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.