Design and fabrication of an integrated polarized light guide for liquid-crystal-display illumination

An integrated polarized light guide was designed and fabricated for use as a liquid-crystal backlight with emphasis on uniformity of the light and conversion of p-polarized to s-polarized light. Two different micro-optical structures were fabricated both on the top and the bottom surfaces of the light guide. On the top surface, a subwavelength grating separates s-polarized and p-polarized light to achieve a polarization-conversion efficiency of 69%. A 1.7 gain factor of polarization efficiency was obtained to increase the utility of light for liquid-crystal illumination.     

Three-port binary reflective grating with high efficiency under second Bragg angle incidence

Abstract

A binary three-port reflective grating under second Bragg angle incidence is designed in this paper. Under second Bragg angle incidence, the grating can separate nearly 33% light wave energy into the 2nd order, the 1st order and the 0th diffractive orders, respectively. Rigorous coupled-wave analysis can give numerical calculation to optimize the three-port grating depths and periods. For the optimized reflective three-port grating, TE polarization and TM polarization can have different values of grating depth and period. Compared with the reported three-port binary grating under Bragg angle incidence, the diffraction efficiencies can be improved. Moreover, the modal method is applied to explain the propagating mechanism. The highly efficient three-port binary reflective grating under second Bragg angle incidence would be manufactured in the emerging industry for its novel performance.     

Measurement of duty cycles of metal grating masks formed on dielectric substrates

A nondestructive method for measuring the duty cycles of metal grating masks formed on top of dielectric substrates is proposed. For a near-normal angle of incidence, the zeroth diffracted order transmission efficiency curves for both TE and TM polarized probe lights, as a function of duty cycles, behave linearly in the duty cycle ranging from 0 to 1. By comparing the measured efficiencies, or the ratio of zeroth-order transmission efficiency for TM polarization to that for TE polarization, with that of the rigorous-coupled wave analysis (RCWA) method for a fixed grating period and depth, one can determine the duty cycle of the grating. By selecting the probe light appropriately, the measurement errors originating from deviations of the incident angle and grating depth can be negligible. This method is applicable for all metal gratings, which are not easy to measure nondestructively due to fine grooves smaller than the wavelength. This method is simple, accurate, nondestructive, and low-cost. The results of experimental verification are presented and show excellent agreement with scanning electron microscope images.     

Nonpolarizing guided-mode resonant grating filter for oblique incidence

A new type of guided-mode resonant grating filter is described. The filter is independent of polarization state for oblique incidence. The filter has a crossed grating structure, and the plane of incidence on the filter contains the symmetric axis of the grating structure. Theoretical considerations and numerical calculations using two-dimensional rigorous coupled-wave analysis show that a rhombic lattice structure is suitable to such filters. In this configuration an incident light wave is diffracted into the waveguide and is divided into two propagation modes whose directions are symmetric with respect to the plane of incidence. In particular, when the propagation directions of the two modes are perpendicular to each other, the fill factor of grating structure can be approximately 50%. The filter was designed for an incident angle of 45 degrees. Tolerances of setting errors and fabrication errors for this filter were estimated by numerical calculations.     

Analysis of diffraction gratings by using an edge element method

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.     

Broadband wide-angle polarization converter for LCD backlight

A novel polarization converter using reflective metallic gratings and a polarization beam splitter is introduced for LCD backlight illumination. These two optical elements form a polarization rotation resonator. Broadband and high optical efficiency of polarization conversion in the visible region is achieved through the resonance of the refracted light and the surface plasmon wave in metallic surface-relief gratings. For wide-angle illumination, the conversion efficiency with arbitrary incident angle is studied. This device can convert unpolarized light to linear polarization with over 85% efficiency.     

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.     

Polarizing color filter based on a subwavelength metal-dielectric grating

We propose a polarizing color filter based on a one-dimensional subwavelength metal-dielectric grating combining the functions of a polarizer and a color filter. The proposed device consists of three parts: a substrate, a dielectric grating, and a metal grating. The effects of the dielectric grating and the metal grating are investigated in detail by rigorous coupled-wave analysis. Performance is enhanced effectively by utilizing a dielectric grating of high equivalent refractive index. Typical optimized structural parameters are obtained, in which more than 72.6% broadband transmission with >21 dB polarization extinction ratio are simultaneously achieved for a tricolor filter. For transverse electric (TE) polarized light, its reflection efficiency is more than 71.8% in the broad passband light range, which can be recycled by rotating the TE polarization in part into transverse magnetic polarization and reimpinging on the designed device to increase the total energy efficiency. Numerical results show that peak transmission efficiency (PTE) is increased by at least 12.9% using recycled TE-polarized light.     

Method of surface polariton field structure measurement using resonance excited in a single planar double split ring

An experimental method of determining the structure and local polarization properties of the fields of surface polaritons is proposed, based on excitation of resonance in a single planar double split ring with a diameter much smaller than the wavelength. The proposed method has been verified in the microwave range. A metasurface for the formation of polaritons was represented by a grating of parallel wires with finite lengths. A more than tenfold increase in the resonance intensity has been observed for the excitation of a ring by surface polaritons as compared to the case of excitation by a plane wave.     

Photopolarimeter based on two gratings recorded in thin organic films

A photopolarimeter based on two different kinds of diffraction gratings (a two-grating photopolarimeter) has been developed for real-time measurements of the four elements of the Stokes vector. The main elements of the device are a pure polarization grating and an ordinary transmission grating, both recorded by means of holographic techniques in thin films of organic materials. The first one consists of a diffraction grating recorded by two interfering opposite circularly polarized beams in a Langmuir-Blodgett film of an azo-compound material. The second component is a grating recorded by two interfering parallel circularly polarized beams in a thin film of a photosensitive polymer. Both gratings offer long time stability and good diffraction efficiency. Four photodiodes collect the first-order diffracted beams from these gratings, the output signals of which are read through an analog-to-digital converter by a PC. The optical alignment of the device is easy and the calibration is realized in a one-step procedure.     

Integration of grating couplers in two-story waveguides for rotary displacement sensing

An integrated-optic device, constructed by stacking two types of grating coupler in a two-story structure of waveguides, is proposed for sensing angular displacement of spindle rotation. In the first story a guided wave is diffracted by a grating coupler and becomes a sensing beam. The sensing beam is reflected by a mirror with a quarter-wave plate attached to a spindle head and is coupled back into the second story by another grating coupler. We measured the rotary displacement of the spindle by detecting variation of polarization direction of the reflected beam. A prototype device has been designed and fabricated, and the operation principle is experimentally confirmed.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

Nonreciprocal microwave transmission in metastructures with transversely magnetized ferrite plate and a grating of resonant elements

Nonreciprocal transmission of a linearly polarized electromagnetic wave at a ferromagnetic resonance (FMR) frequency has been observed in a metastructure comprising a transversely magnetized ferrite plate and a grating of resonant elements. The nonreciprocity of wave transmission is observed for the metastructure arranged along the axis of a rectangular waveguide and even in the free space between transmitting and receiving waveguides, where the effect does not take place when there is no grating. The observed phenomenon is explained by the formation of a surface wave with elliptic or circular polarization on the grating. The nonreciprocity reaches maximum (>35 dB) under the conditions of mutual influence between the FMR and the resonance of grating elements for certain values of the certain frequency and magnetic field, which depend on the distance between the ferrite plate and the grating. The nonreciprocal effects have been observed for grating elements in the form of double split rings, polyhedral loops, and dipoles. The results may be of interest for the development of new nonreciprocal devices and multifunctional metastructures such as decoupling elements for quasi-optical systems and two-frequency decoupling filters for counterpropagating waves in the gigahertz and terahertz range.     

Study of waveguide grating eigenmodes for unpolarized filtering applications

The dispersion relation of eigenmodes of two-dimensional waveguide gratings is studied with a perturbative model. The analytic expression of the complex wavelength of the modes permits us to predict the shape of the anomalies in the grating reflectivity with respect to the wavelength and the polarization of the incident plane wave. The simultaneous excitation of two independent modes is necessary for obtaining high-efficiency filtering of unpolarized light. We show how this requirement can be met.     

Transformation of acoustic waves in periodic metal grating sandwiched between piezoelectric and dielectric

The mechanism of SAW transformation with variation of film thickness is investigated in a piezoelectric substrate with a metal grating overlaid by a dielectric film, via simulation and visualization of the acoustic fields. By way of example, two orientations of lithium niobate substrates are analyzed, YX-LN and 128°YX-LN, with a Cu grating and an isotropic silica glass overlay. The motions, which follow the wave propagation in the sagittal plane, are visualized within two periods of the grating, with added contour plots showing the shear horizontal displacements. The continuous transformation of the wave's nature is investigated for each wave propagating in the analyzed material structures when the film thickness is increased from zero to a few wavelengths. The examples of the SAW transformation into boundary waves and into plate modes of different polarization have been found and investigated. The behavior of the SAW characteristics in the grating is correlated with transformation of the wave structure with increasing overlay thickness.     

Polarization of holographic grating diffraction. I. General theory

The full polarization property of volume holographic grating diffraction is investigated theoretically. With a simple volume grating model, the diffracted fields and Mueller matrices are first derived from Maxwell's equations by using the Green's function algorithms. The formalism is derived for the general case that the diffraction beam and the grating wave vector are not in the plane of incidence, where s waves and p waves are not decoupled. The derived photon-momentum relations determine the Bragg angle selectivity. The parameters of diffraction strength related to the hologram-writing process and material are defined and are not necessarily small in general. The diffracted-beam profiles are analytically calculated by using the known grating shape function. This theory has provided a fundamental understanding of the polarization phenomena of a real holographic diffraction grating device. The derived algorithm would provide a simulation-analysis tool for the engineering design of real holographic beam combiner/splitter devices.     

Spectrograph based on a single diffractive element for real-time measurement of circular dichroism

In this study, a novel and simple diffractive spectrographic method for real-time measurements of circular dichroism (CD) is considered from a theoretical and experimental approach. A demonstrator prototype of the CD spectrograph has been developed and its performance has been compared with a commercial phase-modulation CD spectrometer. The main element of the device is a polarization holographic grating, recorded in a thin photosensitive organic film, by two interfering opposite circularly polarized beams. A peculiarity of this grating is that the amplitude of the +1 (-1) order of diffraction is proportional to the right (left) circular polarization component of the incoming beam. Here we demonstrate that the CD spectrum of a specimen can be easily evaluated from the intensities of the diffracted beams. A white light beam passing through the specimen is diffracted from the grating and the intensities of the +/-1 orders of diffraction are measured. Due to the spectral selectivity of the grating, the CD at each wavelength can be evaluated at the same time using two linear array detectors.     

Effect of reconstruction beam polarization on the kinetics of anisotropic gratings in bacteriorhodopsin

Anisotropic gratings are recorded on bacteriorhodopsin films by two parallelly polarized beams, and the effect of the polarization orientation of the reconstructing beam on the diffraction efficiency kinetics is studied. A theoretical model for the diffraction efficiency kinetics of the anisotropic grating is developed by combining Jones-matrix and photochromic two-state theory. It is found that the polarization azimuth of the reconstructing beam produces a cosine modulation on the kinetics of the diffraction efficiency, being positive at the peak efficiency and negative for steady state. By adding auxiliary violet light during grating formation, the saturation of the grating can be restrained. As a result, the negative cosine modulation for the steady-state diffraction efficiency changes to a positive one. In addition, the steady-state diffraction efficiency is increased appreciably for all reconstructing polarization orientations.     

Study of an ultrafast analog-to-digital conversion scheme based on diffractive optics

A potentially ultrafast optical analog-to-digital (A/D) converter scheme is proposed and was partly studied experimentally. In the A/D converter scheme the input signal controls the wavelength of a diode laser, whose output beam is incident on a grating. The beam from the grating hits a diffractive optical element in an array. The wavelength determines which element is illuminated. Each element fans out a unique spot-pattern bit code to be read out in parallel by individual detectors. In the experiment all patterns but one from 64 array elements were read out correctly.