In optical thin-films and surfaces, geometric phase is utilized to control the phase beyond that possible through optical path differences. Geometric-phase lenses, which are significantly thinner than refractive lenses for the same numerical aperture (NA), most commonly use a spherical phase profile. This is especially effective for normally incident light, but like other thin lenses, the performance degrades noticeably for off-axis incidence and wider fields-of-view. In this study, we investigate whether or not various aspheric designs provide better off-axis performance. We simulate aspheric singlet and doublet liquid crystal geometric-phase lenses (24.5 mm diameter, 40 mm back focal length at 633 nm), aiming to optimize spot size performance at 0, 3, and 7 degrees field angles, using Zemax OpticStudio 16.5. By using Zernike fringe phase expansions, we find conditions which provide improved off-axis performance. We demonstrate improved performance of a compact lens system utilizing these polarization-dependent optics.
A prior simulation-only study of aspherical phase profiles [Hornburg et al, Proc SPIE 10743, 10743-4 (2018)] in geometric-phase lenses (GPLs) indicated that aspherical doublet lens systems should provide substantially improved off-axis performance than those using spherical phase profiles. In this work, we fabricate a liquid crystal GPL doublet (24.5 mm diameter, 40 mm back focal length at 633 nm) and compare it to with a reference spherical GPL singlet. We characterized the liquid crystal alignment quality, efficiencies, and spot performance. With these compact GP lens systems, we realize improved performance for wider fields of view, while maintaining low loss.
Here, we demonstrate a liquid crystal (LC) polymer Bragg polarization grating (PG) with large angular band- width and high efficiency in transmission-mode for 532 nm wavelength and 400 nm period. The field-of-view (FOV ) is increased significantly while preserving high diffraction efficiency by realizing a monolithic grating comprising two different slants. Using rigorous coupled-wave analysis simulation, we identified a structure with 48° FOV and 70% average first-order efficiency. We then experimentally fabricated and characterized the grating with a photo-aligned LC polymer network, also known as reactive mesogens. We measured 40° FOV and nearly 80% average diffraction efficiency. With this broadened and fairly uniform angular response, this wide FOV Bragg PG is a compelling option for large deflection-angle applications, including near-eye display in augmented reality systems, waveguide based illumination, and beam steering.
We report on the numerical analysis of Bragg polarization gratings (PGs), especially those formed with liquid crystals, and study their general diffraction properties by Rigorous Coupled-Wave Analysis (RCWA). Different from traditional Bragg (isotropic) gratings, Bragg PGs are verified to have high diffraction efficiency for large field of view, which is ideal for exit-pupil-expanders in waveguide-based head-mounted-displays, spectroscopy, and fiber-optic telecommunication systems. The RCWA approach allows for a rigorous and accurate solution without paraxial approximations to be obtained with much lower computational cost and time, as compared to finite-element, finite-difference, or analytical coupled-wave approaches. Therefore, it enables the study of the complete transmittance and reflectance behavior of Bragg PGs in the most computationally efficient way. Diffraction characteristics including angular response and polarization sensitivity are investigated. The spectral response and thickness dependence are also examined.
We report on the numerical analysis of polarization gratings (PGs) and study their general diffraction properties by using the Rigorous Coupled Wave Analysis (RCWA) method. With this semi-analytical method, we can perform rigorous simulation without paraxial approximation and have a complete understanding of diffraction behavior of PGs, including those with complex twisted layers. We first adapt the formulation of conventional RCWA to simulate grating made by anisotropic material, as appropriate for the PG profile. We then validate our RCWA method by comparing its result with that given by finite-difference time-domain (FDTD) method. Diffraction characteristics including the spectral response, angular response, and polarization dependence are investigated. A comparison of the stability and computation performance between the two methods is also briefly discussed.
We demonstrate a novel class of elements called Far-Field Geometric Phase Holograms (FGPH) capable of producing far-field output images free of chromatic distortion for a broad range of input wavelengths. The FGPH utilizes the geometric phase which applies the same phase profile to any incident wave regardless of wavelength. Thus, the fidelity of an image produced by an FGPH is the same for all wavelengths. However, being a diffractive element, the FGPH is still dispersive in that the size of a generated image depends on the replay wavelength according to the diffraction equation. In this paper, we give theory for the ideal FGPH element, describing its replay characteristics and unique polarization properties. We experimentally realize an FGPH element using photo-aligned liquid crystals patterned with a direct-write system. We characterize the fabricated element and show the theory to be valid. Generally, this new class of polarization sensitive elements can produce broadband undistorted images with high diffraction efficiency.