Liquid Crystal Flat Optics for Near-Eye Displays

University of Central Florida STARS

Electronic Theses and Dissertations, 2020-

2021

Liquid Crystal Flat Optics for Near-eye Displays

Tao Zhan University of Central Florida, [email protected]

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STARS Citation Zhan, Tao, "Liquid Crystal Flat Optics for Near-eye Displays" (2021). Electronic Theses and Dissertations, 2020-. 591. https://stars.library.ucf.edu/etd2020/591 LIQUID CRYSTAL FLAT OPTICS FOR NEAR-EYE DISPLAYS

TAO ZHAN B.S. Nanjing University, 2016

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Optics and Photonics at the University of Central Florida Orlando, Florida

Spring Term 2021

Major Professor: Shin-Tson Wu

ii ABSTRACT

Augmented reality (AR) and virtual reality (VR) displays, considered as the next-

generation information platform, have shown great potential to revolutionize the way how we

interact with each other and the digital world. Both AR and VR are disruptive technologies that

can enable numerous applications in education, healthcare, design, training, entertainment, and

engineering. Among all the building blocks of these emerging devices, near-eye displays (NEDs)

play a critical role in the entire system, through which we can perceive the virtual world as the real

one. However, the visual experience offered by existing NED technologies is still far from

satisfying the human vision system regarding the display resolution, image clarity, and light

efficiency.

This dissertation provides original solutions to remove the abovementioned roadblocks

using a novel type of liquid crystal (LC) planar optics based on the Pancharatnam-Berry phase

(PBP). Firstly, we demonstrated a polarization-multiplexed method that can double the perceived

angular resolution of most NEDs, utilizing the polarization-sensitivity of a customized

Pancharatnam-Berry phase deflector (PBPD). Secondly, a broadband Pancharatnam-Berry phase lens (PBPL) is developed and integrated with conventional VR optics, such that both monochromatic and chromatic aberrations (CAs) are reduced by more than two times, offering significantly sharper imagery to the viewer. Also, a diffractive deflection film (DDF) based on

PBP is designed with a directional display panel to reduce the wasted light in current VR devices, which can boost the system light efficiency by more than two times. Furthermore, novel fabrication methods of the PBP optical elements are invented for the need of mass-production.

iii The proposed methods and designs are examined in both optical simulation and prototype hardware with public demonstrations. The verified performance enhancement proves that the proposed LC-based PBP optical elements offer considerable value and potential for practical applications in next-generation NEDs.

To my family

v ACKNOWLEDGMENT

This Ph.D. dissertation is a culmination and synthesis of all the work consolidated in the past several years and shaped by an entire community of professors, students, and experts. I feel enormously grateful for all the support, scientifically and personally, that I have received during my time at CREOL. It would be much more challenging without all of you here with me.

I would like to start by expressing my deepest appreciation to my Ph.D. advisor and life- long friend Dr. Shin-Tson Wu for his visionary leadership, patient mentorship, and continuous encouragement. “What’s your biggest contribution to the world so far?” the first question Prof.

Wu asked me when he picked me up from the Orlando International Airport, has been the source

of my self-motivation throughout my graduate work and keeps me focused on meaningful ideas

and impactful projects. I would also like to render my warmest thanks to his better half Cho-Yan

Hsieh for her love and care during this endeavor of mine.

I’d like to thank my committee members, Prof. Jim Moharam, Prof. Patrick L. LiKamWa, and

Prof. Yajie Dong, for inspiring discussions and constructive feedback on the ideas presented in this dissertation and elsewhere. Their willingness and dedication to foster understanding and discovery in young scientists are totally beyond my expectation. Paticularly, the RCWA method invented and taught by Prof. Moharam is of great significance to my research, and I feel very grateful to have the chance to take his courses at CREOL.

In Wu’s group, I have had the wonderful opportunity to meet and collaborate with so many

kind and talented people, particularly Yi-Hsin Lin, Yan Li, Ethan Cheng, Fenglin Peng, Ruidong

Zhu, Haiwei Chen, Juan He, Fangwang Gou, Yuge Huang, Ziqian He, Kun Yin, Jianghao Xiong,

Md Javed Rouf Talukder, Yannanqi Li, En-lin Hsiang, Junyu Zou, Zhiyong Yang, Qian Yang,

vi Hao Chen, Caicai Zhang, Yishi Weng, and Zhenyi Luo. Special thanks to John Lee and Guanjun

Tan for introducing me to liquid crystal research and numerical simulation when I started my Ph.D. journey and continuously supporting me with invaluable discussions, fruitful collaborations, and

lots of fun late-night chats.

Last but by no means least, I would like to express my deepest appreciation to my family

for their education, support, and love through my academic endeavors.

vii TABLE OF CONTENTS

LIST OF FIGURES ...... x

LIST OF TABLES ...... xv

LIST OF ABBREVIATIONS AND ACRONYMS ...... xvi

CHAPTER 1: INTRODUCTION ...... 1

1.1 Near-Eye Display Basics ...... 1

1.2 Motivation and Objectives ...... 4

CHAPTER 2: PANCHARATNAM-BERRY PHASE OPTICAL ELEMENTS ...... 8

2.1 Background ...... 8

2.2 Bandwidth Broadening ...... 11

2.3 Fabrication Methods ...... 15

CHAPTER 3: RESOLUTION ENHANCEMENT ...... 21

3.1 Background ...... 21

3.2 System Design ...... 23

3.3 PBP Deflector Fabrication ...... 26

3.4 Image Factorization ...... 27

3.5 System Integration ...... 29

3.6 Summary ...... 33

CHAPTER 4: ABERRATION CORRECTION ...... 34

4.1 Background ...... 34

viii 4.2 System Design ...... 38

4.3 PBP Lens Fabrication ...... 42

4.4 System Integration ...... 45

4.5 Catadioptric VR Optics ...... 47

4.6 Summary ...... 49

CHAPTER 5: LIGHT EFFICIENCY IMPROVEMENT ...... 50

5.1 Background ...... 50

5.2 Directional Display ...... 53

5.3 Diffractive Deflection Film ...... 56

5.4 Experiment ...... 57

5.5 Summary ...... 61

CHAPTER 6: SCALE-UP FABRICATION ...... 63

6.1 Background ...... 63

6.2 Paraxial Analysis ...... 64

6.3 Mask Fabrication and Characterization ...... 66

6.4 PBPOE Printing ...... 69

6.5 Summary ...... 71

CHAPTER 7: CONCLUSION ...... 72

APPENDIX: STUDENT PUBLICATIONS...... 74

REFERENCES ...... 82

LIST OF FIGURES

Figure 1-1: Illustration of the mixed reality continuum...... 1

Figure 1-2: Optical layout of NEDs in VR and AR devices...... 2

Figure 1-3: Comparison of input and output images of a VR NED using Fresnel singlet...... 5

Figure 2-1: Schematic illustration of LC axis orientation in a PBPD (a) and lens (b); Corresponding

phase change along the horizontal axis (c, d) and illustration of polarization selectivity (e, f). .... 9

Figure 2-2: Schematic illustration of actively switching PBP optical elements...... 10

Figure 2-3: Simulated first-order diffraction efficiency of PBPD using LC materials with different

resonance wavelengths...... 12

Figure 2-4: Simulated first-order diffraction efficiency of a PBPD using the negative-dispersion

LC material...... 13

Figure 2-5: (a) Schematic illustration of LC orientation in the multi-layer twisted PBP optics

elements. (b) Simulated first-order diffraction efficiency of the PBP elements with these twist

structures...... 14

Figure 2-6: Schematic illustrations of polarized exposure setups based on the (a) two-beam, (b)

Sagnac, (c) Michelson, and (d) Mach-Zehnder interferometer. (S: substrate; M: mirror; TL: template lens; HWP: half-wave plate; QWP: quarter-wave plate; NPBS: non-polarizing beam splitter) ...... 17

x dimensional scanner. (L: lens; S: substrate; M: mirror; P: polarizer; RP: rotatable polarizer; CL: cylindrical lens; QWP: quarter-wave plate; SLM: spatial light modulator; NPBS: non-polarizing beam splitter; CCD: charge-coupled device; MS: motorized motion stage) ...... 18

Figure 2-8: Schematic illustration of the fabrication process of (a) LC polymer PBP optical elements and (b) switchable LC PBP optical elements...... 20

Figure 3-1: Schematic diagram describing the principle of resolution enhancement by the shifted superimposition method. (a) From the perspective of pixel, each original pixel (green) with pitch

P is separated diagonally into two virtual pixels (blue and yellow). (b) From the panel perspective, the original panel is split into two virtual panels. (c) A new pixel grid (orange) with half of the pixel pitch (P/2) is formed by superimposition of two virtual panels...... 23

Figure 3-2: A typical optical design for VR headsets. Pixel locations in the panel are mapped to different directions of nearly collimated beams by the lens...... 24

Figure 3-3: Illustration of orientation distribution of local LC anisotropy director in a polymer

PBPD. The thickness d satisfies the half-wave plate condition, and the period is determined by the desired separation angle of the two virtual pixel grids...... 𝚲𝚲 25

Figure 3-4: Schematic illustration of the resolution enhanced NED system based on polarization multiplexing. PML: polarization modulation layer...... 26

Figure 3-5: Polarization holography setup for generating the LC orientation pattern in PBPD devices. (M: mirror; OL: objective lens; PH: pinhole; CL: collimating lens; BS: beam splitter;

QWP: quarter-wave plate; S: substrate) ...... 27

Figure 3-6: (a) Pixel illustration and (b) mapping matrix construction for image generation...... 29

xi Figure 3-7: Schematic illustration of the polarization modulation layer. The polarization orientation angle of the light from the display is rotated by the PR. Then a quarter-wave plate is

utilized to convert the TE/TM ratio to RCP/LCP ratio for the desired separation ratio after PBPD.

...... 30

Figure 3-8: Photograph of the assembled prototype installed on an optical table...... 31

Figure 3-9: Images captured through a camera with (a) original and (b) enhanced resolution of a

“Siemens star” resolution target and an athletic shirt. The screen door effect is reduced, and the

pixel density is doubled simultaneously...... 32

Figure 4-1: Illustration of transverse CAs in a) a compact refractive Fresnel lens, b) a diffractive

LC lens, and c) the proposed hybrid doublet exhibiting achromatic performance...... 37

Figure 4-2: Optical layout of the proposed VR optics, including a PBPL for the optical CAC. .. 38

Figure 4-3: Illustration of polarization state changes through the planar optical parts in the

proposed system...... 39

Figure 4-4: Standard spot diagram with RMS spot radius for (a) Fresnel singlet and (b) proposed

hybrid optics. Color by wavelength, Red: 610nm, Green: 540nm, Blue: 450nm...... 40

Figure 4-5: The lateral color shift of the VR viewing optics with and without PBPL...... 42

Figure 4-6: Schematic illustration of LC anisotropy axis orientation in the PBPL with flat geometry

and a twist-homo-twist structure for broadband operation...... 43

Figure 4-7: Measured zero-order leakage of the ultra-broadband PBPL and the emission spectrum

of the LCD displaying white light. Inside is a photo of the fabricated 2-inch PBPL...... 45

Figure 4-8: (a)Half-ﬁeld CA testing pattern displayed on the LCD and the resulting images

captured through the (b) conventional and (c) proposed viewing optics...... 46

xii Figure 4-9: Full-field black-and-white image displayed on the LCD and the resulting images captured through the conventional and proposed hybrid viewing optics. The three enlarged parts are center field and edge fields at 0° and 45° azimuth from left to right...... 47

Figure 4-10: The lateral color shift of a pancake VR viewing optics with a PBPL...... 48

Figure 4-11: Standard spot diagram with RMS spot radius of the pancake lens integrated with a

PBPL. Color by wavelength, Red: 610nm, Green: 540nm, Blue: 450nm...... 48

Figure 5-1: Illustration of a typical VR display module with a wide-view display...... 51

Figure 5-2: (a) Optical layout of the VR display module used in the simulation; (b) Exemplary

angular intensity profiles of the display panel described in Equation (1)...... 54

Figure 5-3: Simulated luminous efficiency of a single pixel in the VR optical module depicted in

Fig. 2(a) with the angular luminance distributions shown in Equation 1 and Figure 2(b)...... 55

Figure 5-4: (a) Illustration of the directional VR display module; (b) Illustration of the directional

VR display module with a laminated DDF on the display panel...... 57

Figure 5-5: Schematic illustration of the experiment setup...... 58

Figure 5-6: Scattering angular distributions of the diffusers used in the experiment. Diffuser A represents a directional display, while Diffuser B represents the conventional LCD...... 59

Figure 5-7: Measured luminous efficiency in the exemplary VR display module...... 60

Figure 6-1: (a) Local transmission direction followed by (b) front and (c) side view of the dichroic

dye director orientations in absorption-based a-PGs...... 66

Figure 6-2: Fabrication process of the a-PG, including two spin-coating and exposure steps. .... 67

xiii Figure 6-3: Polarization response of absorption-based PGs. (a) Measurement setup including a

linearly polarized laser and a rotatable quarter-wave plate to control the incident polarization. (b)

Measured and calculated diffraction response to the rotation of a quarter-wave plate...... 69

Figure 6-4: Photopatterning using a-PGs as the polarization mask. (a) Contact photopatterning

setup, including a flashlight as the light source and an optical mount to fix the a-PG and PAL-

coated substrate. POM images of the (c) a-PG mask and (d) optically imprinted PBPD, where the period is around 60 µm...... 71

xiv LIST OF TABLES

Table 2-1: Driving mechanism and the consequent responses of PBP defectors and lenses...... 11

Table 4-1: Recipe of the materials and spin-coating in the PBL fabrication (by weight)...... 44

xv LIST OF ABBREVIATIONS AND ACRONYMS

A-PG Absorption-Based Polarization Grating

AR Augmented Reality

BY Brilliant Yellow

CA Chromatic Aberration

CAC Chromatic Aberration Correction

DDF Diffractive Deflection Film

DMD Digital Micro-Mirror Device

DMF Dimethylformamide

DPSS Diode-Pumped Solid-State

IPD Interpupillary Distance

IPS In-Plane Switching

ITO Indium Tin Oxide

L/RCP Left/Right Circularly Polarized

LC Liquid Crystal

LCD Liquid Crystal Display

LCOS Liquid Crystal On Silicon

LED Light-Emitting Diode

MVA Multi-Domain Vertical Alignment

NED Near-Eye Display

OLED Orangic Light-Emitting Diode

PAL Photo-Alignment Layer

xvi PBP Pancharatnam-Berry Phase

PBPD Pancharatnam-Berry Phase Deflector

PBPL Pancharatnam-Berry Phase Lens

PBPOE Pancharatnam-Berry Phase Optical Element

PBS Polarizing Beam Splitter

PG Polarization Grating

PMMA Polymethyl Methacrylate

POM Polarized Optical Microscope

PR Polarization Rotator

RM Reactive Mesogen

RMS Root Mean Square

TN Twisted-Nematic

UV Ultra-Violet

VR Virtual Reality

μ-LED Micro Light-Emitting Diode

μ-OLED Micro Organic Light-Emitting Diode

xvii CHAPTER 1: INTRODUCTION

1.1 Near-Eye Display Basics

As an essential component of modern civilization, information display technologies have

undergone rapid and considerable development since the third industrial revolution. In the past

few decades, mainstream display technologies evolved from conventional cathode ray tubes to

various flat panels such as liquid crystal display (LCD) [1] and organic light-emitting diode

(OLED) [2], which act as an indispensable cornerstone of the current mobile internet era. More

recently, the emerging NED [3,4,5] is painting a stimulating portrait of the future, where all types

of displays can be replaced by a pair of glasses, or even contact lenses, that stay with the user anywhere and anytime, if needed. It is believed that this next-generation display technology will

become a novel user interface coupled with the human vision system and be able to revolutionize the user experiences of displays.

Figure 1-1: Illustration of the mixed reality continuum. The way how human beings interact with each other and the surrounding environment will no longer be the same as previously after the widespread use of consumer electronics integrated

NEDs. As shown in Fig. 1-1, at one end of the spectrum is VR deceives that completely block the

1 surrounding environment and create a virtual world where the user is immersed, which also means an arbitrary environment can be recorded and then reconstructed by the NED. At the other end is

AR devices that provide a high-quality optical-see-through view of surroundings and also enrich the real world by digital contents. It is worth mentioning that VR devices can also transform to AR using the same NED by adding the digital video-see-through capability.

Figure 1-2: Optical layout of NEDs in VR and AR devices. The optical layouts of NEDs in VR and AR are significantly different from each other, as compared in Fig. 1-2. Both of them need an image generation unit, i.e., a display and an optical

2 system to project the image to the eye. For optical-see-through NEDs, an optical combiner is

needed to overlay the virtual image from the display on the physical world.

NEDs in VR can be as simple as a display panel coupled with a viewing lens since the

essence of VR NEDs is just magnifying the display panel’s image with extremely compact optics.

Common display panels include LCDs and OLEDs, which are similar to those used in smartphones.

Emerging display technologies based on micro light-emitting diode (μ-LED) [6] and micro OLED

(μ-OLED) [7] are also under development for application in VR for higher resolution and efficiency.

The complexity of AR NED systems is much higher than that of VR. Aside from a display engine for content generation, an optical combiner is necessary for optical-see-through VR devices.

There are, in general, two types of AR light engines: emissive and non-emissive ones. The emissive light engine employs emissive display panels, such as μ-LED, and a projection system. The non- emissive light engines typically have an illumination system and a spatial light modulator, such as liquid-crystal-on-silicon (LCOS) [8] or digital micro-mirror device (DMD) [9]. The optical combiners for AR NEDs can also be classified as free-space combiners and waveguide combiners.

The free-space combines are essentially beam splitters in various forms, such as cube beam splitters, curved partial reflectors [10], and freeform prisms [11]. The other kind, waveguide combiners [12,13], is more compact but also complex. The images rays produced by the light engine are initially coupled into the waveguide and propagate along the wavelength by total internal reflection until coupled out in front of the eye. The couplers used in waveguide combiners can be reflective, refractive, and diffractive.

3 Enabled by continuously advancing optical technologies, AR and VR NEDs exhibit the

potential to trigger attractive applications, including but not limited to education, design, training,

retail, and entertainment. The ultimate goal of AR and VR display development is to offer reality- like images that can simulate, merge into physical reality. This target is still not easy to achieve at

the current stage due to the demanding requirements of our human vision system, and many

challenges remain to be addressed in the future.

1.2 Motivation and Objectives

The performance of NEDs is still not satisfying enough regarding the user experience,

which significantly slows down the widespread application of VR and AR devices. Rather than polishing up the existing technologies used in NEDs, we propose to introduce novel LC flat optics as a disruptive technology to tackle the most critical challenges in NEDs, as discussed below.

A critical optical issue of NEDs is the limited angular resolution in a large field of view.

The human vision system is sensitive to spatial and angular resolution, and this factor is critical

for the realism of a display. The angular frequency people with normal vision can resolve is around

30 cycles per degree, which is also mentioned as 20/20 vision. This means an angular resolution

of 1 arcmin for a single feature or 2 arcmins of a contrasting intensity cycle. Currently, the angular resolution of mainstream VR headsets still falls short of the 20/20 vision acuity. Most of them

offer an angular resolution of ~15 pixels per degree or 4 arcmins in a ~100° field of view. As a

result, users with normal eyesight can observe the boundary of single pixels when wearing the VR

headset. An example image displayed in a VR NED is shown in Fig. 1-3. This phenomenon is also

referred to as the screen-door effect because the clear boundaries of pixels lead to the feeling that

4 user is watching the virtual world behind a screen-door. For a high-quality visual experience, significant enhancement of angular resolution is necessary.

Figure 1-3: Comparison of input and output images of a VR NED using Fresnel singlet.

5 The imaging performance of viewing optics in NEDs also needs improvement. Most VR headsets employ a single Fresnel lens as the viewing optics, resulting in apparent chromatic and monochromatic aberration, especially at peripheral fields. Therefore, most VR headsets adopt digital CAC at the cost of considerable computation recourses. Otherwise, the imaging quality will not be acceptable. Nevertheless, the digital compensation can only correctly handle the peak wavelengths of RGB color channels and is useless regarding monochromatic aberrations and sub- channel CAs as exhibited in Fig. 1-3. In most cases, crystal-clear imagery should be the baseline for display technologies.

In addition to image clarity issues, most current NEDs are not light efficient. The display panels used in mainstream NEDs are LCD or OLED displays that are originally designed for direct-view applications, such as smartphones. Thus, these panels manifest a large viewing angle, typically larger than ±40°. However, in VR NEDs, only rays emitting at a small angle can pass through the lens and enter the eyebox. The wasted stray rays outside of the effective cone may also bounce back and forth between the display and the view optics, resulting in a lower contrast ratio in the perceived image.

In this dissertation, theory, designs, and experiments are demonstrated to address the abovementioned issues and improve the key parameters in NEDs with versatile LC flat optics.

Firstly, the working principle of the PBP LC optics is introduced, and improved fabrication processes are explained in Chapter two. Next, a polarization-multiplexed resolution enhancement approach using the PBPD is presented to double the apparent angular resolution of VR NEDs and reduce the screen-door effect in Chapter three. Chapter four describes an optical chromatic aberration correction (CAC) method based on our homemade multilayer ultra-broadband PBPL,

6 which is able to considerably reduce both chromatic and monochromatic aberrations caused by the refractive index dispersion. Chapter five is about an optical design for achieving higher light efficiency in VR NEDs, where a PBP-based DDF is designed and integrated with a directional backlight such that the system light efficiency can be boosted by more than two times. Chapter six provides a summary and conclusion.

7 CHAPTER 2: PANCHARATNAM-BERRY PHASE OPTICAL ELEMENTS

2.1 Background

The LC Pancharatnam-Berry phase optical elements (PBPOEs) [14-17], also known as

geometric phase optics, diffractive waveplate, and geometric phase hologram, are functional

optical structures with patterned anisotropy. Different from convention refractive optical elements based on dynamic phase or optical path difference [18,19], PBPOEs offer spatial phase change through patterning the local anisotropic axes. Compared with refractive optics, LC PBPOEs have several distinct properties, including but not limited to compact form factor, high diffraction efficiency [20,21], strong polarization selectivity, and even flexibility in some cases [22].

PBPOEs are essentially half-wave plates with patterned fast axis orientations, whose working principle can be explained by Jones Calculus. For circularly polarized light input:

1 = , ± ± (2-1) 1 𝐽𝐽 √2 � � where and represents the Jones vector of LCP 𝑗𝑗and RCP light, respectively. When the light

+ − passes 𝐽𝐽through𝐽𝐽 a half-wave plate, the output ± becomes: ′ 𝐽𝐽 ± ± = ( ) ( ) ( ) ± = , (2-2) ′ 2𝑗𝑗𝑗𝑗 where R is the rotation matrix,𝐽𝐽 𝑅𝑅W− 𝜓𝜓is 𝑊𝑊the 𝜋𝜋half𝑅𝑅 -𝜓𝜓wave𝐽𝐽 retardation−𝑗𝑗𝑒𝑒 𝐽𝐽 ∓matrix. Equation (2-2) The handedness switches when circularly polarized light passes through a half-wave plate. The phase delay accumulated is proportional to the orientation angle of the fast axis . When the fast axis rotates from 0 to , the phase delay varies from 0 to 2 . Such a mapping from𝜓𝜓 orientation angle to phase can avoid the𝜋𝜋 phase discontinuity from 2 to 0 and𝜋𝜋 therefore enables smooth phase transition.

𝜋𝜋

Figure 2-1: Schematic illustration of LC axis orientation in a PBPD (a) and lens (b); Corresponding phase change along the horizontal axis (c, d) and illustration of polarization selectivity (e, f). Based on the abovementioned principle, an arbitrary phase pattern can be achieved by patterning the LC or LC polymer on a flat surface. Although various types of PBP optical elements

9 have been demonstrated, including deflectors [23-28], lenses [29-36], axicons [37], and q-plates

[39-41], PBPDs and lenses are of more interest in NED applications. Fig. 2-1(a) displays the LC

orientation in a PBPD with a linear phase change as plotted in Fig. 2-1(c), and Fig. 2-1(b) shows

that in a PBPL that has a parabolic phase pattern shown in Fig. 2-2(d). It should be mentioned that

the PBP optical elements have conjugate responses to LCP and RCP light, as indicated in Equation

(2-2). Thus, PBPDs can split RCP and LCP lens into opposite directions but with the same

transitional momentum as Fig. 2-1(e) depicts. Similarly, Fig. 2-1(f) indicates that PBPLes have

opposite optical power for the orthogonal circular polarizations. Due to this distinct polarization

dependency, the behavior of PBP optical elements can be switched by changing the input

polarization state, for example, using a switchable half-wave plate made of a LC cell.

Figure 2-2: Schematic illustration of actively switching PBP optical elements. Moreover, for PBP elements made of LCs, the functionality of the patterning can be erased

by adding a voltage between the two substrates coated with transparent electrodes, such as indium

tin oxide (ITO), as illustrated in Fig. 2-2. Table 1 summarizes the behavior of PBPD and lens under

switching.

10 Table 2-1: Driving mechanism and the consequent responses of PBP defectors and lenses.

w/o voltage w/ voltage

input polarization RCP LCP RCP LCP

PBPL optical power K −K 0 0

PBPD diffraction order 1 −1 0 0

Output polarization LCP RCP RCP LCP

2.2 Bandwidth Broadening

For applications in NEDs, it is essential for PBP optical elements to manifest high

diffraction efficiency within the entire display spectrum, approximately 450–650 nm, or at least at

three primary wavelengths for laser sources. The Jones Calculus analysis is based on the ideal half-

wave plate assumption, but the actual diffraction efficiency strongly depends on the actual phase

retardation of the LC layer, which can be expressed as [42]:

= ( nd ), (2-3) 2 𝜋𝜋Δ where n is the LC birefringence, d𝜂𝜂 denotes𝑠𝑠𝑠𝑠𝑠𝑠 the thickness�𝜆𝜆 of the LC layer, and represents the workingΔ wavelength. In the off-resonance region, the birefringence can be fitted by𝜆𝜆 the following

equation [43]:

n = ( ), (2-4) 2 ∗2 𝜆𝜆 𝜆𝜆 � 2 ∗2 where G is the proportionality constantΔ and𝐺𝐺 represents𝜆𝜆 − 𝜆𝜆 the working wavelength. Broadband PBP ∗ optics elements should keep their retardation𝜆𝜆 as close to half-wave as possible. Since the thickness cannot be changed at will after the fabrication process, the ratio of the LC birefringence to the working wavelength cannot have a large variation within the target spectral band. According to

11 Equation (2-4), the birefringent of most LC material decreases as wavelength increases within the

visible spectrum. As a result, the diffraction efficiency usually varies considerably across the

display spectrum. For achieving a larger spectral bandwidth𝜂𝜂 , a possible method is choosing LC or

LC polymer materials with a short resonance wavelength, as shown in Fig. 2-3.

Figure 2-3: Simulated first-order diffraction efficiency of PBPD using LC materials with different resonance wavelengths. However, it is still very challenging to keep the first-order diffraction efficiency larger than

90% within the working spectrum, even with the selected LC material. A potential approach to

further enlarge the spectral bandwidth of PBP optics elements is employing two LCs materials with distinct resonance wavelengths. Basically, the two LC layers are attached together, and the

LC orientations within these two layers are perpendicular to each other. The effective birefringence can be expressed as:

12 = (1 ) , (2-5) 2 ∗2 2 ∗2 𝑎𝑎 𝑏𝑏 𝑒𝑒𝑒𝑒𝑒𝑒 𝑎𝑎 𝜆𝜆 𝜆𝜆 2 ∗2 𝑏𝑏 𝜆𝜆 𝜆𝜆 2 ∗2 Δ𝑛𝑛 𝜌𝜌𝐺𝐺 � � 𝑎𝑎 � − − 𝜌𝜌 𝐺𝐺 � � 𝑏𝑏 � where and (1- ) is the relative layer𝜆𝜆 − thickness𝜆𝜆 , , and , represent𝜆𝜆 − 𝜆𝜆 the proportionality ∗ 𝑎𝑎 𝑏𝑏 𝑎𝑎 𝑏𝑏 constant𝜌𝜌 and resonance𝜌𝜌 wavelength of the LC materials,𝐺𝐺 respectively.𝜆𝜆 In this way, the ratio of the

LC birefringence to the working wavelength can be maintained at a stable level within a certain

range. This approach is similar to the optical CAC method used in the achromatic doublet lens

designs, but here we address the birefringence dispersion instead of refractive index dispersion.

Figure 2-4: Simulated first-order diffraction efficiency of a PBPD using the negative- dispersion LC material. Recently, a new type of polymerizable LC material with negative dispersion has been developed and recorded [44,45], which can be used to fabricate broadband PBP optical devices with only a single layer. Fig. 2-4 plots the simulated first-order diffraction efficiency of a PBPD

made of this material.

Figure 2-5: (a) Schematic illustration of LC orientation in the multi-layer twisted PBP optics elements. (b) Simulated first-order diffraction efficiency of the PBP elements with these twist structures. Another method to broaden the spectral bandwidth is to produce a twisted structure in the

LC layer in the vertical direction. Fig. 2-5(a) and Fig. 2-5(b) illustrate two broadband twist structures and their spectral responses, respectively. The two-layer dual-twist structure developed by Oh et al. [46] can significantly enlarge the working spectral bandwidth of PBP elements in the

14 Raman-Nath regime. The three-layer structure [47], including a non-twist layer sandwiched by

two symmetrically twisted layers, can further enlarge the spectral bandwidth and render the PBP

elements acceptable for display applications. It should be noted that the detailed twist structure depends on the actual LC material used in fabrication. The structure displayed in Fig. 2-5(a) is

optimized using typical birefringence data with G =2.4 µm−2 and λ*= 0.23 µm in Equation (2-4).

The twist direction and amplitude can be tailored by controlling the type and dosage of chiral

dopant added to the LC material.

2.3 Fabrication Methods

Photo-alignment is currently the most established way to pattern the LCs or LC polymers

for fabricating the PBP elements. There are two key steps in photo-alignment-based fabrication.

The target polarized light pattern needs to be constructed in the first place. Then, the constructed

orientation pattern needs to be recorded and transferred to LC.

The polarized light pattern can be provided by polarization interferometry, which is the

most common method used in PBP elements’ fabrication. Several classic interferometers are

modified for the fabrication process of PBPDs and lenses, as summarized in Fig. 2-6. The standard

two-beam exposure setup for PBPDs [48,49] is shown in Fig. 2-6(a). The input linearly polarized

light is split into two beams by a beam splitter. Two quarter-wave plates are used to convert the

linear polarization to circular polarization with opposite handedness in the two arms. As a result,

a linearly rotating polarization field, similar to Fig. 2-1(a), can be generated on the substrate. By

controlling the angle between two recording beams, the grating period is easily under control.

15 Therefore, this setup is particularly advantageous in fabricating PBPDs with a large deflecting

angle.

Fig. 2-6(b) illustrates a modified Sagnac interferometer designed for both PBPD and PBPL

fabrications [50]. A half-wave plate is placed before the linearly polarized light enters the

polarizing beam splitter to control the ratio between the s and p polarized light after the beam

splitting. The p-wave and s-wave propagate around the full loop in opposite directions before they

are combined together at the output of the interferometer. A quarter-wave plate is placed at the

exit to convert the s and p polarization into RCP and LCP, respectively. Simply tilting the center

mirror can generate the desired linear rotating orientation pattern for PBPDs. In the case of PBPL

fabrication, a template lens is placed in the loop to offer a parabolic phase difference on the

substrate. Compared with the two-beam setup, this modified Sagnac interferometer exposure

arrangement is exceptionally tolerant to environmental disturbance because it has a common path

for the s and p waves. Furthermore, there is an alternative common-path exposure setup utilizing

Wollaston prisms [51,52] to produce the linear pattern for fabricating PBPDs, which can be viewed

as a modified Fresnel’s biprism interferometer.

Fig. 2-6(c) illustrates a Michelson exposure setup, which can be considered as a folded version of the Mach-Zehnder setup displayed in Fig. 2-6(d). Both of them are suitable for the

fabrication of PBPLes and PBPDs with a small deflecting angle. If possible, all interferometers

should be installed on an optical table with a vibration isolation system and covered with enclosures to increase the quality of fabricated PBP optical elements. Although the Sagnac setup is not convenient for fabricating PBPDs with a large deflecting angle, it is a decent choice for PBP optics fabrication when the vibration isolation system and optical enclosure are not available.

Figure 2-6: Schematic illustrations of polarized exposure setups based on the (a) two-beam, (b) Sagnac, (c) Michelson, and (d) Mach-Zehnder interferometer. (S: substrate; M: mirror; TL: template lens; HWP: half-wave plate; QWP: quarter-wave plate; NPBS: non- polarizing beam splitter) The interferometry-based fabrication process is convenient for fabricating PBP gratings and lenses, but they are not appropriate for generating complex two-dimensional patterns. For more degrees of freedom, spatial light modulators and laser scanning methods can be applied in the exposure process.

Figure 2-7: Schematic illustration of non-interferometric optical setups for the fabrication of PBP optical elements. (a) Digital polarization holography using a LC spatial light modulator. (b) Digital lithography using a digital micro mirror device. Direct-writing method with (c) one- and (d) two-dimensional scanner. (L: lens; S: substrate; M: mirror; P: polarizer; RP: rotatable polarizer; CL: cylindrical lens; QWP: quarter-wave plate; SLM: spatial light modulator; NPBS: non-polarizing beam splitter; CCD: charge-coupled device; MS: motorized motion stage) Fig. 2-7(a) illustrates a digital polarization holography setup using a LC modulator [53].

The linearly polarized input light is firstly converted to circularly polarized light and then reflected

by a LC spatial light modulator. After being modulated by the programmable LC layer, the recording beam is switched back to linear polarization by the second quarter-wave plate, and the

18 phase pattern is now coded in the polarization directions. Fig. 2-7(b) displays another recording

setup with a DMD [54,55], which only records one polarization direction at a time. By

synchronizing the digital pattern on the DMD and the transmitting angle of the polarizer, an

arbitrary digital pattern can be generated after multiple exposure steps.

Aside from using spatial light modulators, there is another non-interferometry approach

called direct writing [56-58]. Generally, a polarization rotator (PR) and a motion stage are

synchronized together to scan a focused laser spot on the substrate and simultaneously print the

local polarization directions, as shown in Figs. 2-7(d). This straightforward approach can also create arbitrary patterns but may be very time-consuming if the sample is large and the resolution is high. If the desired pattern is symmetric in one direction, then a cylindric lens can replace the focusing lens and generate a focused line for scanning, as depicted in Figs. 2-7(c), which can considerably reduce the printing time.

All the pattern recording setups discussed above are applicable for both PBP LC polymer films and switchable PBP LC cells. Fig. 2-8(a) shows the detailed fabricating procedure of PBP polymer film. The first step is spin-coating the photo-alignment material [59], such as Brilliant

Yellow (BY), on a cleaned substrate. Then, the substrate is exposed using the designed polarization pattern and coated with the LC reactive mesogen (RM), such as RM257. The final step is curing the coated RM material with an ultra-violet (UV) lamp, forming the solid polymer film with the

expected optical functionality. The film thickness can be manipulated by the spin-coating speed or

RM solution concentricity. In the fabrication process of broadband PBP elements, RM coating and

UV polymerization processes are repeated for realizing the multi-layer structure. Fig. 2-8(b)

illustrates the fabrication process of switchable PBP LC cells, where two ITO substrates coated

19 with the photo-alignment layer (PAL) are required and assembled together as a cell. Then the cell is filled with LC via capillary action.

Figure 2-8: Schematic illustration of the fabrication process of (a) LC polymer PBP optical elements and (b) switchable LC PBP optical elements.

20 CHAPTER 3: RESOLUTION ENHANCEMENT

3.1 Background

Thanks to the rapid development of mobile processors, display panels, and motion tracking technologies, current VR headsets can offer users realistic-feeling experiences with the computer- generated immersive environment. NEDs in the VR system play a critical role in such an eye- opening experience by providing a field-of-view larger than 100°, which is a rare functionality among all display technologies. However, such a large field of view also decreases the angular resolution with the same pixel number. Currently, typical commercial VR product manifests ~6 arcmins angular resolution with 100° field of view, while people with 20/20 vision can resolve one arcmin. Thus, a six-fold enhancement in resolution density is required for ideal VR headsets. The user experience can be significantly affected by the screen-door effect caused by the black matrix in the low-resolution panels. For mitigating the screfen-door effect, display panels with reasonable size and a large number of pixels per inch are in need. Lately, flat panels with over 1000 pixels per inch have been fabricated and demonstrated [60], even though it is not in large-scale production yet. Such a 1000-pixel-per-inch display still fall short of the normal human eye acuity by half. In addition to the challenges in manufacturing high resolution panels, display brightness also drops since the aperture ratio decreases as the pixel density increases [61], and the data flow rate in driving electronics will also rise accordingly. Based on the spatial-varying resolution in the human visual system, foveated displays offer a high resolution in the fovea region but a low one in the peripheral. This method can redefine the stringent balance between the field of view and angular resolution, lowering the total pixel numbers while delivering reasonable high-resolution imagery.

21 However, it demands extra gaze-tracking apparatus [64] and a beam steering module in the headset

to maintain a decent resolution in the gaze area.

Preciously, different methods were proposed to boost the apparent pixel density of various

display systems. For instance, a mechanical image shifter [65] can be utilized to generate spatially

shifted pixel grids in a series of sub-frames and then overlay them together to achieve higher

resolution for projection displays. However, a mechanically oscillating image shifter is a decent

solution in projection systems but not in head-mounted NEDs. Additionally, this technique also

results in a reduced framerate, which is undesirable in VR since the images cotents need fast

motion picture response time to suppress image motion blurs [66]. Other methods based on optical

overlaying and stacking displays were developed [67–69] to avoid mechanical vibration and framerate reduction. Even though these methods can provide higher pixel density, using multiple

display panels usually causes decreased aperture ratio and low optical efficiency.

Here, an optical approach based on polarization multiplexing instead of time multiplexing in our previous work [70] is presented to enhance the pixel density without reducing the frame rate.

This method consists of dividing each pixel optically into two virtual pixels by a passive LC-

polymer-based PBP [71,72] deflector [73-76], which creates a new pixel grid with a smaller pixel pitch. Also, a pixelated polarization management layer is employed to control the separation ratio between two split pixels, such that the two split pixel grids can display images at the same time without losing frame rate. With this versatile method, the pixel density can be doubled for all types of flat panel displays used in VR headsets.

22 3.2 System Design

The operation principle of our method is to separate each original pixel into two virtual

pixels optically and thus create a new pixel grid with higher pixel density, as Fig. 3-1 illustrates.

For a display panel with pixel pitch , the diagonal shifting length from original pixel to virtual pixels should be 2 /4, so that a new𝑃𝑃 pixel grid with half of the pixel pitch can be generated.

√ 𝑃𝑃

Figure 3-1: Schematic diagram describing the principle of resolution enhancement by the shifted superimposition method. (a) From the perspective of pixel, each original pixel (green) with pitch P is separated diagonally into two virtual pixels (blue and yellow). (b) From the panel perspective, the original panel is split into two virtual panels. (c) A new pixel grid (orange) with half of the pixel pitch (P/2) is formed by superimposition of two virtual panels. In a VR system, the light from each pixel is collimated by a refractive lens before entering

the observer’s eye, as Fig. 3-2 depicts. In other words, the different locations of each pixel are

mapped onto different directions of a collimated light beam. Therefore, instead of mechanically

23 shifting the display panel, it is also possible to get the desired image displacement by changing the direction of light after the collimating lens. A grating can achieve this functionality.

Figure 3-2: A typical optical design for VR headsets. Pixel locations in the panel are mapped to different directions of nearly collimated beams by the lens. Here, a PBPD in the Raman-Nath regime [77] is chosen to function as the pixel separation component, considering its high diffraction efficiency in the ±1 orders and polarization selective nature. Polymer-based PBPDs have shown great potential for display applications [78,79] because of their nearly 100% diffraction efficiency and fabrication simplicity. Figure 3-3 illustrates the LC orientation and characteristic polarization selectivity of a PBPD. If an unpolarized light or linearly polarized light is incident on a PBPD, then the LCP and RCP components are deflected into +1 and -1 order, respectively.

Figure 3-3: Illustration of orientation distribution of local LC anisotropy director in a polymer PBPD. The thickness d satisfies the half-wave plate condition, and the period is determined by the desired separation angle of the two virtual pixel grids. 𝚲𝚲 Making use of the polarization selective nature of PBPD, the brightness separation ratio between two virtual pixels can be tuned by modulating the ratio between LCP and RCP fraction of input light using a pixelated polarization modulation layer (PML). Each pixel of the PML is a twisted nematic (TN) LC cell, applied to change the polarization state of the output beam. With pixelized intensity and polarization modulation from the display panel and PML, the pixel value of the two separated pixels from an original pixel can be assigned independently and simultaneously. Thus, the desired image content can be displayed on the two virtual pixel grids at the same time, as Fig. 3-4 shows. Without a pixelated PML, the PBPD may still help to fill the black matrix but does not enhance the resolution because the two orthogonal polarizations share the same image content.

Figure 3-4: Schematic illustration of the resolution enhanced NED system based on polarization multiplexing. PML: polarization modulation layer.

3.3 PBP Deflector Fabrication

The photoalignment method is applied to fabricate the PBPD. A thin photoalignment film

(BY, from Sigma-Aldrich) was spin-coated on a glass substrate. The coated substrate was directly exposed by the desired interference pattern generated by the circularly polarized beams with opposite handedness. For minimizing environmental perturbations during the device fabrication process, a modified Sagnac interferometer was applied to fabricate the PBPD [50], as Fig. 3-5 shows. The collimated linearly polarized laser beam (λ=457 nm) is split into two beams with TE and TM polarizations by a polarizing beam splitter (PBS). Both beams emerging from the PBS travel around all three arms in opposite directions and recombine with each other at the PBS. Then the TE and TM beams are converted to LCP and RCP with only one quarter-wave plate. This

26 common-path exposure design for PBPD is robust to environmental vibrations, offering excellent

contrast and fringe stability yet with a reduced requirement in laser coherence length, which

increases the yield rate of high-quality PBPD with a lower-cost laser.

Figure 3-5: Polarization holography setup for generating the LC orientation pattern in PBPD devices. (M: mirror; OL: objective lens; PH: pinhole; CL: collimating lens; BS: beam splitter; QWP: quarter-wave plate; S: substrate) After exposure, the substrate was coated with a diluted LC monomer (RM257), whose

thickness satisfies the half-wave requirement at green wavelength, and then cured by a UV light,

forming a cross-linked LC polymeric grating film. More details about PBPD fabrication

procedures are described in [50].

3.4 Image Factorization

In order to generate two low-resolution images for the virtual panels, an optimization

process is constructed to achieve the desired high-resolution image [70]:

arg min , = , = 𝑇𝑇1 (3-1) 2 𝑽𝑽𝟏𝟏 𝑇𝑇2 ‖𝑹𝑹 − 𝑻𝑻‖ 𝑹𝑹 𝑴𝑴 � � 𝑻𝑻 � � 𝑽𝑽𝟐𝟐 ⋮ 𝑇𝑇𝐾𝐾

27 where is a vector made up of the pixel values from the target high-resolution image to be displayed,𝑻𝑻 is the mapping matrix between image contents on the two virtual panels ( and )

𝟏𝟏 𝟐𝟐 and generated𝑴𝑴 image from the proposed system. Without losing generality and for𝑽𝑽 a simple𝑽𝑽 example, the mapping𝑹𝑹 procedure is demonstrated in Fig. 3-6. The pixel values are rearranged as vectors in the manner shown in Fig. 3-6(a). In this case, the elements in the 9th row of mapping matrix , corresponding to the 9th pixel in the high-resolution image, are zeros except for the 2nd and the𝑴𝑴 P+6th columns, representing the pixel locations to be added in two virtual panels. For a high-resolution input image, it is factorized into two low-resolution images by Equation (3-1).

Then, the calculated pixel values from two virtual panels are compared to determine the luminance separation ratio for each pixel. The separation ratio is then passed to a calibrated PML to generate needed polarization states for each pixel. Meanwhile, the pixel values from two virtual panels are added together and then passed to the display panel to provide the total needed luminance before pixel separation. The algorithm here is developed for the square pixel lattice, but the principle can be applied to other pixel arrangements, such as the PenTile matrix for OLED. Without the algorithm, the overlapping of shifted pixels may lead to considerable crosstalk between adjacent pixels, especially for the panels with a large aperture ratio.

Figure 3-6: (a) Pixel illustration and (b) mapping matrix construction for image generation.

3.5 System Integration

Several methods have been developed to modulate the polarization state (LCP/RCP ratio)

of light from each pixel, among which the combination of a PR and a quarter-wave (λ/4) plate is

commonly used, as shown in Fig. 3-7. Firstly, the orientation angle of linearly polarized light from

the display is rotated by PR, such that the desired separation ratio is embedded as the TE/TM ratio.

After that, all the polarized lights with different orientation angles are converted to elliptically

polarized beams by the λ/4 plate. In this way, the TE/TM ratio is remapped as the LCP/RCP ratio, which is the intrinsic orthogonal polarization pair of PBPDs. As a proof of concept, in the

demonstration system, a pixelated TN LC panel and a λ/4 plate are combined together to work as

the PML. The TN LC cell is acquired by peeling off a polarizer from an LCD panel. TN LCD [80]

29 has been widely used in the display industry for its broadband performance, and here it works as

a PR to rotate the polarization orientation angle. With linearly polarized input, the polarization

state of the output beam from a TN cell can be tuned by applying a different voltage across the

cell. It should be noticed that, although the output light is no longer linearly polarized, the ratio

between TE and TM polarizations can still be tuned through the TN PR.

Figure 3-7: Schematic illustration of the polarization modulation layer. The polarization orientation angle of the light from the display is rotated by the PR. Then a quarter-wave plate is utilized to convert the TE/TM ratio to RCP/LCP ratio for the desired separation ratio after PBPD. Figure 3-8 shows the picture of the assembled prototype. In the experiment, a resolution

target, ‘Siemens star,’ was used as an example to demonstrate the resolution enhancement effect.

The display panel and the PML have a resolution of 800x480 and a size of 5 inches. The focal

length of the viewing lens is 55 mm, and the period of the fabricated PBPD is controlled to be ~0.6

mm for the desired shift.

Figure 3-8: Photograph of the assembled prototype installed on an optical table. In comparison with the apparent image captured at the original resolution displayed in Fig.

3-9(a), the resolution enhancement is clearly observed, especially at the sloped contours as Fig. 3-

9(b) shows. Moreover, the screen-door effect is significantly reduced, and the boundaries between pixels are not so apparent as the original image. It should be mentioned that the PML adapted from a commercial LCD panel is not designed for polarization modulation, which may lead to some crosstalk between adjacent pixels, depending on the distance between the definition layers of PML and the display panel. A display panel with a relatively confined angular intensity distribution could be helpful to reduce the pixel crosstalk. Besides, as a common issue for cascaded panels,

Moiré patterns induced by the similar spatial frequency of display panel and PML may decrease the image quality, although it is not very apparent in our experimental results. Additional optical engineering may be needed to eliminate the Moiré patterns, such as using a diffuser film in between two panels. Moreover, the PBPD can also be placed between the PML and the lens in Fig. 3-4, reducing the angle of incidence on it, which can be helpful to avoid reduced diffraction efficiency

31 of PBPD at oblique incidence. Since the grating period of PBPD utilized here is around one

thousand times longer than the visible wavelength, the chromatic dispersion of deflection angle

induced by PBPD is negligible. Although the off-axis shifting angle of PBPD is different from the on-axis one, a corrected image is still achievable through an improved image rendering process

together with the digital aberration correction for the eyepiece lens.

Figure 3-9: Images captured through a camera with (a) original and (b) enhanced resolution of a “Siemens star” resolution target and an athletic shirt. The screen door effect is reduced, and the pixel density is doubled simultaneously.

32 3.6 Summary

A resolution enhancement method for NEDs is proposed and experimentally validated.

This system, benefiting from the polarization selective nature of PBPDs, can provide high- resolution images for viewers without sacrificing the display frame rate. The screen-door effect is also significantly reduced since the original black matrix is now filled by shifted pixels. The proposed resolution enhancement method has potential applications for projection and NEDs.

33 CHAPTER 4: ABERRATION CORRECTION

4.1 Background

Recent advances in VR technology, enabled by high-pixel-density displays and powerful mobile processors, have provided unprecedented ability to immerse the user in a virtual world. VR has already demonstrated its ability to transform how people interact with each other and their environment. Despite how widely VR has been used for gaming, this technology is expanding to a plethora of applications, including but not limited to education, retail, and healthcare.

Although more than 10 million VR devices have been shipped since 2016, the imaging quality of current VR products is still not satisfactory when compared with that of the real world.

Since compact and lightweight are always desired for head-mounted displays, only one singlet lens is employed in most commercialized VR devices, making it quite challenging to keep a decent imaging performance within the whole field of view, which is usually >100° for an immersive impression [81]. As a consequence, fringes of color at the edges of objects can be clearly observed due to CAs at the margins of the displayed image. Even though the significance of this effect is dependent on the image content and users’ gaze point, it is still preferable to provide CAC for a better user experience.

Digital CAC is usually utilized in current VR devices. With extra graphics computation, the perceived CA can be substantially reduced by means of image pre-processing [82]. The digital image compensations are applied to each color channel independently, employing different coefficients to each color channel. With correct subpixel implementation, the CA can be reduced appreciably. However, from the system perspective, the digital CAC still has several challenges and may compromise the display performance:

34 1. Sub-channel aberrations. There is a range of wavelengths within each color channel, and

each part of it suffers from a different lateral shift. Thus, digital CAC is for the peak

wavelength, thus cannot correct the CA in each color channel. This impotency would put

an extra burden on display color accuracy.

2. Interpupillary distance (IPD) variation. Since the digital CAC is usually set for a fixed point

in the eyebox, this method cannot offer the ideal correction for users with different IPDs.

3. Image rendering. Digital CAC would exaggerate the pressure for image rendering, which

is already quite challenging for high-resolution and high-quality graphics in VR. To share

the burden on the graphic processing unit, a new display processing unit has been

developed, dedicated to supporting CAC in VR [83].

4. Processing time. High framerate is usually required in VR devices for a small latency. The

digital correction would occupy extra time in each frame, and it will be longer with a higher

display resolution.

Therefore, the software-based digital pre-distortion is not an ideal solution to CA in VR

displays at present. Optical CAC has been widely applied as a useful and necessary part of

chromatic imaging systems since the 18th century. The conventional optical CAC approach

utilizes two or more lens materials with different refractive index dispersions, or Abbe numbers,

in the system to unite the focal length at two or more wavelengths [84]. However, achromatic doublets are more expensive and heavier than singlets in head-mounted display systems, causing discomfort to the users. In the late 1900s, another approach based on the hybrid of diffractive and refractive lenses was developed [85], exploiting the negative Abbe number of diffractive elements.

35 Despite their demanding fabrication process, diffractive Fresnel phase lenses have been integrated

into consumer lens systems to pursue compact size and better imaging performance [86].

In this chapter, we demonstrate a hardware-based CAC approach using novel flat optics, a

PBPL made of LC polymer that shows negative chromatic dispersion. After the hybridization of a plastic Fresnel lens and a PBPL, the CA can be evidently reduced, as illustrated in Fig. 4-1. Firstly, the system configuration is determined by the sequential raytracing simulation. Then, the desired broadband LC lens is fabricated, characterized, and then assembled with a plastic Fresnel lens as the achromatic viewing optics in our VR prototype. Finally, the CAC performance of the proposed system is experimentally evaluated, and its potential application in folded VR optics is also discussed.

Figure 4-1: Illustration of transverse CAs in a) a compact refractive Fresnel lens, b) a diffractive LC lens, and c) the proposed hybrid doublet exhibiting achromatic performance.

37 4.2 System Design

The system configuration of the proposed VR viewing optics is presented in Fig. 4-2.

Compared with conventional VR optics, our design only attaches three laminated flat optics parts,

including a quarter-wave plate, a PBPL, and a circular polarizer, adding negligible weight and

volume to the existing system. The flat optical parts are attached to the Fresnel surface of the plastic lens for the convenience of alignment. Also, the PBPL is placed between the display and the Fresnel lens, where the angle of incidence is smaller than that after the Fresnel lens, leading to a higher diffraction efficiency at the PBPL surface.

Figure 4-2: Optical layout of the proposed VR optics, including a PBPL for the optical CAC. Figure 4-3 illustrates the polarization changes through flat optical parts. The polarization state of the light from the display panel is firstly converted from linear to circular polarization by the quarter-wave plate.

Figure 4-3: Illustration of polarization state changes through the planar optical parts in the proposed system. After passing through the PBPL, the polarization handedness of the first-order diffracted

light would be switched while that of the zero-order leakage remains unchanged, as indicated in

Equation (2-2). A circular polarizer is inserted between the PBPL and Fresnel lens to block the

stray light from the PBPL’s zero-order leakage, especially from the oblique incidence. In this manner, only the desired diffracted light can pass through the imaging system and enter the eye.

If the light emitting from the display is unpolarized, such as μ-LED, then a polarization converter

or a polarizer should be attached to the panel to keep the output linearly polarized. There is no

denying that this may cut half of the light efficiency, but fortunately, high brightness is not a

necessity in VR displays.

Figure 4-4: Standard spot diagram with RMS spot radius for (a) Fresnel singlet and (b) proposed hybrid optics. Color by wavelength, Red: 610nm, Green: 540nm, Blue: 450nm. The optical power of the PBPL needs to be designed for an optimized imaging performance with the Fresnel lens. Generally, similar to the design of an achromatic double [87], the following constraint should be satisfied:

+ = 0 (4-1) 𝐾𝐾𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐾𝐾𝑃𝑃𝑃𝑃𝑃𝑃 �𝑉𝑉𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 �𝑉𝑉𝑃𝑃𝑃𝑃𝑃𝑃

40 where K and V are the optical power and Abbe number of the optics. As a diffractive lens, the

Abbe number of PBPL is unique since it is equal to -3.45, no matter what kind of LC material it is

made of. The Fresnel lens is made of polymethyl methacrylate (PMMA), whose Abbe number is

58. Thus, the optical power of the PBPL should be ~16 times smaller than that of the Fresnel lens.

Then, sequential ray-tracing simulation and optimization are applied using OpticStudio from

Zemax. The PBPL is modeled as a holographic diffractive optical element with 100% first-order

diffraction efficiency. Stray light caused by the PBPL leakage is not considered in this evaluation.

The polychromatic root-mean-square (RMS) spot radius of the Fresnel singlet and proposed hybrid optics are compared in Fig. 4-4. The three color channels are significantly separated when the field is larger than 30° in the Fresnel singlet VR devices. According to the simulated design, the proposed hybrid viewing optics can enhance the resolution by ~ 2.5 times, making the image much sharper from 0° to 50° field. At the 0° field, adding a PBPL could make the RMS spot smaller than the Airy disk, which is 5.6 microns in radius, making the whole system diffraction-limited at the center field of view. To quantitatively evaluate the CAC potential of

PBPL, the lateral color shift is also calculated for the viewing optics with and without PBPL compensation, as presented in Fig. 4-5. As expected, the PBPL is able to shrink the color shift of the Fresnel singlet by > 10 times within the ±50° field of view.

Figure 4-5: The lateral color shift of the VR viewing optics with and without PBPL.

4.3 PBP Lens Fabrication

For achieving a wide spectral bandwidth covering most display spectrum, a tailored axial molecule orientation should also be adopted, including a twist-homo-twist three-layer structure, as

shown in Fig. 4-6. The first and third LC polymer layers should manifest a twist with opposite

direction by doping chiral dopants with opposite handedness, while the second LC polymer layer

is not twisted. This waveplate broadband operation principle was firstly proposed by Pancharatnam

with stacked discrete waveplates with designed orientation angles between their optical axis [88],

then extended to waveplate with continuously rotating optical axis using TN LC cells [89] and

multilayer LC polymer films [23,47]. The proposed three-layer sandwich-like structure should be

able to cover most of the light spectrum of the LCD panel, which is around 430nm-680nm.

Moreover, from the material perspective, polymerizable LC material with small or even negative

42 birefringence dispersion is ideal for a reduced variation of retardation over the visible spectrums.

However, these materials are relatively expensive for applications in large-volume consumer devices at this stage. Thus, in this work, we chose one of the most cost-effective LC materials,

RM257, even though it has a relatively large birefringence dispersion.

Figure 4-6: Schematic illustration of LC anisotropy axis orientation in the PBPL with flat geometry and a twist-homo-twist structure for broadband operation. The designed PBPL is fabricated based on the photo-alignment method with multiple coating and curing processes. Firstly, a PAL was created on a glass substrate by spin-coating a 0.2% solution of BY in dimethylformamide (DMF) solvent. The designed lens profile with a 2-inch diameter was encoded on the BY layer using the polarization holography method to achieve the

LC axis orientation pattern. Then, four LC RM layers were spin-coated on the aligned surface one by one, while each coated layer is crosslinked by UV light to form a solid surface and provide alignment for the next layer. The detailed spin-coating recipe is listed in Table 2. The fabricated

43 PBPL shows clear image quality and wide spectral bandwidth, manifesting <3% zero-order leakage over the display spectrum of the LCD panel, as Fig. 4-7 shows.

Table 4-1: Recipe of the materials and spin-coating in the PBL fabrication (by weight). Solution Solute Solvent Solute: Solvent Coating speed 500(5s) BY layer Brilliant Yellow DMF ~1:500 +3000(30s) RM257 (95.05%) Irgacure 651 (2.34%) 1st RM layer Toluene ~1:3.81 1900(90s) Zonyl 8857A (0.95%) R811 (1.66%) 2nd RM layer RM257 (97.11%) 1000(90s) Irgacure 651 (1.92%) Toluene ~1:3.89 rd 3 RM layer Zonyl 8857A (0.97%) 850(90s) RM257 (95.48%) Irgacure 651 (1.93%) 4th RM layer Toluene ~1:3.83 950 (90s) Zonyl 8857A (0.927%) S811 (1.66%)

Figure 4-7: Measured zero-order leakage of the ultra-broadband PBPL and the emission spectrum of the LCD displaying white light. Inside is a photo of the fabricated 2-inch PBPL.

4.4 System Integration

As a demonstration of the CAC performance of the proposed hybrid lens, an image was displayed on the LCD screen without barrel distortion correction, which includes a set of evenly spaced bars with RGB segments, as plotted in Fig. 4-8. When viewing through the plastic Fresnel singlet, the test pattern bars are blurred, and the RGB colors are apparently displaced due to the transverse CA at the peripheral field of view. When the proposed planar optics module, including a PBPL sandwiched by a λ/4 plate and a circular polarizer, is attached to the Fresnel surface of the plastic lens, the color breakup at the periphery is signiﬁcantly reduced.

Figure 4-8: (a)Half-ﬁeld CA testing pattern displayed on the LCD and the resulting images captured through the (b) conventional and (c) proposed viewing optics. Figure 4-9 shows another testing result with a black-and-white image. Utilizing the proposed optical building, the CA can be rectified at the expense of three planar optical elements without changing the compact form factor of the system.

Figure 4-9: Full-field black-and-white image displayed on the LCD and the resulting images captured through the conventional and proposed hybrid viewing optics. The three enlarged parts are center field and edge fields at 0° and 45° azimuth from left to right.

4.5 Catadioptric VR Optics

Although the PBPL is applied to offer optical CAC for a Fresnel singlet in this work, other

VR viewing optics can also benefit from PBPL, such as the folded pancake VR lens [90], as Fig.

4-10 depicts. This catadioptric lens system has smaller CAs than the Fresnel lens since the achromatic reflective surface contributes a large optical power to the system. However, the refractive part of the lens still generates CAs, and there are also monochromatic aberrations.

Therefore, the PBPL can still help reduce the overall aberrations, as shown in Fig. 4-11, and render the imaging even shaper.

Figure 4-10: The lateral color shift of a pancake VR viewing optics with a PBPL.

Figure 4-11: Standard spot diagram with RMS spot radius of the pancake lens integrated with a PBPL. Color by wavelength, Red: 610nm, Green: 540nm, Blue: 450nm.

48 4.6 Summary

The proposed optical CAC approach provides a cost-effective hardware alternative to the

conventional digital correction based on software rendering. The optical approach using flat optics

is able to provide better imaging performance since it can correct the CAs in each color channel,

which is not achievable using digital correction. From the system perspective, the digital correction

would put an extra burden on computation load, memory usage, and power drainage, while the

optical approach just needs a flat polymer lens in the optical parts. Thus, the proposed system may

benefit the future development of VR devices, offering better imaging quality while reducing the

computation load and power consumption. Moreover, the proposed principle could also be applied

to general imaging systems where CAC is desired.

In summary, we have designed and demonstrated a prototype VR display system with

significantly reduced CAs using planar diffractive optics. We fabricated a key optical element, an

ultra-broadband planar polymer lens employing the Pancharatnam-Berry phase, manifesting high diffraction efficiency (>95%) over most of the visible spectrum. And due to the low-cost manufacturing of the planar polymer lenses and convenient additive adaptation from current VR devices, the proposed method and system should find widespread applications in the NED industry.

49 CHAPTER 5: LIGHT EFFICIENCY IMPROVEMENT

5.1 Background

After rapid development in the past decade, VR headsets have become more powerful, and

they can offer a relatively comfortable and immersive experience for users. In the meantime, the

continuous evolution of NEDs inside VR headsets is also remarkable. About five years ago, the

mainstream VR headsets still required a smartphone screen to function as the display panel.

Nowadays, most VR devices are integrated with one or two custom-built high-resolution display panels. In parallel, VR optics is gradually evolving from simple dioptric singlets to catadioptric

‘pancake’ lenses [91]. Thanks to their folded optical path, VR NEDs using polarization-based pancake lenses allow the display to be significantly closer to the lens and therefore manifest a more compact form factor than those employing conventional singlets. However, a big tradeoff is that the total light efficiency is limited to 12.5% and 25% for an unpolarized and polarized display light source, respectively [90]. As a result, the peak brightness of pancake VR headsets is usually lower than that of conventional ones, and the display module needs to drain more power for maintaining the same brightness. This issue is more critical for a standalone VR headset powered by an internal battery. Thus, there is an urgent need to enhance the optical efficiency of VR headsets for higher brightness and extended battery life.

From the optical system perspective, the light efficiency can be enhanced by improving the display panel or the VR optics or making them coupled better with each other. The display panels in current VR headsets are adopted from those in direct-view electronics, such as smartphones, with limited modification in the optical architecture. This adoption is doable, but there is still much room for improvement because direct-view display panels are not originally designed and

50 optimized for VR applications. In most direct-view displays, continuous efforts have been made

to maintain decent display quality within a large viewing angle. For example, multi-domain

vertical alignment (MVA) and in-plane switching (IPS) technologies were invented for wide-view

and high contrast LCDs. Also, in OLED displays, there is often a tradeoff between light extraction

efficiency and angular color uniformity due to micro-cavity effects [92,93], so the light efficiency

is not usually maximized. It should be mentioned that the circumstance is different in VR headsets,

where the display panel is fixed relative to the eye, and a magnifying lens is also placed between

them, as illustrated in Figure 5-1.

Figure 5-1: Illustration of a typical VR display module with a wide-view display. From the system viewpoint, applying a direct-view display panel in VR headsets may result in several issues that affect users’ experience. Firstly, direct-view display panels emit light within

51 a large solid angle, while in VR headsets, only the light rays radiating from a small solid angle can

reach the pupil, as depicted in Figure 5-1. As a result, a considerable amount of display light is

wasted. This issue is more critical in VR headsets with catadioptric (pancake) optics, where the

lens transmittance is already lower than 25%. Secondly, the stray rays outside the effective solid

angle cannot enter the exit pupil. These rays may bounce back and forth between the VR lens and

the display panel, causing background noise and reducing the contrast ratio of front-of-screen imagery. Also, direct-view display panels usually manifest higher luminance in the direction normal to the panel surface, which leads to a relatively darker peripheral field, i.e., vignetting. The spatial varying size and orientation of the effective solid angle also exaggerate the luminance variation across the field of view. Last but not least, for OLEDs, the microcavity utilized in RGB pixels can narrow the emission spectra but may also cause color shift across the viewing angle due

to the variance in RGB Fabry–Perot resonance [93]. In a VR headset, this angular color shift can

lead to apparent color variation across the field of view. Because of the abovementioned issues,

the wide-view display panel is not an ideal choice for VR displays.

In this chapter, we propose to tailor the VR display panels for better coupling with the VR lens and achieve a higher light efficiency at the system level. The essence of this design is to use a directional display to narrow the emitting angle and a DDF to direct more light toward the eyebox.

Such an arrangement serves two important reasons: the first being the small etendue of the

directional display, which matches better with the small etendue at the eyebox. The other reason

is that the DDF can correct the orientation of emitting solid angles based on the lens design and

alleviate potential vignetting. We demonstrate the design and simulation process using non-

sequential ray-tracing analysis. This is followed by a proof-of-concept experiment that can validate

52 the light efficiency enhancement with our proposed design. The limitations and further

improvements of the proposed method are thoroughly discussed before the summary.

5.2 Directional Display

As mentioned above, direct-view displays’ emitting solid angle is usually larger than the

effective solid angle determined by the VR optical system, which is the primary cause of light

efficiency issue for both dioptric and catadioptric VR display modules. Here, we demonstrate a

VR optical design where the display panel and the lens are better coupled with each other to boost

the system-level efficiency.

The first part of our design is to apply a directional display panel with a narrower emitting angle than conventional direct-view displays. Figure 5-2(a) depicts the cross-section view of an exemplary VR display module using a singlet with a Fresnel surface and an aspheric surface [94].

This PMMA lens has a focal length of 35mm, and the field of view of the VR display module is

~100 °. Similar to most commercial VR headsets, this example has spatial-varying effective solid angle sizes and orientations across the display panel, as depicted in Figure 5-2(a).

Figure 5-2: (a) Optical layout of the VR display module used in the simulation; (b) Exemplary angular intensity profiles of the display panel described in Equation (1). After finishing the sequential design in Zemax OpticStudio, we reconstructed the same

optical layout in Synopsis LightTools to conduct the non-sequential light efficiency analysis. For

simplicity yet without losing generality, the angular intensity profiles are set as Lambertian and its

exponentiations in the simulation, as represented by Eq. (1):

( ) = cos( ) , (5-1) 𝑛𝑛 where is the incident angle on the panel surface.𝐼𝐼 𝜃𝜃 Figure𝐼𝐼0 5-𝜃𝜃2(b) displays the angular profiles in a

2D polar𝜃𝜃 coordinate system, where the 0-degree direction is normal to the panel surface. In the non-sequential simulation, the circular receiver is located at the exit pupil and has a diameter of

9.5 mm. Only a single pixel is turned on at each simulation, and the luminous efficiency of each pixel is defined as:

= / , (5-2)

𝜂𝜂 𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝐿𝐿𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 54 where is the luminance power emitting from each pixel, and indicates the luminous

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 flux received𝐿𝐿 by the circular receiver at the eyebox. One million rays𝐿𝐿 are traced in each simulation

to provide a decent accuracy.

Figure 5-3: Simulated luminous efficiency of a single pixel in the VR optical module depicted in Fig. 2(a) with the angular luminance distributions shown in Equation 1 and Figure 2(b). Figure 5-3 displays the simulated light efficiency of pixels located across the display panel.

Five different angular intensity distributions described by Equation (5-1) are applied. It is not surprising that only <10% of the light from wide-view display panels (n=8) can reach the receiver, which is inefficient and power-consuming for the VR system. Notably, the use of a highly directional display panel (n=128) allows much higher light efficacy, and the enhancement can be as high as >6 times at center field. Although applying a directional display panel makes better use

55 of light, the perceived brightness across the field of view may manifest a more considerable

variation. This is because the effective solid angle of each field has a distinct orientation. Therefore,

direct narrowing down the emitting angle may lead to apparent vignetting in the perceived imagery,

especially in the fields where the chief ray is not perpendicular to the panel surface. Furthermore,

it is also worth mentioning that utilizing a directional display may render the imagery more

dependent on the eye location and demand users to adjust the headset position for the best

performance.

5.3 Diffractive Deflection Film

One step further, to achieve a higher light efficiency and a smaller vignetting

simultaneously, we propose to attach a DDF on the directional display panel for manipulating the

orientation of the emitting solid angles, as illustrated in Figure 5-4. The DDF is a type of PBPOEs

made of LC polymer, which can be considered as a dielectric meta-surface or a patterned half-

wave plate with in-plane spatial-varying orientation. Its working principle can be explained by

Jones calculus in the paraxial approximation as shown in Equation (2-2). Compared to

conventional meta-surfaces based on the PBP, LC-based PBPOEs can offer nearly unit diffraction

efficiency over the entire display spectrum and have a cost-effective fabrication process [50,95].

These are the reasons why we choose PBPOEs over other compact optical elements for this

application.

Figure 5-4: (a) Illustration of the directional VR display module; (b) Illustration of the directional VR display module with a laminated DDF on the display panel.

5.4 Experiment

To evaluate the feasibility of the proposed design, we present below the result of a proof-

of-concept experiment using commercial off-the-shelf components. The experiment setup is

depicted in Figure 5-5. Instead of using a directional display panel, a plastic diffuser film is utilized

as the display panel and illuminated with a laser line (532 nm) to mimic the light emitting from a

single pixel. The laser diode, diffuser film, and DDF are placed on a motion stage that can move

in the direction perpendicular to the optical axis. By changing the position of the motion stage and

collect the light at the eyebox with a power meter, the light efficiency of pixels at different

locations on the display panel can be measured.

Figure 5-5: Schematic illustration of the experiment setup. The scattering angular distribution of the diffusers at normal incidence is shown in Figure

5-6. Diffuser B (Brightview Technology, C-HE55) behaves like a typical LCD, while diffuser A

(Brightview Technology, C-HE05) represents the proposed directional display. At each pixel location in the measurement process, the relative position of the PBPOE (Edmund Optics, #34-

463) to the laser line is adjusted to maximize the intensity shown on the power meter (Thorlabs,

PM100D).

Figure 5-6: Scattering angular distributions of the diffusers used in the experiment. Diffuser A represents a directional display, while Diffuser B represents the conventional LCD. Figure 5-7 shows the measured luminous efficiency using three different configurations: diffuser A, diffuser B, and diffuser A with DDF. These results match well with our simulations, showing that a directional display (diffuser A) shows higher light efficiency than a wide-view display (diffuser B). However, this advantage comes at the cost of stronger intensity variation across the field of view. The use of a DDF on top of the display allows a significant alleviation of this side effect and allows higher average efficiency over the entire display panel.

Figure 5-7: Measured luminous efficiency in the exemplary VR display module. Although the proof-of-concept experiment presented above indicates that the proposed approach is highly promising to deal with the light efficiency issue in a VR optical system, there are still some concerns that cannot be ignored in practical applications.

A common issue of using diffractive optical components in display systems is their chromatically dispersive optical response over the display spectrum [19]. In the proposed application, the PBPOE-based DDF may possibly result in an angular color shift that is substantial enough to affect the front-of-screen imagery. The significance of this issue depends on the maximum angle of the chief rays on the display panel. Since the DDF here is not involved in imaging but only angular profile shaping, a small deflection angle does not induce perceivable color variation across the field of view. In VR lenses with large chief ray angles on the display panel, the DDF period needs to be smaller, and the directionality of the display should be limited

60 to keep the angular color shift at an acceptable level. Also, in this case, other achromatic flat optics,

such as lithography-based metasurfaces [96-99], can be a better choice than the LC-based DDF.

Using a directional display panel is another demanding requirement of the proposed approach because most display panels in mass-production are not directional. Although directional displays are not as popular as the wide-view ones, it is actually not that hard to produce them by modifying the current manufacturing process. Firstly, for LCDs, numerous directional backlight designs have been proposed and employed to enhance the contrast and transmittance of LCD

[100,101]. These are naturally suitable for the proposed approaches. Secondly, in OLED display panels, there is usually a tradeoff between angular color shift and light extraction efficiency [6].

Since the angular color shift is not a big concern in our approaches, it is feasible to apply strong cavities for a high-intensity directional OLED emission [102]. Also, RGB μ-LEDs with the nanowire structure have shown promise to exhibit low dislocation densities and improved light extraction efficiency, and the emission divergence angle can be as small as ±5° [103]. Last but not least, meta-surface can be fabricated on top of the LED chips to control the light emission [104], which can also be a neat option for the proposed concept.

5.5 Summary

We have proposed a light-efficient VR display module and experimentally demonstrated

the feasibility of this design with a proof-of-concept experiment. The proposed design mainly consists of a directional display pane and a PBPOE-based DDF made of LC polymer. We used the directional display to confine the emitting solid angel of light and the DDF to direct more light into the eyebox. The light efficiency of the proposed VR display module can be >2x higher than

61 conventional ones. Given the advantages demonstrated in this study, we expect the proposed concept and design to emerge as a useful technology for next-generation VR displays and to become one of the most practical applications of flat optics.

62 CHAPTER 6: SCALE-UP FABRICATION

6.1 Background

The management and measurement of polarization are ubiquitously important in a plethora

of optical systems, including but not limited to displays, polarimetry, ellipsometry, remote sensing,

and quantum computing. As a compact alternative to the polarizing beam splitter, conventional

PBPD [105], which is a special type of polarization grating (PG) [106], has been extensively

studied and developed during this decade due to its high diffraction efficiency and polarization

sensitivity. The spatially varying anisotropy in PBPDs can be achieved through patterning LCs

[107] and LC polymers [108] or lithography-based nanofabrication [109]. Most of the conventional PBPDs are retardation-based PGs that show 100% diffraction efficiency when the half-wave retardation condition is satisfied. Thus, such PBPDs are also called diffractive waveplates [73]. Besides the retardation-based PGs, spatially varying anisotropic absorption also has the potential to enable polarization-sensitive gratings [106]. To distinguish this type of PGs from conventional ones, here we call them absorption-based polarization gratings (a-PGs).

In this chapter, we demonstrate a-PGs formed with a dichroic dye and a polymerizable LC

RM. In theory, this periodic anisotropic absorption profile manifests ~25% diffraction efficiency for a circularly polarized input light across the absorption band of the dye material. In this case, another 25% is directly transmitted as the zero-order leakage and maintains the original polarization state. Since a-PGs can separate orthogonal circular polarizations to distinct first orders,

they can be employed in polarimetry systems similar to conventional PBPDs [108]. Also, photopatterning of LCs can also be simplified using a-PGs because they are naturally polarization masks that are compatible with broadband light sources, such as LEDs.

63 6.2 Paraxial Analysis

The paraxial diffraction behavior of a-PGs can be derived analytically with Jones calculus

as presented by Gori [106], where the a-PGs are theoretically proposed for polarimetry

applications. Since the dichroic dye molecule orientation rotates 180° in one period, the direction

of the in-plane transmission axis in a-PGs can be described by

= , (6-1) 𝜋𝜋𝜋𝜋 where is the orientation angle relative to𝜑𝜑 the �axisΛ (the periodic direction), and denotes the grating𝜑𝜑 period. For simplicity, the a-PG profile𝑥𝑥 is modeled in a single period. TheΛ output local

polarization direction associated with the dichroic dye orientation is illustrated in Fig. 6-1.

It is convenient to achieve this profile using dichroic-dye-doped RMs since they can be photo-aligned by a polarized light field and then fixed after photopolymerization. Under paraxial approximation, the output electric field after the a-PG can be expressed by transforming the input field with the local Jones matrix of the polarizer grating ( ). Based on these assumptions,

𝑖𝑖𝑖𝑖 the far𝑬𝑬-field electric field of diffracted order can be expressed𝑻𝑻 𝑥𝑥as follows:

= ( 𝑚𝑚) exp ( 2 / ) . (6-2) 1 Λ The local Jones matrix of such𝑫𝑫 a𝑚𝑚 polarizerΛ ∫0 𝑻𝑻 can𝑥𝑥 be𝑬𝑬𝑖𝑖𝑖𝑖 described− 𝑗𝑗 as:𝑗𝑗𝑗𝑗𝑗𝑗 Λ 𝑑𝑑𝑑𝑑

sin = ( ) ( ) = . (6-3) 2 𝑐𝑐𝑐𝑐𝑐𝑐 𝜑𝜑 𝜑𝜑𝜑𝜑𝜑𝜑𝜑𝜑𝜑𝜑 𝑻𝑻 𝑹𝑹 −𝜑𝜑 𝑷𝑷𝑷𝑷 𝜑𝜑 � 2 � where and are the Jones matrices of rotation operation𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 and𝑠𝑠 a linear𝑠𝑠𝑠𝑠𝑠𝑠 𝜑𝜑 polarizer, respectively. As the incident𝑹𝑹 field𝑷𝑷 is independent of x , the far-field Fourier components can be written as:

= , (6-4) where the grating transfer matrix: 𝑫𝑫𝑚𝑚 𝜞𝜞𝑚𝑚𝑬𝑬𝑖𝑖𝑖𝑖

= ( )exp ( 2 / ) . (6-5) 1 Λ 𝜞𝜞𝑚𝑚 Λ ∫0 𝑻𝑻 𝑥𝑥 − 𝑗𝑗𝑗𝑗𝑗𝑗𝑗𝑗 Λ 𝑑𝑑𝑑𝑑 64 The grating transfer matrices solved by combining Equations (6-1), (6-3), and (6-5) for all non- zero orders are:

= , (6-6) 1 0 𝜞𝜞 12 𝐼𝐼 = . (6-7) ± 1 1 ∓𝑗𝑗 𝜞𝜞 1 4 � � The diffraction efficiency is then calculated by the∓ ratio𝑗𝑗 of output intensity to input intensity as:

= | | /| | . (6-8) 2 2 𝑚𝑚 𝑚𝑚 𝑖𝑖𝑖𝑖 For the zero and first orders, we have: 𝜂𝜂 𝑫𝑫 𝑬𝑬

= 1/4, (6-9)

0 ±𝜂𝜂= (1 )/8, (6-10) ′ 1 3 where = / is a normalized Stokes𝜂𝜂 parameter.∓ Several𝑆𝑆 essential properties of a-PGs should ′ 3 3 0 be remarked.𝑆𝑆 𝑆𝑆 First,𝑆𝑆 only three diffraction orders exist, which is similar to conventional PBPDs.

Second, the zero-order leakage not only maintains the original polarization state but also manifests

a constant efficiency of 25%, no matter how the input light is polarized. Third, the sum of +1 and

−1 order efficiency is also 25%, although they have a strong dependence on the input polarization

state individually. In all cases, half of the incident light is absorbed by the a-PG.

Figure 6-1: (a) Local transmission direction followed by (b) front and (c) side view of the dichroic dye director orientations in absorption-based a-PGs.

6.3 Mask Fabrication and Characterization

In the proposed a-PGs, the dichroic dye molecules should have a linearly rotating orientation pattern. To achieve this, we usually encode such patterns with a PAL, on which the dye-doped RMs are spin-coated and then photo-polymerized to form a solid thin film, as illustrated in Fig. 6-2. Several methods can provide the designed polarization field for photo-alignment, such as direct laser writing, analog and digital polarization holography, and optical polarization imprinting [110]. For higher stability, a modified Sagnac interferometer is applied in our experiments for offering a periodic polarization field, similar to the fabrication process of conventional PBPDs [50]. The PAL is then coated with dye-doped RMs using a spin-coater before photopolymerization. In a-PGs, it is not necessary to manage the thickness of the self-assembled

LC polymer layer to achieve half-wave retardation for high efficiency since it works by absorption

66 but not by retardation. Instead, the a-PG film could be thinner than conventional PBPDs, especially in the long-wavelength range, if the employed dichroic dye has a high absorption coefficient and a decent dichroic ratio, which makes it an ideal polarizer at each spatial location as required in the assumption of our paraxial analysis.

Figure 6-2: Fabrication process of the a-PG, including two spin-coating and exposure steps. Regarding the fabrication process, the solution for coating PAL is made by dissolving the photo-alignment material BY in DMF with a 0.2 wt% concentration. The precursor is a toluene- based solution, where the solute contains polymerizable LC RM257, dichroic dye DDY426

(Colour Synthesis), photo-initiator Irgacure 651, and surfactant Zonyl 8857A (Dupont) mixed at

1:0.12:0.03:0.01 ratios, and the mass ratio between solute and solvent is around 1:1. The surfactant was added to help form a planar alignment at the RM-air interface after spin-coating. In the photo- alignment process, the PAL is exposed to a polarized light field generated by a modified Sagnac interferometer using a 457-nm laser (Cobolt Twist) light with an intensity of 4 mW/cm2 for 5 minutes. The sample coated with the precursor is then polymerized under a 365-nm UV lamp with a dosage of 1 mW/cm2 for 10 minutes.

67 The fabricated a-PGs exhibit ideal properties with high polarization sensitivity and low

scattering. The gratings were tested with a 457-nm diode-pumped solid-state (DPSS) laser in

parallel with a quarter-wave plate to control the incident polarization state, as illustrated in Fig. 6-

3(a). Most of the output energy is shared by the zero and first different orders. A compact power

meter (Thorlabs PM100D) was used to measure the intensity of each order when the quarter-wave

plate was oriented at different angles. The measured diffraction efficiency of the mth order is

defined as:

= / . (6-11)

𝑚𝑚 th 𝑚𝑚 𝑚𝑚 where is the measured power of the𝜂𝜂 m 𝑃𝑃diffractionΣ𝑃𝑃 order. With this definition, the Fresnel

𝑚𝑚 reflection𝑃𝑃 loss can be avoided, and an ideal a-PG should have 50% diffraction efficiency in the

zero-order for an arbitrary input polarization state. The measured diffraction efficiency is plotted

and compared with the simulation results of an ideal case in Fig. 6-3(b). The agreement is quite

decent. With this distinct polarization selectivity, the a-PGs can find promising applications for

polarimetry as presented by Gori [106] and even spectropolarimetry, similar to conventional

retardation-based PGs [108].

Figure 6-3: Polarization response of absorption-based PGs. (a) Measurement setup including a linearly polarized laser and a rotatable quarter-wave plate to control the incident polarization. (b) Measured and calculated diffraction response to the rotation of a quarter-wave plate.

6.4 PBPOE Printing

In a-PGs, the dichroic dye molecules are well aligned following the polymer networks

formed by the RMs. Due to the special property of anisotropic absorption, dichroic dye molecules

can be considered as small-scale polarizers, although the dichroic ratio is usually in the order of

10:1. Thus, the a-PGs are also promising polarization masks that can be employed in the

photopatterning of LCs, which is comparable to the photomask in the photolithography process.

The difference is that photomasks control the spatial amplitude distribution of light while

polarization masks determine the spatial polarization orientation. The demonstrated a-PGs can significantly simplify the fabrication process of LC-based optical components such as

Pancharatnam-Berry phase optical elements [75] and cholesteric LC optical elements [111], which have attracted considerable interest recently due to their numerous applications in imaging [36],

69 lighting [112], displays [113] and even beam rider [114]. Most LC photo-patterning techniques are bulky and require complex tools such as polarization holography [50], laser-writing [37], two- photon polymerization printing [115], and even atomic force microscopy [116], which may be acceptable for research but not realistic for high-volume production. Previously, Nersisyan et al.

[110] demonstrated the optical imprinting technique for PG fabrication, where a PBPD is used as the polarization mask for fabricating another PBPD whose period is twice as short as the master

PBPD. However, using retardation-based PGs for optical imprinting requires a laser source and strict match between the peak efficiency of master PGs and the laser wavelength.

Here, we demonstrate the photo-patterning ability of our a-PGs, which can even work with

LED light sources. As a proof of concept, we optically imprinted a PBPD with an a-PG using a

LED flashlight (Duracell #922241), which is a broadband, spatially, and temporally incoherent light source. A photo of the optical imprint setup is shown in Fig. 6-4(a), where a glass substrate coated with PAL is attached to the fabricated a-PG and fixed by an optical mount (Edmund Optics

#54-994). Then, the optical mount was placed on the top of the flashlight and exposed for 5 minutes.

The functionality of our a-PGs as polarization masks is well evidenced by the polarized optical microscope (POM) images of the a-PG mask and optically imprinted PBPD, as shown in Fig. 6-

4(b) and Fig. 6-4(c), respectively. It should be noted that the proposed photopatterning process is applicable to arbitrary two-dimensional patterns but not limited to periodic gratings.

Figure 6-4: Photopatterning using a-PGs as the polarization mask. (a) Contact photopatterning setup, including a flashlight as the light source and an optical mount to fix the a-PG and PAL-coated substrate. POM images of the (c) a-PG mask and (d) optically imprinted PBPD, where the period is around 60 µm.

6.5 Summary

In this chapter, we design and fabricate a-PGs based on dye-doped LC RMs. Similar to phase retardation-based PGs, the absorption-based ones also manifest strong polarization sensitivity in their diffraction behaviors. Thanks to its absorptive nature, our a-PGs can function as efficient and LED-compatible polarization masks for high-volume photopatterning in the

fabrication of emerging LC optical devices.

71 CHAPTER 7: CONCLUSION

Augmented reality and virtual reality are fascinating technologies, which have generated various impactful applications to affect human lives. In this dissertation, we contribute several optical innovations to enhance the performance of near-eye displays using the Pancharatnam-Berry phase optical elements, aimed at making the augmented reality and virtual reality even better.

For achieving crystal-clear imagery in virtual reality displays, we proposed and demonstrated liquid-crystal-based optical solutions to enhanced resolution and imaging performance. On one hand, a resolution improvement technique is designed and experimentally validated to double the apparent pixel density of near-eye displays without losing framerate. The essence of this design is to optically split each physical pixel into two pixels, making use of the polarization selective nature of Pancharatnam-Berry phase deflectors. With this approach, the gaps between pixels are also filled with shifted pixels, so the screen-door effect is considerably reduced.

On the other hand, we also re-design the virtual reality viewing optics for better imaging performance by adding a broadband liquid crystal Pancharatnam-Berry phase lens. This lens has a three-layer twisted structure optimized for a wide spectral bandwidth, which makes its first-order diffraction efficiency higher than 95% within the entire display spectrum. Thanks to the diffractive nature of this liquid crystal polymer lens, the chromatic aberrations of the refractive viewing optics are drastically reduced.

Aside from improving the imagery of near-eye displays, we also improve the light efficiency by modifying the display panel with a customized Pancharatnam-Berry phase optical element. The core of this design is to use a directional display panel and a diffractive deflection film made of LC polymer. Directional display panels help confine the display light within a small

72 solid angle, while the deflection film can direct most of the light to the eyebox. Twice higher light efficiency is realized by our design.

Given the advantages of Pancharatnam-Berry phase optical elements and their promising applications in near-eye displays, we further design a new fabrication method based on absorption- based polarization gratings. Similar to conventional polarization gratings, the absorption-based ones also show strong polarization selectivity. Thanks to the absorptive nature, our absorption- based polarization gratings can perform as LED-compatible polarization masks for high-volume photopatterning in the scale-up fabrication of these liquid crystal optical devices.

With all the efforts, we expect the proposed concepts, designs, and devices to emerge as a useful technology for next-generation near-eye displays and become one of the practical applications of flat optics.

73 APPENDIX: STUDENT PUBLICATIONS

74 JOURNAL PUBLICATIONS

[1] Y. Li, T. Zhan, Z. Yang, P. L. Likamwa, K. Li, and S. T. Wu, “Broadband cholesteric

liquid crystal lens for chromatic aberration correction in catadioptric virtual reality optics,”

Opt. Express 29(4), 6011–6020 (2021).

[2] T. Zhan, E.L. Hsiang, K. Li, and S. T. Wu, “Enhancing the Optical Efficiency of Near-Eye

Displays with Liquid Crystal Optics,” Crystals 11, 107 (2021).

[3] T. Lin, T. Zhan, J. Zou, F. Fan, and S. T. Wu, “Maxwellian near-eye display with an

expanded eyebox,” Opt. Express 28(26), 38616–38625 (2020).

[4] Z. Yang, T. Zhan, and S. T. Wu, “Polarization independent guided-mode resonance in

liquid crystal-based polarization gratings,” OSA Continuum 3(11), 3107–3115 (2020).

[5] E. L. Hsiang, Y. Li, Z. He, T. Zhan, C. Zhang, Y. Dong, and S. T. Wu, “Enhancing the

efficiency of color conversion micro-LED display with a patterned cholesteric liquid

crystal polymer film,” Nanomaterials 10(12), 2430 (2020).

[6] J. Xiong, G. Tan, T. Zhan, and S. T. Wu, “Breaking the field-of-view limit in augmented

reality with a scanning waveguide display,” OSA Continuum 3(10), 2730–2740 (2020).

[7] T. Zhan, K. Yin, J. Xiong, Z. He, and S. T. Wu, “Augmented reality and virtual reality:

perspectives and challenges,” iScience 23(8), 101397 (2020).

[8] J. Zou, E. L. Hsiang, T. Zhan, K. Yin, Z. He, and S. T. Wu, “High dynamic range head-up

display,” Opt. Express 28(16), 24298–24307 (2020).

[9] K. Yin, T. Zhan, J. Xiong, Z. He, and S.T. Wu, “Polarization volume gratings for near-eye

displays and novel photonic devices,” Crystals 10(7), 561 (2020).

75 [10] T. Zhan, J. Xiong, G. Tan, and S. T. Wu, “Absorption-based polarization gratings,” Opt.

Express 28(9), 13907–13912 (2020).

[11] J. Xiong, G. Tan, T. Zhan, and S. T. Wu, “Wide-view augmented reality display with

diffractive cholesteric liquid crystal lens array,” J. Soc. Inf. Disp. 28(5), 450–456 (2020).

[12] J. Zou, T. Zhan, J. Xiong, and S. T. Wu, “Increasing the pixel density for VR displays with

a polarization grating,” J. Soc. Inf. Disp. 28(4) 315–323 (2020).

[13] J. He, Z. He, A. Towers, T. Zhan, H. Chen, L. Zhou, C. Zhang, R. Chen, T. Sun, A. J.

Gesquiere, S. T. Wu, and Y. Dong, “Ligand assisted swelling-deswelling

microencapsulation (LASDM) for stable, color tunable perovskite-polymer composites,”

Nanoscale Adv. 2(5), 2034–2043 (2020).

[14] T. Zhan, J. Xiong, J. Zou, and S. T. Wu, “Multifocal displays: review and prospect,”

PhotoniX 1(1), 10 (2020).

[15] Y. Li, T. Zhan, and S. T. Wu, “Flat cholesteric liquid crystal polymeric lens with low f-

number,” Opt. Express 28(4), 5875–5882 (2020).

[16] J. Zou, T. Zhan, J. Xiong, and S. T. Wu, “Broadband wide-view Pancharatnam–Berry

phase deflector,” Opt. Express 28(4), 4921–4927 (2020).

[17] T. Zhan, J. Zou, J. Xiong, X. Liu, H. Chen, J. Yang, S. Liu, Y. Dong, and S. T. Wu,

“Practical chromatic aberration correction in virtual reality displays enabled by large-size

ultra-broadband liquid crystal polymer lenses,” Adv. Opt. Mater. 8(2), 1901360 (2020).

[18] J. Xiong, T. Zhan, and S. T. Wu, “A versatile method for fabricating Pancharatnam-Berry

micro-optical elements,” Opt. Express 27(20), 27831–27840 (2019).

76 [19] T. Zhan, J. Zou, M. Lu, E. Chen, and S. T. Wu, “Wavelength-multiplexed multi-focal-

plane see-through near-eye displays,” Opt. Express 27(20), 27507–27513 (2019).

[20] Z. He, G. Gou, R. Chen, K. Yin, T. Zhan, and S. T. Wu, ‘‘Liquid Crystal Beam Steering

Devices: Principles, Recent Advances, and Future Developments,” Crystals 9(6), 292

(2019).

[21] T. Zhan, J. Xiong, G. Tan, Y. H. Lee, J. Yang, S. Liu, and S. T. Wu, ‘‘Enhancing near-eye

display resolution by polarization multiplexing,”Opt. Express 27(11), 15327–15334 (2019).

[22] T. Zhan, Y. H. Lee, J. Xiong, G. Tan, K. Yin, J. Yang, S. Liu, and S. T. Wu, ‘‘High-

efficiency switchable optical elements for advanced head-up displays,” J. SID 27(4), 223–

231 (2019).

[23] Y. Li, Y. Liu, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su, and S. T. Wu, ‘‘Single-exposure

fabrication of tunable Pancharatnam-Berry devices using a dye-doped liquid crystal,” Opt.

Express 27(6), 9054–9060 (2019).

[24] R. Chen, Y. H. Lee, T. Zhan, K. Yin, Z. An, and S. T. Wu, ‘‘Multi-stimuli-responsive self-

organized liquid crystal Bragg gratings,” Adv. Opt. Mater. 7(9), 1900101 (2019).

[25] Y. H. Lee, T. Zhan, and S. T. Wu, ‘‘Prospects and challenges in augmented reality displays,”

Virtual Reality and Intelligence Hardware 1(1), 10–20 (2019).

[26] T. Zhan, Y. H. Lee, G. Tan, J. Xiong, K. Yin, F. Gou, J. Zou, N. Zhang, D. Zhao, J. Yang,

S. Liu, and S. T. Wu, ‘‘Pancharatnam-Berry optical elements for head-up and near-eye

displays [invited],” J. Opt. Soc. Am. B 36(5), D52–D65 (2019).

77 [27] T. Zhan, J. Xiong, Y. H. Lee, R. Chen, and S. T. Wu, ‘‘Fabrication of Pancharatnam-Berry

phase optical elements with highly stable polarization holography,” Opt. Express 27(3),

2632–2642 (2019).

[28] T. Zhan, J. Xiong, Y. H. Lee, and S. T. Wu, ‘‘Polarization-independent Pancharatnam-

Berry phase lens system,” Opt. Express 26(26), 35026–35033 (2018).

[29] G. Tan, T. Zhan, Y. H. Lee, J. Xiong, and S. T. Wu, ‘‘Polarization-multiplexed multi-plane

display,” Opt. Lett. 43(22), 5651–5654 (2018).

[30] G. Tan, Y. H. Lee, T. Zhan, J. Yang, S. Liu, D. F. Zhao, and S. T. Wu, ‘‘Foveated imaging

for near-eye displays,” Opt. Express 26(19), 25076–25085 (2018).

[31] T. Zhan, Y. H. Lee, and S. T. Wu, ‘‘High-resolution additive light field near-eye display

by switchable Pancharatnam–Berry phase lenses,” Opt. Express 26(4), 4863–4872 (2018).

[32] Y. H. Lee, G. Tan, K. Yin, T. Zhan, and S. T. Wu, ‘‘Compact see-through near-eye display

with depth adaption,” J. SID 26(2), 64–70 (2018).

[33] Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N.V. Tabiryan, S. Gauza,

and S. T. Wu, ‘‘Recent progress in Pancharatnam-Berry phase optical elements and the

applications for virtual/augmented realities,” Optical Data Processing and Storage 3, 79–

88 (2017).

[34] F. Gou, F. Peng, Q. Ru, Y. H. Lee, H. Chen, Z. He, T. Zhan, K. L. Vodopyanov, and S. T.

Wu, ‘‘Mid-wave infrared beam steering based on high-efficiency liquid crystal diffractive

waveplates,” Opt. Express 25(19), 22404–22410 (2017).

[35] Y. H. Lee, T. Zhan, and S. T. Wu, ‘‘Enhancing the resolution of a near-eye display with

Pancharatnam−Berry phase deflector,” Opt. Lett. 42(22), 4732–4735 (2017).

78 CONFERNCE PROCEEDINGS

[1] T. Zhan, J. Xiong, G. Tan, and S.T. Wu, “Fast-Switching Liquid Crystal Devices for Near-

Eye and Head-Up Displays,” SID Symp. Digest 51(1), 567–570 (Aug 2020, San Jose,

California).

[2] J. Zou, T. Zhan, J. Xiong and S.T. Wu, “Increasing the Pixel Density for VR Displays with

a Polymer Grating,” SID Symp. Digest 51(1), 796–799 (Aug 2020, San Jose, California)

[3] T. Zhan, J. Zou, J. Xiong, X. Liu, H. Chen, J. Yang, S. Liu, Y. Dong, and S.T. Wu, “Cost-

efficient polymer flat lens for chromatic aberration correction in Virtual Reality displays,”

SID Symp. Digest 51(1), 579–582 (Aug 2020, San Jose, California).

[4] J. Xiong, G. Tan, K. Yin, T. Zhan and S.T. Wu, “A Scanning Waveguide Display with 100°

FOV,” SID Symp. Digest 51(1), 582–586 (Aug 2020, San Jose, California).

[5] T. Zhan, J. Zou, M. Lu, E. Chen, and S.T. Wu, “Wavelength-multiplexed multifocal

displays,” Proc. SPIE 11304, Advances in Display Technologies X, 1130408 (Feb 2020,

San Francisco, California).

[6] T. Zhan, J. Zou, J. Xiong, X. Liu, H. Chen, S. Liu, Y. Dong, and S. T. Wu, “Planar optics

enables chromatic aberration correction in immersive near-eye displays,” Proc. SPIE

11310, Optical Architectures for Displays and Sensing in Augmented, Virtual, and Mixed

Reality (AR, VR, MR), 1131003 (Feb 2020, San Francisco, California).

[7] T. Zhan, J. Xiong, J. Zou, G. Tan, and S.T. Wu, “Emerging Near-eye Displays with

Pancharatnam-Berry Optical Elements,” International Display Workshop, LCT2–3 (Nov.

2019, Sapporo, Japan).

79 [8] J. Xiong, G. Tan, T. Zhan, Y. H. Lee and S.T. Wu, “Four-Plane Near-Eye Display without

Sacrificing the Frame Rate,” SID Symp. Digest 50(1), 620–623 (May 2019, San Jose,

California).

[9] Y. Liu, M. Wang, Y. Li, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su and S.T. Wu, “Single-

exposure fabrication of geometry phase optical elements with arbitrary wavefronts,” SID

Symp. Digest 50(1), 1866–1869 (May 2019, San Jose, California).

[10] R. Chen, Y. H. Lee, T. Zhan, K. Yin, Z. An and S.T. Wu, “Fast-response polarization

volume gratings for AR/VR displays,” SID Symp. Digest 50(1), 838–841 (May 2019, San

Jose, California).

[11] T. Zhan, Y.H. Lee, J. Xiong, G. Tan, K. Yin, J. Yang, S. Liu and S.T. Wu, “High-Efficiency

Switchable Optical Elements for Advanced Head-up Displays,” SID Symp. Digest 50(1),

676–679 (May 2019, San Jose, California).

[12] G. Tan, Y.H. Lee, T. Zhan, J. Yang, S. Liu, D. Zhao and S.T. Wu, “Near-eye Foveated

Display for Achieving Human Visual Acuity,” SID Symp. Digest 50(1), 624–627 (May

2019, San Jose, California).

[13] G. Tan, T. Zhan, Y. H. Lee, J. Xiong and S. T. Wu, “Near-eye light field display with

polarization multiplexing,” Proc. SPIE 10942, Advances in Display Technologies IX

10942, 1094206 (Feb 2019, San Francisco, California).

[14] R. Sampson, H. Liu, X. Su, B. Huang, J. C. A. Zacarias, T. Zhan, R. A. Correa and G. Li,

“a Turbulence-resistant free-space communication using few-mode pre-amplifiers,” Proc.

SPIE 10947, Next-Generation Optical Communication: Components, Sub-Systems, and

Systems VIII, 1094707 (Feb 2019, San Francisco, California).

80 [15] Y.H. Lee, G. Tan, K. Yin, T. Zhan, and S.T. Wu, Compact See‐through Near‐eye Display

with Depth Adaption,” SID Symp. Digest 49(1), 1060–1063 (May 2018, Los Angeles,

California).

[16] T. Zhan, Y.H. Lee, and S.T. Wu, “Doubling the Pixel Density of Near‐eye Displays,” SID

Symp. Digest 49(1), 13–16 (May 2018, Los Angeles, California).

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