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.

Binary geometric-phase holograms.

Diffractive optics elements have exhibited many novel characteristics through various methods of employing Pancharatnam-Berry, or geometric, phase. One geometric-phase hologram (GPH) subset, consisting of a π-difference binary sampling, shows polarization-independent properties that are not present in the continuous GPH and the dynamic-phase binary analog. Here, we investigate the binary geometric-phase holograms (bin-GPHs) realized with anisotropic liquid crystal (LC) polymers. First, the optical properties of the ideal binary polarization grating are derived and simulated showing 81% cumulative first-order efficiency, polarization-independent diffraction when applying a π-switching scheme, innate odd (m = 2k + 1) diffractive orders, and variable polarization output. After, experimental results of two key bin-GPH elements, the binary polarization grating (Λ = 30µm) and binary geometric-phase lens (f/100), with π-offset regions and a 0.5µm transition pixel are presented. We found that the fabricated non-ideal bin-GPHs exhibit near-maximum theoretical polarization-insensitive diffraction efficiency and tunable polarization outputs. The simple, and scalable, fabrication of the anisotropic bin-GPH provides the potential for implementation within the next-generation near-eye displays for polarization-invariant beam-steering and waveguides.

Color-selective geometric-phase lenses for focusing and imaging based on liquid crystal polymer films.

The geometric-phase lens (GPLs) with small form factor compared to traditional refractive lenses has been identified as a compelling solution in augmented-/virtual-/mixed-reality (AR/VR/MR) headsets. Formed either with liquid crystals (LCs) or metasurfaces, the GPL is a type of emerging leading technology that implements the arbitrary aspheric phase to realize low loss and minimal ghosting. However, the inherent chromatic abberation (CA) of GPLs can significantly degrade the image quality. A possible solution is the independent spectral phase implementation for RGB. In this work, we propose the design of three types of multi-twist LC based color-selective GPLs (CS-GPLs), exhibiting highly chromatic efficiency spectra with diameter 30 mm, focal length around 41.2~mm, and F -number 1.37. Through theoretical and experimental validation, each type of CS-GPL manifests high diffraction efficiency (>91%) on respective primary color of orthogonal polarization and high transmission on the complementary color of input polarization. The triplet composed by RGB CS-GPLs demonstrates relative contrast ratio and minimal ghosting. The strong color and polarization dependency of CS-GPLs not only provide a novel technique to mitigate CA but also offer more design freedom in the AR/VR/MR polarization and imaging system.

Mantis shrimp-inspired organic photodetector for simultaneous hyperspectral and polarimetric imaging.

Combining hyperspectral and polarimetric imaging provides a powerful sensing modality with broad applications from astronomy to biology. Existing methods rely on temporal data acquisition or snapshot imaging of spatially separated detectors. These approaches incur fundamental artifacts that degrade imaging performance. To overcome these limitations, we present a stomatopod-inspired sensor capable of snapshot hyperspectral and polarization sensing in a single pixel. The design consists of stacking polarization-sensitive organic photovoltaics (P-OPVs) and polymer retarders. Multiple spectral and polarization channels are obtained by exploiting the P-OPVs' anisotropic response and the retarders' dispersion. We show that the design can sense 15 spectral channels over a 350-nanometer bandwidth. A detector is also experimentally demonstrated, which simultaneously registers four spectral channels and three polarization channels. The sensor showcases the myriad degrees of freedom offered by organic semiconductors that are not available in inorganics and heralds a fundamentally unexplored route for simultaneous spectral and polarimetric imaging.

Organic-based photodetectors for multiband spectral imaging.

Using organic photodetectors for multispectral sensing is attractive due to their unique capabilities to tune spectral response, transmittance, and polarization sensitivity. Existing methods lack tandem multicolor detection and exhibit high spectral cross talk. We exploit the polarization sensitivity of organic photodetectors, together with birefringent optical filters to design single-pixel multispectral detectors that achieve high spectral selectivity and good radiometric performance. Two different architectures are explored and optimized, including the Solc-based and multitwist-retarder-based organic photodetectors. Although the former demonstrated a higher spectral resolution, the latter enables a more compact sensor as well as greater flexibility in device fabrication.

Improved saturation and wide-viewing angle color filters based on multi-twist retarders.

Birefringent color filters serve a critical role in next-generation display systems, including augmented-/virtual-/mixed-reality headsets, and many types of optical remote sensing. Most prior polarization interference filters (PIFs) employ many individually aligned plates that enable only relatively thick color filters (≥100s of µm), are usually limited to small clear apertures (few cm), and offer poor off-axis performance. Here, we report on a family of monolithic, thin-film, birefringent PIFs formed using liquid crystal polymer (LCP) network materials, also known as reactive mesogens. These multi-twist retarders (MTRs) are only a few µm thick and have a single alignment surface. They offer high color saturation with a notch-type pass/stopband, analogous to Solc PIFs and stable off-axis performance. Here, we apply simplifying assumptions inspired by Solc PIFs, and develop a design method resulting in MTRs with an alternating achiral/chiral architecture. We theoretically and experimentally presented three types of MTR color filters (blue-yellow, green-magenta, and cyan-red), which manifest strong color filtering behavior and improved angular performance (up to ±20°) with larger color space coverage and high total light efficiency compared to their Solc filters counterparts. Such high-saturated and wide-viewing MTR color filters can be promising elements to maintain the system field of view (FOV) in the next-generation displays or spectral imaging applications.

Super achromatic wide-angle quarter-wave plates using multi-twist retarders.

The achromaticity and wide-angle property of quarter-wave plates (QWPs) are crucial for the color uniformity and image resolution of the future displays such as virtual reality (VR) pancake lens and augmented reality (AR) waveguide/focusing systems. However, most reported achromatic wide-angle QWPs designs composed by stacks of different birefringent plates are too complicated with limited achromaticity and wide-angle performance. The multi-twist retarders (MTR) QWPs presented in previous work already showed its potential to achieve high achromaticity in RGB using one monolithic film in normal incidence, but the incompetent polarization control in blue-violet limits its application in LED-based polarization-sensitive AR/VR headsets. In this work, we theoretically investigate a new type of MTR QWPs achieving super achromaticity from violet to red with average ellipticity 43° and simultaneously maintaining wide-viewing angle up to ±45°, which enables a precise polarization control within the field-of-view (FOV) of current AV/VR headset. The new proposed MTR QWP is also reported to obtain average reflection luminance leakage 0.15~% and maximum leakage 0.23~%, making it a promising element to reduce polarization leakage and enhance image resolution in the next-generation displays.

Snapshot channeled imaging spectrometer using geometric phase holograms.

In this paper, we present the design and experimental demonstration of a snapshot imaging spectrometer based on channeled imaging spectrometry (CIS) and channeled imaging polarimetry (CIP). Using a geometric phase microlens array (GPMLA) with multiple focal lengths, the proposed spectrometer selects wavelength components within its designed operating waveband of 450-700 nm. Compared to other snapshot spectral imagers, its key components are especially suitable for roll-to-roll (R2R) rapid fabrication, which gives the spectrometer potential for low-cost mass production. The principles and proof-of-concept experimental system of the sensor are described in detail, followed by lab validation and outdoor measurement results which demonstrate the sensor's ability to resolve spectral and spatial contents under both experimental and natural illumination conditions.

Simultaneous phase and amplitude aberration sensing with a liquid-crystal vector-Zernike phase mask.

We present an enhanced version of the Zernike wavefront sensor (WFS), which simultaneously measures phase and amplitude aberrations. The "vector-Zernike" WFS consists of a patterned liquid-crystal mask, which imposes a ±π/2 phase on the point spread function core through the achromatic geometric phase acting with the opposite sign on opposite circular polarizations. After splitting circular polarization, the ensuing pupil intensity images are used to reconstruct the phase and the amplitude of the incoming wavefront. We demonstrate reconstruction of the complex wavefront with monochromatic lab measurements and show in simulation the high accuracy and sensitivity over a bandwidth up to 100%.

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.

Nanoscale liquid crystal polymer Bragg polarization gratings.

We experimentally demonstrate nearly ideal liquid crystal (LC) polymer Bragg polarization gratings (PGs) operating at a visible wavelength of 450 nm and with a sub-wavelength period of 335 nm. Bragg PGs employ the geometric (Pancharatnam-Berry) phase, and have many properties fundamentally different than their isotropic analog. However, until now Bragg PGs with nanoscale periods (e.g., < 800 nm) have not been realized. Using photo-alignment polymers and high-birefringence LC materials, we employ multiple thin sublayers to overcome the critical thickness threshold, and use chiral dopants to induce a helical twist that effectively generates a slanted grating. These LC polymer Bragg PGs manifest 85-99% first-order efficiency, 19-29° field-of-view, Q ≈ 17, 200 nm spectral bandwidth, 84° deflection angle in air (in one case), and efficient waveguide-coupling (in another case). Compared to surface-relief and volume-holographic gratings, they show high efficiency with larger angular/spectral bandwidths and potentially simpler fabrication. These nanoscale Bragg PGs manifest a 6π rad/µm phase gradient, the largest reported for a geometric-phase hologram while maintaining a first-order efficiency near 100%.

Spatially heterodyned snapshot imaging spectrometer.

Snapshot hyperspectral imaging Fourier transform (SHIFT) spectrometers are a promising technology in optical detection and target identification. For any imaging spectrometer, spatial, spectral, and temporal resolution, along with form factor, power consumption, and computational complexity are often the design considerations for a desired application. Motivated by the need for high spectral resolution systems, capable of real-time implementation, we demonstrate improvements to the spectral resolution and computation trade-space. In this paper, we discuss the implementation of spatial heterodyning, using polarization gratings, to improve the spectral resolution trade space of a SHIFT spectrometer. Additionally, we employ neural networks to reduce the computational complexity required for data reduction, as appropriate for real-time imaging applications. Ultimately, with this method we demonstrate an 87% decrease in processing steps when compared to Fourier techniques. Additionally, we show an 80% reduction in spectral reconstruction error and a 30% increase in spatial fidelity when compared to linear operator techniques.

Achromatic Wollaston prism beam splitter using polarization gratings.

We describe a method to achromatize a Wollaston prism beam splitter by combining it with a polarization grating. The advantage of this technique, compared to refractive methods of correction, is that only one type of birefringent crystal is needed. Additionally, the assembly can be made thinner while remaining achromatized. In this Letter, a model for the achromatized grating prism is formulated. Experimental validation is conducted by achromatizing a calcite Wollaston prism (apex angle of 5.35°) using a polarization grating with a spatial period of 253 µm. We found that the primary dispersion was reduced by approximately 6.5 times for wavelengths spanning the conventional F, d, and C Fraunhofer lines (486 to 656 nm).

Snapshot retinal imaging Mueller matrix polarimeter.

Early diagnosis of glaucoma, which is a leading cause for visual impairment, is critical for successful treatment. It has been shown that Imaging polarimetry has advantages in early detection of structural changes in the retina. Here, we theoretically and experimentally present a snapshot Mueller Matrix Polarimeter fundus camera, which has the potential to record the polarization-altering characteristics of retina with a single snapshot. It is made by incorporating polarization gratings into a fundus camera design. Complete Mueller Matrix data sets can be obtained by analyzing the polarization fringes projected onto the image plane. In this paper, we describe the experimental implementation of the snapshot retinal imaging Mueller matrix polarimeter (SRIMMP), highlight issues related to calibration, and provide preliminary images acquired from the camera.

Direct-writing of complex liquid crystal patterns.

We report on a direct-write system for patterning of arbitrary, high-quality, continuous liquid crystal (LC) alignment patterns. The system uses a focused UV laser and XY scanning stages to expose a photoalignment layer, which then aligns a subsequent LC layer. We intentionally arrange for multiple overlapping exposures of the photoalignment material by a scanned Gaussian beam, often with a plurality of polarizations and intensities, in order to promote continuous and precise LC alignment. This type of exposure protocol has not been well investigated, and sometimes results in unexpected LC responses. Ultimately, this enables us to create continuous alignment patterns with feature sizes smaller than the recording beam. We describe the system design along with a thorough mathematical system description, starting from the direct-write system inputs and ending with the estimated alignment of the LC. We fabricate a number of test patterns to validate our system model, then design and fabricate a number of interesting well-known elements, including a q-plate and polarization grating.

Femtosecond pulse shaping using the geometric phase.

We demonstrate a femtosecond pulse shaper that utilizes polarization gratings to manipulate the geometric phase of an optical pulse. This unique approach enables circular polarization-dependent shaping of femtosecond pulses. As a result, it is possible to create coherent pulse pairs with orthogonal polarizations in a 4f pulse shaper setup, something until now that, to our knowledge, was only achieved via much more complex configurations. This approach could be used to greatly simplify and enhance the functionality of multidimensional spectroscopy and coherent control experiments, in which multiple coherent pulses are used to manipulate quantum states in materials of interest.

Performance characterization of a broadband vector Apodizing Phase Plate coronagraph.

One of the main challenges for the direct imaging of planets around nearby stars is the suppression of the diffracted halo from the primary star. Coronagraphs are angular filters that suppress this diffracted halo. The Apodizing Phase Plate coronagraph modifies the pupil-plane phase with an anti-symmetric pattern to suppress diffraction over a 180 degree region from 2 to 7 λ/D and achieves a mean raw contrast of 10(-4) in this area, independent of the tip-tilt stability of the system. Current APP coronagraphs implemented using classical phase techniques are limited in bandwidth and suppression region geometry (i.e. only on one side of the star). In this paper, we introduce the vector-APP (vAPP) whose phase pattern is implemented through the vector phase imposed by the orientation of patterned liquid crystals. Beam-splitting according to circular polarization states produces two, complementary PSFs with dark holes on either side. We have developed a prototype vAPP that consists of a stack of three twisting liquid crystal layers to yield a bandwidth of 500 to 900 nm. We characterize the properties of this device using reconstructions of the pupil-plane pattern, and of the ensuing PSF structures. By imaging the pupil between crossed and parallel polarizers we reconstruct the fast axis pattern, transmission, and retardance of the vAPP, and use this as input for a PSF model. This model includes aberrations of the laboratory set-up, and matches the measured PSF, which shows a raw contrast of 10(-3.8) between 2 and 7 λ/D in a 135 degree wedge. The vAPP coronagraph is relatively easy to manufacture and can be implemented together with a broadband quarter-wave plate and Wollaston prism in a pupil wheel in high-contrast imaging instruments. The liquid crystal patterning technique permits the application of extreme phase patterns with deeper contrasts inside the dark holes, and the multilayer liquid crystal achromatization technique enables unprecedented spectral bandwidths for phase-manipulation coronagraphy.

Generating and measuring nondiffracting vector Bessel beams.

Nondiffracting vector Bessel beams are of considerable interest due to their nondiffracting nature and unique high-numerical-aperture focusing properties. Here we demonstrate their creation by a simple procedure requiring only a spatial light modulator and an azimuthally varying birefringent plate, known as a q-plate. We extend our control of both the geometric and dynamic phases to perform a polarization and modal decomposition on the vector field. We study both single-charged Bessel beams as well as superpositions and find good agreement with theory. Since we are able to encode nondiffracting modes with circular polarizations possessing different orbital angular momenta, we suggest these modes will be of interest in optical trapping, microscopy, and optical communication.

Multi-twist retarders: broadband retardation control using self-aligning reactive liquid crystal layers.

We report on a family of complex birefringent elements, called Multi-Twist Retarders (MTRs), which offer remarkably effective control of broadband polarization transformation. MTRs consist of two or more twisted liquid crystal (LC) layers on a single substrate and with a single alignment layer. Importantly, subsequent LC layers are aligned directly by prior layers, allowing simple fabrication, achieving automatic layer registration, and resulting in a monolithic film with a continuously varying optic axis. In this work, we employ a numerical design method and focus on achromatic quarter- and half-wave MTRs. In just two or three layers, these have bandwidths and general behavior that matches or exceeds all traditional approaches using multiple homogenous retarders. We validate the concept by fabricating several quarter-wave retarders using a commercial polymerizeable LC, and show excellent achromaticity across bandwidths of 450-650 nm and 400-800 nm. Due to their simple fabrication and many degrees of freedom, MTRs are especially well suited for patterned achromatic retarders, and can easily achieve large bandwidth and/or low-variation of retardation within visible through infrared wavelengths.

Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings.

We present a novel optical element that efficiently generates orbital angular momentum (OAM) of light and transforms light between OAM modes based on a polarization grating with a fork-shaped singularity. This forked polarization grating (FPG) is composed of liquid crystalline materials, and can be made either static or switchable with high diffraction efficiency (i.e., 100% theoretically) into a single order. By spatially varying the Pancharatnam-Berry phase, FPGs shape the wavefront and thus control the OAM mode. We demonstrate theoretically and empirically that a charge l(g) FPG creates helical modes with OAM charge ±l(g) when a gaussian beam is input, and more generally, transforms the incident helical mode with OAM charge l(in) into output modes with OAM charge l(in)±l(g). We also show for the first time that this conversion into a single mode can be very efficient (i.e., ∼95% experimentally) at visible wavelengths, and the relative power between the two possible output modes is polarization-controllable from 0% to ∼100%. We developed a fabrication method that substantially improves FPG quality and efficiency over prior work. We also successfully fabricated switchable FPGs, which can be electrically switched between an OAM generating/transforming state and a transmissive state. Our experimental results showed >92% conversion efficiency for both configurations at 633 nm. These holographically fabricated elements are compact (i.e., thin glass plates), lightweight, and easily optimized for nearly any wavelength from ultraviolet to infrared, for a wide range of OAM charge, and for large or small clear apertures. They are ideal elements for enhanced control of OAM, e.g., in optical trapping and high-capacity information.