Analysis Of Plane Wave Diffraction Research Articles

Full wave analysis of plane wave diffraction by a finite sinusoidal grating: E-polarization case

Plane wave diffraction studies of a finite sinusoidal grating have previously assumed that the grating length is large in wavelengths and the depth of its corrugations is small compared to a wavelength. This paper introduces a rigorous technique, the Method of Analytical Regularization (MAR), which removes these restrictions. The solution obtained by this method is free from limitations on the parameters of sinusoidal grating and possesses the capability to achieve predetermined accuracy of computations uniformly in a wide frequency band. The results of previous studies, which employed the Wiener–Hopf technique combined with a perturbation method, are compared with those obtained by the MAR; excellent concordance of results in the common parameter regimes of applicability of both methods is found. The different regimes of applicability of each approach are identified; within these, the MAR provides effective and efficient solutions to benchmark problems for testing other approximate techniques.

Impact of Radon transform on plane wave diffraction by an impedance step geometry

This work presents a Radon transform analysis of plane wave diffraction by an impedance step, such that the planes and the step have different impedances. Application of Radon transform on diffraction analysis is of vital importance in many real-time applications i.e., medical imaging, geosciences, astronomy, optics, stress analysis etc. Radon transform offers the advantage of introducing freedom in the usage of observer angle, during reconstruction of signal using plane wave diffraction. Radon transform along with Wiener–Hopf technique and asymptotic method of integration are used for computing the far field of the diffracted plane wave. The solution of plane wave diffraction by an impedance step consists of an infinite set of linear equations, which is obtained with the help of a software. Sinograms showing the effect of varying step height and impedance on the scattered field are plotted, compared and discussed. The mathematical analysis and graphical discussion show that Radon transform enables the observer angle to be varied between 0 to 2π. The results are comparable to previous works on plane wave diffraction by an impedance step, when the observer angle is fixed.

Analysis of laser beam diffraction by axicon with the numerical aperture above limiting

The theoretical analysis of plane wave diffraction by axicon in the zone of evanescent waves is executed. The received analytical estimations are qualitatively in accordance with results of numerical calculations in nonparaxial scalar wave model.

A combined three-dimensional finite element and scattering matrix method for the analysis of plane wave diffraction by bi-periodic, multilayered structures

A three-dimensional finite element method (FEM) for the analysis of plane wave diffraction by a bi-periodic slab is described and implemented. A scattering matrix formalism based on the FEM allows the efficient treatment of light reflection and transmission by multilayer bi-periodic structures, and the computation of Bloch modes of three-dimensional arrays. Numerical simulations, which show the accuracy and flexibility of the FEM, are presented.

High Frequency Ray-Mode Coupling Analysis of Plane Wave Diffraction by a Wide and Thick Slit on a Conducting Screen

Diffraction field by a wide and thick slit on a conducting screen has been analyzed. High frequency ray-mode coupling analysis has been utilized, and the total diffracted or radiated field in each region is considered as a summation of successive modal radiation contribution due to the original modal excitation by the incident plane wave. Our derived results are compared with those obtained by other solutions, and good agreement has been observed, and the validity of our formulation is confirmed.

Wiener-Hopf Analysis of Plane Wave Diffraction by an Impedance Strip Attached on a Perfectly Conducting Half-Plane

In this article, diffraction of a plane wave by an impedance strip on a perfectly conducting half-plane, which represents a metallic half-plane with a material coating near its edge, is investigated rigorously. In order to obtain an analytical solution to such a problem, where the lateral boundary conditions are different in the three-part mixed boundary-value problem, the Fourier transform and spectral iteration technique is applied. The diffracted field is analyzed numerically with respect to the surface impedance of the strip and the strip width. The results are illustrated graphically.

An exact transient analysis of plane wave diffraction by a crack in an orthotropic or transversely isotropic solid

A transient plane strain analysis of diffraction of plane waves by a semi-infinite crack in an unbounded orthotropic or transversely isotropic solid is performed. The waves approach the crack at a general oblique angle, and are of two types, a normal stress pulse and a shear stress pulse, i.e. a P- and an SV-wave, respectively, in the isotropic limit. A class of materials that includes this limit and beryl, cobalt, ice, magnesium and titanium is chosen for illustration, and exact solutions are obtained for the initial/mixed boundary value problems. In contrast to related work, a factorization in the Laplace transform space is used to simplify the solution forms and the Wiener-Hopf component of the solution process, and to yield a more compact expression for the Rayleigh wave speed. Calculations for this speed, the two allowable, direction-dependent, plane wave speeds, and quantities related to the Mode I and Mode II dynamic stress intensity factors are given for the five anisotropic materials mentioned.

Numerical Analysis of Plane Wave Diffraction by a Semi-Infinite Grating

Plane wave diffraction by a semi-infinite strip grating is analyzed in order to investigate the end-effect of finite gratings in pure form. In the formulation, the current induced on each strip is divided into periodic current on an infinite strip grating and the correction current induced by the truncation of the periodic structure. These currents are determined by solving a set of integral equations by using the method of moment. Numerical calculations for current distribution, diffraction patterns, and norm of the induced correction currents reveal the end-effects of the semi-infinite grating.

Finite element analysis of plane wave diffraction from anisotropic dielectric gratings

AbstractIn this paper, the formulation of the analysis based on the finite element method is presented for the first time for an anisotropic dielectric grating. By this analysis method, the diffraction characteristics of a plane wave by an anisotropic dielectric grating with an arbitrary shape can be computed easily. The finite element method is applied to the region corresponding to one period containing an anisotropic dielectric grating. The analytical relationships are applied to the boundaries on the incident and transmitted sides while the periodic boundary condition is applied to all other boundaries. Specifically, an index modulated grating and a groove grating are chosen for the analysis of the diffraction characteristics when the TE and TM waves are coupled. From the comparison with the analysis results by the coupled‐mode theory and the spatial harmonic expansion method, the validity of the present method is confirmed.

FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab

A 2-D (two-dimensional) Huygens surface is developed for the finite difference time domain (FDTD) algorithm, allowing the investigation of pulsed plane-wave scattering from arbitrary 2-D structures placed on or in an infinite dielectric slab. Example results are presented for scattering from a perfectly conducting strip on an infinite dielectric slab, and the results are compared with data computed via the method of moments. Additionally, the diffraction from a finite, saw-tooth dielectric grating on an infinite dielectric slab is investigated.

Finite‐element analysis of plane wave diffraction from metallic gratings with arbitrary complex permittivity

AbstractA method of analysis based on the finite‐element method is presented for the problem of plane wave diffraction from metallic gratings with arbitrary complex permittivity. First, the problem of diffraction of a plane wave from the metallic reflected‐type grating is analyzed rigorously as a two‐media boundary value problem by the finite‐element method. Next, a new method is proposed in which an approximate boundary condition using the surface impedance is incorporated into the discretized equations by the finite‐element method. Especially, in the method of using the surface impedance approximation, the region to be analyzed is reduced substantially from the one for the two‐media boundary value problem, and the computational effort is expected to be reduced significantly. The diffraction characteristics of grooved gratings with sinusoidal, triangular and rectangular profiles are actually calculated and the results are compared with those by other methods and experiments. In the case of the TE wave incidence, it is found that the results by the two‐media boundary value problem and those by the surface impedance approximation agree well. On the other hand, in the case of the TM wave incidence, the results are substantially different depending on the grating profile. By comparison of the results with those based on the assumption of a perfect conductor, it is found that the loss in the metal must be considered at a longer wavelength in the case of the TM wave incidence than in the case of the TE wave incidence.

Finite–element analysis of plane wave diffraction from dielectric gratings

AbstractAn analysis method based on the finite element method is proposed for solving the problem of diffraction of a plane wave by a dielectric grating. For both the TE and TM wave incidences, a systematic formulation is presented. Although numerous analysis methods have been reported on dielectric gratings, it is necessary in general to divide a grating into several layered planar dielectric gratings when a dielectric grating with an arbitrary profile is analyzed. On the other hand, the finite element method used in this paper enables direct treatment of a dielectric grating with an arbitrary profile without multilayered division. In practice, gratings made of grooves with rectangular, sinusoidal and trapezoidal profiles created on the surface of a semi‐infinite dielectric medium are analyzed. The results of analysis on the diffraction characteristics are presented. Next, as an example for groove gratings with complex geometry, the analysis results of the diffraction efficiency are presented for a holographic grating fabricated at IBM. The analysis results agree well with those by other methods and with experimental values so that the validity and usefulness of the present method are confirmed.