Nanoscale liquid crystal polymer Bragg polarization gratings

Theoretical efficiency limit of diffractive input couplers in augmented reality waveguides

Considerable efforts have been devoted to augmented reality (AR) displays to enable the immersive user experience in the wearable glasses form factor. Transparent waveguide combiners offer a compact solution to guide light from the microdisplay to the front of eyes while maintaining the see-through optical path to view the real world simultaneously. To deliver a realistic virtual image with low power consumption, the waveguide combiners need to have high efficiency and good image quality. One important limiting factor for the efficiency of diffractive waveguide combiners is the out-coupling problem in the input couplers, where the guided light interacts with the input gratings again and get partially out-coupled. In this study, we introduce a theoretical model to deterministically find the upper bound of the input efficiency of a uniform input grating, constrained only by Lorentz reciprocity and energy conservation. Our model considers the polarization management at the input coupler and can work for arbitrary input polarization state ensemble. Our model also provides the corresponding characteristics of the input coupler, such as the grating diffraction efficiencies and the Jones matrix of the polarization management components, to achieve the optimal input efficiency. Equipped with this theoretical model, we investigate how the upper bound of input efficiency varies with geometric parameters including the waveguide thickness, the projector pupil size, and the projector pupil relief distance. Our study shines light on the fundamental efficiency limit of input couplers in diffractive waveguide combiners and highlights the benefits of polarization control in improving the input efficiency.

Recent Development of Tunable Optical Devices Based on Liquid

Liquid opens up a new stage of device tunability and gradually replaced solid-state devices and mechanical tuning. It optimizes the control method and improves the dynamic range of many optical devices, exhibiting several attractive features, such as rapid prototyping, miniaturization, easy integration and low power consumption. The advantage makes optical devices widely used in imaging, optical control, telecommunications, autopilot and lab-on-a-chip. Here, we review the tunable liquid devices, including isotropic liquid and anisotropic liquid crystal devices. Due to the unique characteristics of the two types of liquids, the tuning principles and tuning methods are distinguished and demonstrated in detail firstly and then some recent progress in this field, covering the adaptive lens, beam controller, beam filter, bending waveguide, iris, resonator and display devices. Finally, the limitations and future perspectives of the current liquid devices are discussed.

Influence of period and surface anchoring strength in liquid crystal optical axis gratings

Liquid crystal (LC) based geometric phase optical elements are widely used to effectively change the wavefront or propagation direction of light. Using photoalignment, the liquid crystal can be aligned according to the designed pattern, leading to components such as gratings, lenses or general wavefront shaping devices. The functionality and efficiency of the component is strongly influenced by how well the LC follows the imposed alignment pattern. Next to a considerable tilting of the LC at the air interface, we report on the observation of symmetry breaking in polymerized LC polarization gratings. By carefully analyzing the experimental and numerical data for gratings with different periods, we conclude that the non-negligible homeotropic anchoring strength at the air interface is responsible for the tilt angle and the symmetry breaking. The role of anchoring strength at the photoaligned and air interface and other parameters are investigated.

A Review of Two-Dimensional Liquid Crystal Polarization Gratings

In the past two decades, polarization gratings (PGs) have attracted intensive attention due to the high-efficient diffraction and polarization selectivity properties. On one hand, the one-dimensional (1D) PGs have been investigated widely and adapted to various applications. On the other hand, optical signal manipulation stimulates the development of multibeam optical devices. Therefore, the development of two-dimensional (2D) PGs is in demand. This review summarizes the research progress of 2D PGs. Different designs and fabrication methods are summarized, including assembling two 1D polarization patterns, a 2D holographic lithography by polarization interference and a micro-pixelated electric field stimulated 2D liquid crystal (LC) structure. Both experiments and analyses are included. The design strategy, diffraction property, merits and demerits are discussed and summarized for the different methods.

Recent Advances in Photoalignment Liquid Crystal Polarization Gratings and Their Applications

Liquid crystal (LC) circular polarization gratings (PGs), also known as Pancharatnam–Berry (PB) phase deflectors, are diffractive waveplates with linearly changed optical anisotropy axes. Due to the high diffraction efficiency, polarization selectivity character, and simple fabrication process, photoalignment LC PGs have been widely studied and developed especially in polarization management and beam split. In this review paper, we analyze the physical principles, show the exposure methods and fabrication process, and present relevant promising applications in photonics and imaging optics.

Miniature planar telescopes for efficient, wide-angle, high-precision beam steering

Non-mechanical beam steerers with lightweight, compact, high-efficiency, high-precision, and/or large-angle are pivotal for light detection and ranging (LiDAR) of autonomous vehicles, eye-tracking for near-eye displays, microscopy, optical tweezers, and high-precision three-dimensional (3D) printing. However, even the most matured optical phased array can only provide quasi-continuous, efficient beam steering within a small angle range. A telescope module with an angle magnification function can be coupled to enlarge the steering range or precision. But obtaining a compact, low-cost, lightweight, high-quality telescope module with conventional optics remains challenging. Patterned liquid crystal-based planar optical elements offer great design freedom for manipulating the phase profile of light in 2D space. Owing to the advantages of high efficiency, thinness, low cost, easy processing, flexibility, and response to environmental stimuli, a plethora of high-quality optical devices have been demonstrated. Here, a miniature planar telescope mediated by liquid crystal polymers is proposed to offer angle magnification independent of incident spatial location. It consists of two cascaded liquid crystal planar optical elements, each performing a predefined mathematical transformation. By this concept, planar optical elements are fabricated using a new exposure method and assembled into planar telescopes with different magnification factors. Within the incident field range, over 84.6% optical efficiency is achieved with small wavefront distortion. Such a miniature planar telescope shows the potential of cascaded liquid crystal planar optical elements for realizing functionalities that cannot be fulfilled by single optical elements, and enables lightweight, low loss, passive optical transmitters for widespread applications.

Compensator design for polarization state management in waveguide displays based on polarization volume gratings

In this work, we focus on the polarization state management in optical devices using optical elements based on circular polarization. As an example, we point out the issue in a waveguide display using circular polarization optical elements as input/output couplers, where the polarization state of the light can change as it propagates in the waveguide due to total internal reflection (TIR). This has a negative effect on the waveguide output coupler efficiency, image uniformity, and the polarization multiplexing capability. To address this problem, we discussed two different methods to compensate the polarization state change. With the compensator applied to correct the polarization state change in the waveguide, the optical elements based on circular polarization can be used with their advantages as input/output couplers for waveguide displays.

Liquid Crystal Devices for Beam Steering Applications

Liquid crystals are valuable materials for applications in beam steering devices. In this paper, an overview of the use of liquid crystals in the field of adaptive optics specifically for beam steering and lensing devices is presented. The paper introduces the properties of liquid crystals that have made them useful in this field followed by a more detailed discussion of specific liquid crystal devices that act as switchable optical components of refractive and diffractive types. The relative advantages and disadvantages of the different devices and techniques are summarised.

Twisting Structures in Liquid Crystal Polarization Gratings and Lenses

Recently, diverse twisting structures have been discovered to be a potential approach to design liquid crystal polarization gratings and lenses (LCPGs and LCPLs) with a high diffraction efficiency, broad bandwidth, wide view, and large diffraction angle. In this review, we divide these twisting structures into two main types, namely, multi-layer twisting structures with phase compensation and twisting structures forming Bragg diffraction. We found that multi-layer twisting structure LCPGs and LCPLs presented a broader bandwidth and a wider view angle by phase compensation. While for transmissive or reflective Bragg LCPGs, a large diffraction angle with high diffraction efficiency could be achieved. Based on the theoretical analysis in the review, potential research directions on novel twisting structures were prospected.

Closer look at transmissive polarization volume holograms: geometry, physics, and experimental validation

In this work, we took a closer look at transmissive polarization volume holograms (T-PVH) to provide clarifications on their geometry, physics, and optical responses by finite-difference time-domain (FDTD) simulation and experimental validation. First, we introduced the four possible geometries of T-PVH and simulated their optical responses in terms of diffraction efficiency, polarization selectivity, and polarization output. It is shown that the configuration we called "Slanted T-PVH (B-θ/D-θ+90)," where the director is perpendicular to the Bragg planes, has the advantageous property of maintaining circular output polarization states. For this configuration, a detailed simulation of spectral, angular, and polarization responses was completed. Finally, we validated the FDTD simulation results of the Slanted T-PVH (B-θ/D-θ+90) structures with experiments.

Design of Tunable Holographic Liquid Crystalline Diffraction Gratings

Tunable diffraction gratings and phase filters are important functional devices in optical communication and sensing systems. Polarization gratings, in particular, capable of redirecting an incident light beam completely into the first diffraction orders may be successfully fabricated in liquid crystalline cells assembled from substrates coated with uniform transparent electrodes and orienting layers that force a specific molecular distribution. In this work, the diffraction properties of liquid crystal (LC) cells characterized by a continually rotating cycloidal director pattern at the cell substrates and in the bulk, are studied theoretically by solving a relevant set of the Euler-Lagrange equations. The electric tunability of the gratings is analyzed by estimating the changes in liquid crystalline molecular distribution and thus in effective birefringence, as a function of external voltage. To the best of our knowledge, such detailed numerical calculations have not been presented so far for liquid crystal polarization gratings showing a cycloidal director pattern. Our theoretical predictions may be easily achieved in experimental conditions when exploiting, for example, photo-orienting material, to induce a permanent LC alignment with high spatial resolution. The proposed design may be for example, used as a tunable passband filter with adjustable bandwidths, thus allowing for potential applications in optical spectroscopy, optical communication networks, remote sensing and beyond.

Voltage-controlled liquid crystal Pancharatnam-Berry phase lens with broadband operation and high photo-stability

Pancharatnam-Berry phase optical elements (PBOEs) have received much attention due to their ability to generate complex structured light or to manipulate the shape of a light beam. This work demonstrates a tunable liquid crystal (LC) Pancharatnam-Berry (LCPB) lens using a simple and cost-effective PB phase hologram optical setup and thermal polymerization to form an irreversible photo-patterning alignment layer. The LCPB lens with high photo-stability supports ultra-broadband operation and provides a diffraction efficiency of ∼90% throughout the visible spectral range, achieved by applying the appropriate voltages. The LCPB lens functions as a convex or a concave lens, depending on the handedness of the circularly polarized incident light, so its image reduction and magnification functions are demonstrated, and its photo-stability is characterized. The fabrication of the proposed LC PBOEs is simpler and more cost-effective than previous methods, and the irreversible photo-patterning alignment layer that is formed by thermal polymerization allows larger operational bandwidths, supporting new applications.

A Different Perspective on Cholesteric Liquid Crystals Reveals Unique Color and Polarization Changes

Planar cholesteric liquid crystals (CLCs) are well known for having vibrant reflective coloration that is associated with the handedness and the pitch length of the helicoidal twist of the liquid crystalline molecules. If one observes these films at oblique angles, the reflected colors blue-shift with increasing angles from normal. On the other hand, uniform lying helix (ULH) CLCs, where the helicoidal axis lies in the plane of the substrate, are well-known but are not typically associated with vibrant colors. Here, we examine the unique optical properties of CLCs at oblique incidence angles, specifically the spectral and polarization changes associated with switching between planar and ULH CLCs for various incidence angles. At small angles of incidence (0° < ψ < 45°, where ψ is the angle of incidence relative to the surface normal at the substrate-CLC interface), the electrically driven helical reorientation from planar to ULH results in a blue-shifting of the color and circularly polarized to unpolarized switching behavior. At large angles (45° < ψ < 90°), the behavior is reversed, with a red-shifting color change occurring and the polarization switching from unpolarized to circularly polarized. Modeling of the light propagation through ULH CLCs is used to confirm the change in position and polarization characteristic of the reflection band with incidence angle observed experimentally. This study provides a new perspective on ULH CLCs and reveals a unique reconfigurable angular chromaticity.

Polarization Volume Gratings for Near-Eye Displays and Novel Photonic Devices

Liquid crystal-based reflective polarization volume grating (PVG), also known as a linear Bragg–Berry phase optical element or a member of volume Bragg gratings (VBGs), is a functional planar structure with patterned orientation of optical axis. Due to the strong polarization selectivity, nearly 100% diffraction efficiency, large diffraction angle, and simple fabrication process, PVGs have found potential applications in novel photonic devices and emerging near-eye displays. In this review paper, we describe the operation principles, discuss the optical properties, present the fabrication methods, and provide promising applications of PVGs for near-eye displays and novel photonic devices.

Ring-shaped liquid crystal structures through patterned planar photo-alignment

Patterned liquid crystal (LC) configurations find widespread applications in functional devices such as lenses, gratings, displays and soft-robots. In combination with external stimuli such as an applied electric field, photo-alignment at the surfaces offers an attractive way to stabilize different LC structures in the bulk of a device. Herein, a planar LC cell is developed using a photo-alignment layer at the bottom substrate and a rubbed nylon film at the top substrate. Patterned planar photo-alignment is achieved by modulating the linear polarization with a spatial light modulator (SLM) and projecting the pattern onto the bottom substrate. A ring pattern is written into the photo-alignment layer with a continuous rotation between an inner radius and an outer radius. In the other regions the alignment is parallel to the rubbing direction at the top substrate. Four different LC configurations are observed: structure A in which a ring-shaped region is formed with an out of plane (vertical) orientation perpendicular to the substrate, structure B which has a single disclination loop and a 180° twist at the inner region of the photo-patterned ring (r < r_in), structure C which has no discontinuities but a 360° twist in the inner region of the photo-patterned ring (r < r_in) and structure D with 2 disclination loops. The LC director configuration for all 4 structures is simulated through finite element (FE) Q-tensor simulations and the optical transmission for each structure is simulated using a generalized beam propagation method.

Extended-viewing-angle waveguide near-eye display with a polarization-dependent steering combiner

A waveguide-based near-eye display (WNED) with an extended viewing angle using a polarization-dependent steering combiner (PDSC) is proposed. The novel eyepiece-combiner is composed of polarization gratings and polarization optics attached to the outcoupler part of the waveguide, which can control the output beam path depending on the polarization state. The viewing angle limited by the grating properties can be extended up to twice. Also, an ultrathinness of about 1.4 mm is suitable for the WNED. The demonstrated prototype system achieves a horizontal field of view of 33.2°, which is 2 times wider than the conventional structure (without the PDSC). The proposed configuration can resolve the viewing angle issue for the WNED.

Retinal projection type lightguide-based near-eye display with switchable viewpoints

We present a retinal-projection-based near-eye display with switchable multiple viewpoints by polarization-multiplexing. Active switching of viewpoints is provided by the polarization grating, multiplexed holographic optical elements and polarization-dependent eyepiece lens that can generate one of the dual-divided focus groups according to the pupil position. The lightguide-combined optical devices have a potential to enable a wide field of view (FOV) and short eye relief with compact form factor. Our proposed system can support a pupil movement with an extended eyebox and mitigate image problem caused by duplicated viewpoints. We discuss the optical design for guiding system and demonstrate that proof-of-concept system provides all-in-focus images with 37 degrees FOV and 16 mm eyebox in horizontal direction.

Device simulation of liquid crystal polarization gratings

Liquid crystal polarization gratings manifest several unique features, such as high diffraction efficiency, polarization selectivity, and fast switching time. However, few works address the chiral-doped liquid crystal alignment issue in such gratings. Here, we develop an improved relaxation method to analyze the liquid crystal director distribution in chiral-doped polarization gratings. Our simulation result agrees well with experimental data on a polarization volume grating. The criteria for forming planar or slanted polarization grating are discussed.

Liquid Crystal Beam Steering Devices: Principles, Recent Advances, and Future Developments

Continuous, wide field-of-view, high-efficiency, and fast-response beam steering devices are desirable in a plethora of applications. Liquid crystals (LCs)—soft, bi-refringent, and self-assembled materials which respond to various external stimuli—are especially promising for fulfilling these demands. In this paper, we review recent advances in LC beam steering devices. We first describe the general operation principles of LC beam steering techniques. Next, we delve into different kinds of beam steering devices, compare their pros and cons, and propose a new LC-cladding waveguide beam steerer using resistive electrodes and present our simulation results. Finally, two future development challenges are addressed: Fast response time for mid-wave infrared (MWIR) beam steering, and device hybridization for large-angle, high-efficiency, and continuous beam steering. To achieve fast response times for MWIR beam steering using a transmission-type optical phased array, we develop a low-loss polymer-network liquid crystal and characterize its electro-optical properties.

Dynamic control of diffraction angle and separation properties of wavelength and polarization by quaternary liquid crystal grating

A quaternary liquid crystal (LC) grating simultaneously performs dynamic control of diffraction angle, polarization, and wavelength-separation properties as shown in the following: (1) Diffraction orders in which light waves are diffracted can be selected by applying a voltage, (2) the efficiency of each diffraction order can be controlled depending on a wavelength of an incident beam, and (3) a pair of counter-rotated circular polarizations or linear polarizations with an orthogonal relationship are diffracted simultaneously, and this property can be controlled by applying a voltage. These diffraction properties and LC alignment structures are proposed based on theoretical analyses using Jones calculus, and their properties are now demonstrated experimentally. The quaternary LC grating can be used as an advanced optical element for industrial applications such as tunable polarization beam splitters and dynamic switching of propagation directions of light depending on wavelength.

Fabrication of Pancharatnam-Berry phase optical elements with highly stable polarization holography

Polarization-dependent diffraction based on Pancharatnam-Berry phase optical elements (PBOEs) offers considerable benefits compared to conventional metasurfaces, such as negligible absorption, nearly 100% diffraction efficiency and an inexpensive fabrication process. Polarization holography is a simple way to fabricate PBOEs, which entails the interference of beams with different polarizations to generate a spatial-varying polarization field. Thus, the quality of recorded PBOEs manifests high sensitivity to the length change and phase shift between polarized beams, usually caused by environmental vibration and air flow. Here, new polarization holography based on modified Sagnac interferometry is developed for fabricating liquid crystal-based PB gratings and lenses, where the pitch of grating and optical power of lens could be easily tuned. This approach offers high tolerance to environmental disturbance during the exposure process. Detailed design parameters are analyzed, and the fabricated PBOEs with high optical quality are also demonstrated.

Polarization-independent Pancharatnam-Berry phase lens system

The conventional liquid crystal-based Pancharatnam-Berry (PB) phase lens exhibits distinct polarization selectivity, manifesting opposite optical power to circularly polarized light with opposite handedness. Here, a polarization-independent liquid crystal PB lens system is theoretically predicted and experimentally verified. Such a lens system consists of at least four PB lenses, with specific distances in between them. This enables the PB lens to be applied in polarization-independent optical systems.

Liquid-crystal-based polarization volume grating applied for full-color waveguide displays

In this Letter, we demonstrate polarization volume grating (PVG)-based couplers for a double-layer waveguide display to realize a full-color near-eye display. The polarized interference exposure with photo-alignment methods was employed to generate a birefringent spiral configuration with two-dimensional periodicity in a chiral-dopant reactive mesogen material. Such a structure presents a unique highly efficient single-order Bragg diffraction with polarized selectivity. The prepared PVG couplers exhibited over 80% diffraction efficiency with large diffraction angles at spectra of blue (457 nm), green (532 nm), and red (630 nm). The demonstrated waveguide prototype showed a full-color display with a diagonal field of view of around 35°. The overall optical efficiency was measured as high as 118.3  cd/m² per lumen with a transparency of 72% for ambient light.

Bragg polarization gratings for wide angular bandwidth and high efficiency at steep deflection angles

Optical films and surfaces using geometric phase are increasingly demonstrating unique and sometimes enhanced performance compared to traditional elements employing propagation phase. Here, we report on a diffraction grating with wider angular bandwidth and significantly higher average first-order efficiency than the nearest prior art of metasurfaces, volume holographic gratings, and surface-relief gratings configured to achieve a steep deflection angle. More specifically, we demonstrate a liquid crystal (LC) polymer Bragg polarization grating (PG) with large angular bandwidth and high efficiency in transmission-mode for 532 nm wavelength and 400 nm period. Angular bandwidth was significantly increased by arranging two slanted grating layers within the same monolithic film. First, we studied the optical properties with simulation and identified a structure with 48° angular bandwidth and 70% average first-order efficiency. Second, we fabricated a sample using a photo-aligned chiral nematic LC, where the two grating slants were controlled by the chiral dopants. We measured 40° angular bandwidth, 76% average efficiency, and 96% peak efficiency. Strong input polarization sensitivity (300:1 contrast) and spectral bandwidth (200 nm) mostly matched prior PGs. This approach is especially advantageous for augmented-reality systems and nonmechanical beam steering.

Reflective polarization volume gratings for high efficiency waveguide-coupling augmented reality displays

We demonstrate a reflective liquid-crystal polarization volume grating with high efficiency for augmented reality displays. The coupling efficiency was measured to be 90% at 650 nm and 50° deflection angle. The angular dependence of reflection band agrees well with Bragg condition, and the transmittance of environment light is high with negligible scattering. The bandwidth can be tailored by controlling the layer periodicity, allowing versatile applications and design freedom not only for augmented realities but also for other photonic devices.