Periodic Inhomogeneous Medium Research Articles

STUDY ON EVOLUTION MODEL OF GASEOUS DETONATION WAVE IN PERIODIC INHOMOGENEOUS MEDIUM

The initiation, steady propagation and failure mechanism of gaseous detonation wave in periodic inhomogeneous media are very complex, and many physical mechanisms are still unclear, which is an active topic in detonation physics. Numerical simulation of propagation of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The influence of temperature disturbance with different wavelength and amplitude on the structure of wave front is analyzed. The results show that, the transition of ZND detonation to cellular detonation under artificial temperature disturbance is mainly controlled by two competitive factors: one is the intrinsic instability of detonation wave, the other is the wavelength and amplitude of artificial disturbance, the former is the internal factor, the latter is the external factor. The existence of artificial temperature disturbance delays the evolution of ZND detonation to cellular detonation by suppressing the development of shear wave, and the increase of internal instability can slow down this delay phenomenon. This shows that the artificial temperature disturbance can restrain the development of cell instability in a certain range, but it cannot stop the process. The discontinuity of temperature makes the detonation wave front more distorted, which leads to the existence of a weak triple-wave structure near the shear wave, which is, the artificial disturbance increases the inherent instability of detonation wave and changes the propagation mechanism of detonation wave front. The propagation of detonation and the instability of detonation are restrained by the artificial temperature disturbance with large amplitude. The formation of detonation front cellular structure depends on the artificial temperature disturbance and its own instability.

A high-order perturbation of envelopes (HOPE) method for scattering by periodic inhomogeneous media

The interaction of linear waves with periodic structures arises in a broad range of scientific and engineering applications. For such problems it is often mandatory that numerical simulations be rapid, robust, and highly accurate. With such qualities in mind High-Order Spectral methods are often utilized, and in this paper we describe and test a perturbative method which fits into this class. Here we view the inhomogeneous (but laterally periodic) permittivity as a perturbation of a constant value and pursue (regular) perturbation theory. We demonstrate that not only does this lead to a fast and accurate numerical method, but also that the expansion of the field in this geometric parameter is valid for large deformations (up to topological obstruction). Finally, we show that, if the permittivity deformation is spatially analytic, then so is the field scattered by it.

Mathematical methods for holographic mask with layered structure synthesis

In this paper variouslayeredholographic mask structures are proposed and their effectiveness is assessed. A method for diffraction modelling, suitable for use in layered structures of such masks, is proposed. A software module that allows to calculate the transmission and reflection of a plane wave of arbitrary polarization on periodic inhomogeneous medium with a cylindrical structure is developed. This software module is intended to be used for the study of applicability limits of some approximate methods for solving diffraction problems. The developed methods and programs have also been used to solve problems in other fields of electrodynamics, for example, in the problem of ocean surface radiolocation. Mathematical modelling of effects such as Brewster angle and Wood’s anomaly was performed with the resulting software module. Quantitative modelling results coincide with the analytical formulas with good accuracy.

Bloch modes at the surface of a photonic crystal interacting with a waveguide.

We theoretically studied the influence of an infinite set of waveguides on the evanescent field of Bloch waves at the surface of a one-dimensional photonic crystal (PC) excited by a TE Gaussian beam undergoing total internal reflection. The set of waveguides is regarded as a periodic inhomogeneous medium with period a. Numerical results are presented for the case in which a is greater than λ, which is the wavelength used to excite the surface mode. When the waveguide tip is very close to the surface of the PC, a fraction of the surface wave is reflected by the tip, producing an interference pattern that can be observed in the near field. In this case, the system simulates scanning tunneling optical microscopy in 2D geometry, and an image of the field distribution of the surface mode is obtained by quantifying the flux energy throughout the waveguide.

A sampling method for the inverse transmission problem for periodic media

This paper is concerned with the inverse scattering problem of reconstructing the support of a periodic inhomogeneous medium from knowledge of the scattered field measured on a straight line above and below the periodic structure. A linear sampling method is proposed to reconstruct the support of the periodic inhomogeneous medium based on a linear operator equation. The mathematical analysis of the sampling method is developed and numerical examples are given showing the practicality of the reconstruction algorithm.

An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

This article is concerned with uniqueness for reconstructing a periodic inhomogeneous medium sitting on a perfectly conducting plate. We deal with the problem in the framework of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation is obtained for two refractive indices and then used to prove that the refractive index can be uniquely identified from a knowledge of the incident fields and the total tangential electric field on a plane above the inhomogeneous medium, utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm–Liouville eigenvalue problem.

High-frequency homogenization for periodic media

An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.

Scattering from a periodic inhomogeneous medium with a rough interface

AbstractA hybrid technique that utilizes the finite‐element method (FEM) and an analytic solution is presented for the analysis of the scattering of a plane wave from a periodic inhomogeneous medium, having arbitrary geometry and material properties. This medium is overlaid with a homogeneous one that presents a rough interface with the space from which the incident plane wave originates. The rough interface is studied with a perturbative method, whereas the inhomogeneous medium is examined with the finite‐element procedure. The two methods are matched imposing the continuity of the fields into the homogeneous medium.

Existence of planar flame fronts in convective-diffusive periodic media

We prove the existence of planar travelling wave solutions in a reaction-diffusion-convection equation with combustion nonlinearity and self-adjoint linear part in Rn, n≧1. The linear part involves diffusion-convection terms and periodic coefficients. These travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media. We use the method of continuation, spectral theory, and the maximum principle. Uniqueness and monotonicity properties of solutions follow from a previous paper. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.

Reflection of electromagnetic waves by a layer of periodically stratified dielectric medium—a remedy for TV signal interference caused by tall buildings

AbstractThis paper deals with numerical analysis of the reflection of electromagnetic waves from a conductive plate with periodic dielectric distribution. Analysis is based on the Fourier series expansion method (FEM) whereby (i) the EM fields in a periodic inhomogeneous medium are Fourier‐expanded and from this the propagation constant and modal function are found by an eigenvalue equation and (ii) the reflection coefficient is obtained from the boundary conditions between the inhomogeneous medium and free space. Previously, when the dielectric constant E(x) was Fourier‐expanded but the expansion coefficients did not converge absolutely, this method would be abandoned and another method would be sought. In this paper, even in this case, we show that the FEM is still effective. If ε(x) is expressed as ε(x) / ε0 = q(x)/r(x) and the expansion coefficient of q(x) and r(x) can be obtained analytically, it can be shown that there is no need for numerical integration. As a result, the applicability of the FEM for systematic numerical analyses of periodic and inhomogeneous media is greatly extended. Actual numerical analysis is applied to the cases of square, cubic and exponential distributions of the dielectric constant toward avoidance of reflections of the periodic, inhomogeneous layers of the medium. Also, this method may be applied to optical grating problems.