Broadening the angular tolerance in two-dimensional grating resonance structures at oblique incidence

Broadening of the angular response of two-dimensional (2D) guided mode resonant spectral filters at oblique incidence is investigated. Coupling into multiple fundamental guided resonant modes having the same propagation constant but propagating in different planes (inherent multiple-plane diffraction by 2D gratings) is shown to significantly broaden the angular tolerance while maintaining narrow linewidth. Resonances have symmetric and broad angular responses when the incident wave is coupled to four resonant modes in a structure with a hexagonal grating pattern. Further broadening is implemented by enhancing the second Bragg diffraction of the 2D grating structure. Resonance with a narrow spectral linewidth (Dlambda(FWHM) approximately 1.6 x 10(-4)lambda(0)) and angularly tolerant to an ~6 mum beam diameter is obtained. A second approach utilizing a dual 2D grating configuration with a second grating on the substrate side is shown to increase the lateral confinement, causing the merging of two successive resonant bands. This results in further improvement of the angular/spectral linewidth ratio by ~80%.     

Design and characteristics of polarization-insensitive resonant gratings for color filtering

A method of designing polarization-insensitive color filters with guided-mode resonance grating is presented. The influence of incident conditions on exciting waveguide mode is investigated, and we find that polarization insensitivity may occur at the full conical incidence. Using rigorous coupled-wave analysis, we mainly analyze the effects of waveguide thickness and fill factor on the diffracted efficiency of the grating filter. The final structural parameters of the devices for three primary colors are collected after optimization, and the calculated results show that the spectral reflectance of each color filter is basically identical for different polarization states of incident light. Moreover, field analysis by the finite-difference time-domain technique indicates that two symmetric modes are excited between the waveguide layer and substrate under full conical incidence, which is coincident with the previous theoretical study. The reported work will eliminate the restriction of polarization-dependence of color filters and greatly expand their application range.     

Numerical analysis of plasmon-resonance absorption in bisinusoidal metal gratings

We numerically investigate plasmon-resonance absorption of incident light energy by a bisinusoidal metal grating, i.e., one whose surface profile is sinusoidally corrugated in two orthogonal directions with a common period. Employing Yasuura's modal expansion method, we solve the problem of plane-wave diffraction by the grating and evaluate the absorption, which is observed as dips in diffraction efficiency curves. We examine the field distribution and energy flow in detail at the angles of incidence at which the absorption occurs. We show that the absorption is caused by coupling of the TM component of an evanescent order with surface plasmons. A phase-matching condition is used in the prediction of the incident angle at which the absorption occurs. This, together with the field profile in the presence of the resonance absorption, explains the mechanism of the absorption. We then illustrate interesting features of the absorption: enhancement of polarization conversion between the incident light and the reflected light and simultaneous excitation of two plasmon waves in directions that are symmetric with respect to the plane of incidence.     

Multiple scattering of electromagnetic waves by an aggregate of uniaxial anisotropic spheres

An exact analytical solution is obtained for the scattering of electromagnetic waves from a plane wave with arbitrary directions of propagation and polarization by an aggregate of interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes. The expansion coefficients of a plane wave with arbitrary directions of propagation and polarization, for both TM and TE modes, are derived in terms of spherical vector wave functions. The effects of the incident angle α and the polarization angle β on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres are numerically analyzed in detail. The characteristics of the forward and backward RCSs in relation to the incident wavelength are also numerically studied. Selected results on the forward and backward RCSs of several types of square arrays of SiO? spheres illuminated by a plane wave with different incident angles are described. The accuracy of the expansion coefficients of the incident fields is verified by comparing them with the results obtained from references when the plane wave is degenerated to a z-propagating and x- or y-polarized plane wave. The validity of the theory is also confirmed by comparing the numerical results with those provided by a CST simulation.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.     

Reduction of polarization-induced artifacts in grating-based spectrometers

An optical device that converts unpolarized light into a single polarization state is described. The device is based on a polarizing beam splitter that separates the two polarization directions. The beam splitter is combined with two pairs of equilateral prisms that are used to collimate the two beams in terms of both propagation and polarization directions. When it is used in combination with a blazed diffraction grating, this device is shown to effectively remove the polarization dependence of the first-order diffracted power. The device has an insertion loss of approximately 14% for purely s-polarized light. However, for unpolarized light incident upon the two gratings studied here, the increased throughput of the p-polarized component leads to an average relative gain in overall efficiency of 13%-19%, depending on the grating. In collimating the two polarization directions, the device may cause a reduction in spectral resolution for a rectangular entrance slit. As a result, the device is more likely to find use in spectrometers that have a circular aperture, such as that provided by an optical fiber.     

Group-theoretic approach to enhancing the Fourier modal method for crossed gratings of plane group p3

The Fourier modal method for crossed gratings is reformulated by use of a group-theoretic approach when the grating structures, according to plane crystallography, are of plane group p3. By exploiting the structural symmetries of the grating, i.e. the invariance of grating pattern after rotations about the normal of the mean grating plane through angles n(2π/3), a general diffraction problem with asymmetrical incidence is decomposed into three so-called symmetrical basis problems whose field distributions are the symmetry modes of the grating. Then by solving the symmetrical basis problems instead of the original problem, we reduce the memory occupation and time consumption in numerical computation to 1/3 and 1/9 of those of the original formulation, respectively, if the truncated reciprocal lattice of the diffracted field also has the symmetry of the grating structure. For the special case of normal incidence, the reduction factor can be further reduced to 2/27. Numerical examples are provided to illustrate the effectiveness of the new formulation.     

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.     

Guided-mode resonant grating filter with an antireflection structured surface

We describe a new structure of guided-mode resonant grating (GMRG) filters with low sideband reflectance. This GMRG filter consists of a high-index thin film on an antireflective structured surface called "moth-eye structure." Since the high-index film undulates along the surface structure, the film acts as a modulated optical waveguide. An incident light wave satisfying a resonant condition is reflected by the GMRG filter, and nonresonant light waves pass through the filter. This GMRG filter is valid for reducing reflection of nonresonant light waves in a wide spectral range. The resonant reflection of this new filter was investigated by numerical calculation based on an electromagnetic grating analysis. In the case of a triangular antireflective surface structure whose thickness is 2x greater than its period, the sideband reflectance for nonresonant light waves was lower than 0.5% for TM-polarized light in a wide range of wavelengths.     

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.     

Effective grating theory for resonance domain surface-relief diffraction gratings

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.     

Interface between transparent isotropic and uniaxial absorbing dielectric media: equations for ray tracing and for the direction of propagation

In this work we analyze the propagation of a plane wave that passes from an isotropic transparent medium to a uniaxial absorbing medium. Detailed expressions that give the real directions of propagation of the wave and the energy of the reflected and refracted ordinary and extraordinary waves are obtained. These expressions are valid for every orientation of the optic axis of the uniaxial medium and for every direction of propagation of the incident wave. Expressions are tested in the case of an interface between a transparent and an absorbing isotropic media and for the air-rutile (TiO2) interface. The effect of absorption has been evaluated by comparing the results obtained in rutile with the results obtained in a transparent uniaxial medium with the same real refractive indices. Results are presented for different values of the angle of incidence and the orientation of the plane of incidence.     

Unidirectional wavelength filtering characteristics of the two-dimensional triangular-lattice photonic crystal structures with elliptical defects

The unidirectional wavelength filtering characters of the two-dimensional triangular-lattice photonic crystal structures consisting of two waveguides and an elliptic defect are theoretically studied by the finite-difference time-domain method. Through designing the coupling regions between the elliptical defect and the adjacent waveguides, the unidirectional wavelength filtering is achieved owing to the modes’ match and mismatch between the elliptical defect and waveguides, which converts the incident fundamental even-symmetric modes to the higher order odd modes. Based on the abundant defective modes with different symmetries supported by the elliptical defect, this kind of wavelength filters can allow the unidirectional light propagation with inverse forward directions, and the bidirectional propagation through the same structure at different wavelengths.     

Anomalous propagation of elastic waves through a boundary between liquid and magnetoacoustic material

We consider a longitudinal acoustic wave incident onto a plane boundary between a liquid and a magnetoacoustic medium representing an antiferromagnetic material with anisotropy of the easy plane type, occurring in the vicinity of an orientational phase transition with respect to magnetic field. The directions of propagation and the amplitudes of reflected and transmitted longitudinal and transverse waves are determined. The possibility of an effective field control for the refraction angle and the wave type transformation is demonstrated. Beginning with a certain critical angle of incidence, the longitudinal and, eventually, the transverse waves in the magnetic medium become inhomogeneous and slide along the interface. If the magnetic material is sufficiently close to the phase transition point, the waves can be reirradiated into the liquid medium.     

Achromatic quarter-wave plates using the dispersion of form birefringence

We propose achromatic quarter-wave plates of a subwavelength grating structure. When the period of the grating structure is smaller than the wavelengths of the incident light, the structure is considered to be an optically anisotropic medium. The effective refractive indices strongly depend on the wavelengths, especially when the period is close to the wavelength. Using this feature, we can design a grating quarter-wave plate whose phase retardation is maintained at pi/2 for a wide wavelength range. A design method using the effective medium theory is described, and the wave plates designed were evaluated by numerical calculation with a rigorous electromagnetic grating theory. The calculation results led to the possibility of an achromatic quarter-wave plate whose retardation errors are smaller than 3 degrees for a +/-10% change in wavelength.     

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Abstract

A rigorous modal analysis of lamellar gratings, i.e. gratings having rectangular grooves, in conical mountings is presented. It is an extension of the analysis of Botten et al. which considered non-conical mountings. A key step in the extension is a decomposition of the electromagnetic field in the grating region into two orthogonal components. A computer program implementing this extended modal analysis is capable of dealing with plane wave diffraction by dielectric and metallic gratings with deep grooves, at arbitrary angles of incidence, and having arbitrary incident polarizations. Some numerical examples are included.     

Quasi-Talbot effect of a grating in the deep Fresnel diffraction region

Based on the theory of scalar diffraction, the diffraction of gratings in the deep Fresnel diffraction region is developed, and the general formula of the diffraction intensity of the one-dimensional grating is presented by using the Hankel function. Through numerical calculations, some interesting diffraction phenomena are found. In the deep Fresnel diffraction region, the dominant effects, with increasing propagation distance from the grating, are, in order, the geometrical effect, the quasi-geometrical effect, and the interference and diffraction effects. Furthermore, the diffraction intensities vary periodically in the diffraction effect region with increasing propagation distance. Quasi-Talbot imaging of the grating exists in the interference and diffraction regions, and the intensity distributions most similar to the structure of the grating are not at the exact Talbot distances. These phenomena in the deep Fresnel diffraction region are distinct from those in the Fresnel diffraction region. The formation origin of quasi-Talbot imaging of the grating is also discussed, and the numerical calculations powerfully verify the theoretical results.     

Forbidden gaps in periodic anisotropic layered media

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented.     

计算气动声学中的高阶Nodal-DG方法研究

气动噪声的直接模拟对数值格式的色散、耗散特性提出了严格的要求。基于描述声波的线性双曲方程,运用本征值方法分析了高阶Nodal-DG方法的色散、耗散特性。结果发现,对于任意给定的m阶多项式基函数,数值波解有m+1个值,但仅有一个能够表示对应微分方程的物理波传播方式,其余的都是寄生波,且两种波型的传播方向相反。通过与Tam的DRP格式和Lele的六阶紧致格式进行比较,发现在相同的计算精度下,Nodal-DG方法的有效求解波数范围介于DRP格式和六阶紧致格式之间。通过对初始扰动为高斯波形的计算比较发现,在较少的网格数下,Nodal-DG方法的计算结果可以与紧致格式的计算结果相比,但优于DRP格式的计算结果,非常适合于气动声学的数值模拟,为气动声场的直接计算提供了一种新的方法