()b the) the one-dimension one-dimension exit pupil exit pupil effect effectof red, ofgreen, red, and green, blue; and (c) the blue; two- (c) the two-dimensiondimension exit exit pupil pupil effect effect of ofred, red, green, green, and and blue. blue.

It can be seen from Figure 5 that, compared with one-dimension exit pupil, the two- dimension structure expands exit pupil in two directions. However, some dark lines appear at four corners in Figure 5c, which is actually because of the angle bandwidth limitation of the intermediate grating. This problem can be solved out by overlapping several gratings which have different angle bandwidth range to enlarge the total angle bandwidth. Besides, we can achieve the chromatic diffraction feature by superimposing two waveguides, as previous work did, because the propagation of RGB three-color light is independent of each other. The simulation result of the full-color display with a white light source is shown in Figure 6. It can be seen that the simulation results are also closer to the original picture.

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It can be seen from Figure5 that, compared with one-dimension exit pupil, the two- dimension structure expands exit pupil in two directions. However, some dark lines appear at four corners in Figure5c, which is actually because of the angle bandwidth limitation of the intermediate grating. This problem can be solved out by overlapping several gratings which have different angle bandwidth range to enlarge the total angle bandwidth. Besides, we can achieve the chromatic diffraction feature by superimposing two waveguides, as previous work did, because the propagation of RGB three-color light is independent of each other. The simulation result of the full-color display with a white light source is shown CrystalsCrystals 2021 2021, 11,, x11 FOR, x FOR PEER PEER REVIEW REVIEW 8 of 812 of 12 in Figure6. It can be seen that the simulation results are also closer to the original picture.

Figure 6. Two-dimensional pupil expansion simulation results when white light is incident. FigureFigure 6. 6.Two-dimensionalTwo-dimensional pupil pupil expansion expansion simulation simulation results results when when white white light light is is incident. incident.

TheTheThe PVGs PVGs PVGs in in thisin this this work work work were were were fabricated fabricated fabricated using using using the the the following following following procedure. procedure. procedure. First, First, First, high high high indexindexindex glass glass glass used used used as as theas the the substrate substrate substrate to togetto getget a larger aa largerlarger field ﬁeldfield of view of view was was was clea clea cleanednedned by bysonication by sonication sonication in in glassinglass glass detergent, detergent, detergent, deionized deionized deionized water, water, water, and and ethyl ethyl alcohol alcoholalcohol for for for10 10min10 minmin in in eachin each each solvent solvent solvent and and and then then then thethethe substrate substrate substrate was was was cleaned cleaned cleaned by by byultraviolet ultraviolet ultraviolet ozon ozone ozone fore for for15 15 min.15 min. min. Subsequently, Subsequently, Subsequently, we we werecorded recorded recorded a a a polarizationpolarizationpolarization volume volume volume grating grating grating on on onthe the the photo-al photo-alignment photo-alignmentignment material; material; material; then then then we we weused used used a amixture a mixture mixture of of of chiralchiralchiral liquid liquid liquid crystal crystal crystal and and and prepolymer prepolymer prepolymer to to coveto cover cover andr and and be be beoriented oriented oriented by by bythe the the formerly formerly formerly prepared prepared prepared layerlayerlayer in in orderin order order to to getto get get a a 2D 2Da 2Dperiodical periodical periodical structure structure structure (as(as (as depicteddepicted depicted inin Figure Figurein Figure2 );2); ﬁnally, 2);finally, finally, this this structure this struc- struc- turewasture was frozen was frozen frozen by by the bythe UV the UV curing UV curing curing process. process. process. A A more more A more detailed detailed detailed preparation preparation preparation process process process is is shown shown is shown in inFigure Figurein Figure7 .7. 7.

Figure 7. The fabrication process of PVG. FigureFigure 7. 7.TheThe fabrication fabrication process process of of PVG. PVG.

TheTheThe first ﬁrst first step step step was was was to spin-coatspin-coatto spin-coat thethe photo-alignmentthe photo-alignment photo-alignment material. material. material. Brilliant Brilliant Brilliant yellow yellow yellow (BY) (BY) was (BY) wasselectedwas selected selected as theas theas photo-alignment the photo-alignment photo-alignment material material material [29 ][29] and [29] and in and the in experiment,thein the experiment, experiment, 0.06 0.06 g BY0.06 g dissolved BY g BYdis- dis- solvedinsolved 9.94 in g9.94 in DMF 9.94 g DMF g was DMF was an was appropriatean appropriatean appropriate proportion. prop proportion.ortion. BY BY was BYwas was spin-coatedspin-coated spin-coated on on oncleaned cleaned cleaned glass glass glass waveguidewaveguidewaveguide substrate substrate substrate at at 500 at 500 500 rpm rpm rpm for for for5 5s 5and s s and and then then then 3000 3000 3000 rpm rpm rpm for for for30 30 s30 to s sto obtain to obtain obtain uniform uniform uniform films. ﬁlms. films. ForForFor the the the second second second step, step, step, the the the glass glass glass coated coated coated with with with th thee th photo-alignmente photo-alignment photo-alignment material material material was was was placed placed placed in in thein the the opticaloptical path path and and then then was was exposed exposed to the to the opposite opposite circularly circularly polarized polarized light light by twoby two beams. beams. In ourIn our experiment, experiment, a 457 a 457 nm nm laser laser was was used used as theas the recording recording light. light. Two Two opposite-handed opposite-handed circularlycircularly polarized polarized beams beams were were overlapped overlapped on onthe the sample sample with with a certain a certain angle angle to gener-to generate atethe the polarized polarized interference interference patterns patterns recorded recorded in thein the BY BYfilm. film. It is It worth is worth noting noting that that we we neededneeded to exposeto expose three three (in-coupling, (in-coupling, intermediat intermediate, ande, and out-coupling) out-coupling) gratings gratings at onceat once by by rotatingrotating the the glass glass substrate. substrate. The The in-coupling in-coupling grating grating was was first first exposed, exposed, and and then then the the glass glass substratesubstrate was was rotated rotated counterclockwise counterclockwise by 50°by 50° to obtain to obtain an intermediatean intermediate coupling coupling grating, grating, andand finally, finally, the the glass glass substrate substrate was was rotated rotated counterclockwise counterclockwise by by50° 50° again again to exposeto expose the the out-couplingout-coupling grating. grating. For For in-coupling in-coupling gratin grating (org (orout-coupling out-coupling grating) grating) and and intermediate intermediate couplingcoupling grating grating PVGs, PVGs, the the half half of exposure of exposure angle angle 𝜃 was𝜃 was set setas 38° as 38° and and 72.3°, 72.3°, respectively, respectively,

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optical path and then was exposed to the opposite circularly polarized light by two beams. In our experiment, a 457 nm laser was used as the recording light. Two opposite-handed circularly polarized beams were overlapped on the sample with a certain angle to generate the polarized interference patterns recorded in the BY film. It is worth noting that we needed to expose three (in-coupling, intermediate, and out-coupling) gratings at once by rotating the glass substrate. The in-coupling grating was first exposed, and then the glass substrate was rotated counterclockwise by 50◦ to obtain an intermediate coupling grating, and finally, the glass substrate was rotated counterclockwise by 50◦ again to expose the out-coupling grating. For in-coupling grating (or out-coupling grating) and intermediate coupling grating PVGs, the half of exposure angle θ was set as 38◦ and 72.3◦, respectively, to achieve the desired different horizontal periods. The third step was to prepare the liquid crystal layer. The liquid crystal material was then sprayed with a spray gun to the position of the three gratings. The reason for choosing spraying is that (1) the concentration of the liquid crystal material solution required for different gratings is different, and different gratings can be distinguished by spraying; (2) compared with the spin coating method, the surface of the grating obtained by spraying is flatter. In this paper, the RM257 (ne = 1.678, no = 1.508 at 550 nm) with chiral dopant R5011 and Irgacure 651 were used as the chiral twist liquid crystal (LC) polymer precursor and the photoinitiator, respectively. Toluene was employed as a solvent to dissolve all the solute materials after oscillation with a proportion of 1:8. The mass fractions of each solute material for proposed PVGs (taking green for example) are listed in Table1. The fourth step was to UV-cure the spin-coated glass substrate.

Table 1. The mass fractions of each solute material for proposed PVGs.

PVGs RM257 R5011 Irgacure651 In/out-coupling PVG 0.8310 g 0.0200 g 0.0437 g Intermediate coupling PVG 1.2564 g 0.0200 g 0.0661 g

The optical setup, including schematic light path diagram and real light path we used, is shown in Figure8. The intensity of each path beam for interference was equal, and the exposure dosage was 1 J/cm2. After the light beam is emitted from the laser, it first passes through the first half-wave plate. The function of this half-wave plate is to control the light intensity ratio of the two orthogonally polarized P waves and S waves that are split by the following PBS. This is because in the final exposure, it is necessary to control the two coherent polarized lights with different rotation directions to have the same light intensity, so that a clearer polarization pattern can be obtained, so it is very necessary to place a half-wave plate in front of the PBS. Then, the beam is filtered through a spatial filter. The spatial filter plays a filtering role to obtain a more ideal Gaussian beam, so as to make the most central part of the Gaussian beam as large as possible. The beam is then expanded by a beam expander. The beam expander is composed of a small hole and a double cemented lens, which can complete the beam expansion and collimation of the beam. In the actual experimental operation, the beam diameter after beam expansion can reach 2~3 cm. After the expanded beam is split by the PBS, a P wave and an S wave are formed respectively, and the intensity of the two beams is the same. The quarter-wave plate converts the two linearly polarized beams into left-handed circularly polarized light and right-handed circularly polarized light, respectively. Crystals 2021, 11, x FOR PEER REVIEW 9 of 12

to achieve the desired different horizontal periods. The third step was to prepare the liquid crystal layer. The liquid crystal material was then sprayed with a spray gun to the position of the three gratings. The reason for choosing spraying is that 1) the concentration of the liquid crystal material solution required for different gratings is different, and different gratings can be distinguished by spraying; 2) compared with the spin coating method, the surface of the grating obtained by spraying is flatter. In this paper, the RM257 (ne = 1.678, no = 1.508 at 550 nm) with chiral dopant R5011 and Irgacure 651 were used as the chiral twist liquid crystal (LC) polymer precursor and the photoinitiator, respectively. Toluene was employed as a solvent to dissolve all the solute materials after oscillation with a proportion of 1:8. The mass fractions of each solute material for proposed PVGs (taking green for example) are listed in Table 1. The fourth step was to UV-cure the spin- coated glass substrate.

Table 1. The mass fractions of each solute material for proposed PVGs.

PVGs RM257 R5011 Irgacure651 In/out-coupling PVG 0.8310 g 0.0200 g 0.0437 g Intermediate coupling 1.2564 g 0.0200 g 0.0661 g PVG

The optical setup, including schematic light path diagram and real light path we used, is shown in Figure 8. The intensity of each path beam for interference was equal, and the exposure dosage was 1 J/cm2. After the light beam is emitted from the laser, it first passes through the first half-wave plate. The function of this half-wave plate is to control the light intensity ratio of the two orthogonally polarized P waves and S waves that are split by the following PBS. This is because in the final exposure, it is necessary to control the two coherent polarized lights with different rotation directions to have the same light intensity, so that a clearer polarization pattern can be obtained, so it is very necessary to place a half-wave plate in front of the PBS. Then, the beam is filtered through a spatial filter. The spatial filter plays a filtering role to obtain a more ideal Gaussian beam, so as to make the most central part of the Gaussian beam as large as possible. The beam is then expanded by a beam expander. The beam expander is composed of a small hole and a double cemented lens, which can complete the beam expansion and collimation of the beam. In the actual experimental operation, the beam diameter after beam expansion can reach 2~3 cm. After the expanded beam is split by the PBS, a P wave and an S wave are Crystals 2021, 11, 333formed respectively, and the intensity of the two beams is the same. The quarter-wave 9 of 11 plate converts the two linearly polarized beams into left-handed circularly polarized light and right-handed circularly polarized light, respectively.

Crystals 2021, 11, x FOR PEER REVIEW 10 of 12

Figure 8. The optical setup: (a) the schematic light path diagram; (b) the real light path. Figure 8. The optical setup: (a) the schematic light path diagram; (b) the real light path.

3. Results and3. Results Discussion and Discussion The desiredThe vertical desired periodical vertical periods periodical for each periods PVG for were each generated PVG were after generated the spray- after the spray- coating of preparedcoating of chiral prepared dopant chiral solutions dopant until solutions sufficient until sufﬁcientthickness thickness(> 4.5 μm). (> As 4.5 aµ m).re- As a result, sult, the moleculesthe molecules of birefringent of birefringent materials materials formed formedan inclined an inclinedhelical structure, helical structure, provided provided by

by the anchoringthe anchoring power of power photoalignment of photoalignment layers and layers helix and twist helix power twist of power chiral ofdopant chiral dopant to to produce theproduce designed the designedtwo-dimensional two-dimensional periodic structure periodic after structure the partial after theevaporation partial evaporation of the solvent.of theThe solvent.coated substrate The coated was substrate then cured was with then 365 cured nm UV with light 365 at nm a dosage UV light of 5 at a dosage 2 J/cm2 in a nitrogenof 5 J/cm environment.in a nitrogen The environment. glass substrates The used glass here substrates have a rectangular used here have shape arectangular (30 mm × 30shape mm) with (30 mm a thickness× 30 mm) of with1 mm, a thicknessand the refractive of 1 mm, index and the is 1.8. refractive index is 1.8. The imagingThe effects imaging of red, effects green, of and red, blue green, are and shown blue in are Figure shown 9. inA Figurecolorful9. Aimage colorful image was used aswas the usedexample as the input, example and a input, monoch andromatic a monochromatic light source light(red, sourcegreen, (red,and blue, green, and blue, respectively)respectively) was used. A was camera used. was A cameraplaced wasin front placed of the in frontout-coupler of the out-coupler with a designed with a designed eye-relief of 18 mm to capture the output image. The image within the range of 35◦ diagonal eye-relief of 18 mm to capture the output image. The image within the range of 35° diag- FOV was fully and clearly observed without signiﬁcant color shift or distortion. The size onal FOV was fully and clearly observed without significant color shift or distortion. The of the exit pupil was measured to be 18 mm long and 17 mm wide. In fact, the exit pupil size of the exit pupil was measured to be 18 mm long and 17 mm wide. In fact, the exit size can be enlarged more by using a larger out-coupler. pupil size can be enlarged more by using a larger out-coupler.

Figure 9. PhotographFigure 9. of Photograph the output imageof the output of the proposed image of waveguidethe proposed near-eye waveguide display near-eye system. display (a) red system. image; (a ()b ) green image; (c) bluered image. image; (b) green image; (c) blue image

The optical Theefficiency optical of efficiency the proposed of the proposedsystem was system measured. was measured. The input The luminous input luminous flux 2 flux of a fullof awhite fullwhite image image was wasmeasured measured as 77.3 as 77.3 lm, lm, and and output output luminance luminance was was 9142 (nit)cd/m , (nit)cd∕m2, whichwhich corresponds corresponds to anan efficiencyefficiencyof of 118.3 118.3 nit/lm nit/lm per per lumen. lumen. We We also also measured meas- efficiency ured efficiencyfor threefor three primary primary color color images, images, and and got got 121.0 121.0 nit/lm, nit/lm, 132.4 132.4 nit/lm, nit/lm, andand 96.7 nit/lm per nit/lm per lumenlumen for for red, red, green, green, and and blue blue im images,ages, respectively. respectively. Meanwhile, Meanwhile, we we measured measured the light the light luminanceluminance from from a D65 a D65 light light source source before before and and passing passing through through the the out-couplers out-couplers area and area and obtainedobtained a 72% a 72% transmittance, transmittance, which which indicates indicates good good transparency transparency for for the the ambi- ambient light. ent light.

4. Conclusions In summary, we demonstrated a two-dimensional exit pupil expansion structure based on PVG for a waveguide display system. The proposed PVG couplers have a two- dimensional anisotropic periodic structure and present a unique highly efficient single- order Bragg diffraction with polarized selectivity. We employed the scheme of multiple PVG layers to achieve the chromatic diffraction features for PVG couplers and designed the matching double-layer waveguide structure to realize a full-color near-eye display by Zemax. The polarized interference exposure with photo-alignment methods was utilized to fabricate the proposed PVG and the prepared PVG couplers exhibited over 70% diffraction efficiency with large diffraction angles at spectra of blue, green, and red. We also demonstrated a prototype to validate the monochromatic-color display function of our designs, and the results showed that a clear full-color display with a diagonal FOV of around 35° and an exit pupil of 18 mm long and 17 mm wide was achieved. The overall optical efficiency was measured as high as 118.3 nit/lm per lumen with a transparency of

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4. Conclusions In summary, we demonstrated a two-dimensional exit pupil expansion structure based on PVG for a waveguide display system. The proposed PVG couplers have a two-dimensional anisotropic periodic structure and present a unique highly efficient single- order Bragg diffraction with polarized selectivity. We employed the scheme of multiple PVG layers to achieve the chromatic diffraction features for PVG couplers and designed the matching double-layer waveguide structure to realize a full-color near-eye display by Zemax. The polarized interference exposure with photo-alignment methods was utilized to fabricate the proposed PVG and the prepared PVG couplers exhibited over 70% diffraction efficiency with large diffraction angles at spectra of blue, green, and red. We also demonstrated a prototype to validate the monochromatic-color display function of our designs, and the results showed that a clear full-color display with a diagonal FOV of around 35◦ and an exit pupil of 18 mm long and 17 mm wide was achieved. The overall optical efficiency was measured as high as 118.3 nit/lm per lumen with a transparency of 72% for ambient light. This work makes the PVG with the proposed waveguide structure a promising candidate for AR applications with two-dimension exit pupil expansion.

Author Contributions: Conceptualization, J.C. and Y.Z.; methodology, J.C.; software, J.C.; validation, J.C. and Y.Z.; writing—original draft preparation, J.C.; writing—review and editing, J.C. and Y.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data is contained within the article. Acknowledgments: We would like to express our sincere appreciations to the anonymous referee for valuable suggestions and corrections. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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