crystals 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 q n ypupil q (1) Licensee MDPI, Basel, Switzerland. where q 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, q0 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 ⋅ ⋅= ⋅ ⋅ (1) where represents the semi-field of view at the entrance pupil, is the radius of the pupil in object space, is the refractive index in the object space, is the chief ray angle at the exit pupil, is the radius of the exit pupil, and 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% vignet- ting 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 pa- in 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.