Multilayer Approximation Method Research Articles

Analysis of Electromagnetic Fields in Inhomogeneous Media by Fourier Series Expansion Methods--The Case of a Dielectric Constant Mixed a Positive and Negative Regions--

In this paper, we propose a new method for the electromagnetic fields with inhomogeneous media mixed a positive and negative regions by the combination of improved Fourier series expansion method using the extrapolation method which obtains the correct value of the eigenvalue and eigenvectors for the case of TM wave. Numerical results are given for the power reflection and transmission coefficient, the energy absorption, the electromagnetic fields, and the power flow in the inhomogeneous medium mixed the positive and negative regions including the case when the permittivity profiles touches zero for the TM wave. The results of our method are in good agreement with exact solution which is obtained the modified multilayer approximation method.

Evaluation method of small anechoic chamber by site attenuation distribution using spherical dipole antenna

AbstractSite attenuation has been evaluated by means of a half‐wave dipole antenna. Since this antenna type requires a size on the order of a half wavelength, it is not suitable for evaluation of small anechoic chambers. In this paper, a method of evaluation of small anechoic chambers using a spherical dipole antenna with a diameter of 15 cm is discussed. First, the spherical dipole antenna is modeled by wire grids and the site attenuation and antenna factor are derived. It is found that in the range of 30 MHz through 1000 MHz the discrepancy between the analytical values and the measured values of the site attenuation is less than ±4 dB, while that of the antenna factor is less than ±2 dB. Next, the site attenuation taking account of the reflection characteristics of the anechoic chamber is analyzed by the ray tracing method. As parameters, the antenna factor and the radiation pattern derived from the wire grid model are used for the antenna characteristics, and the reflection coefficient derived from the multilayer plane approximation method is used for the reflection characteristics of the absorber. It is found that the discrepancy between the analytical values and the measured values for the site attenuation distribution at a frequency of 600 MHz is less than ±3 dB, and the ray tracing method is found useful for the analysis of the site attenuation distribution using a spherical dipole antenna. Further, when the new approach is applied to a small anechoic chamber in which absorbers with different characteristics are included, the present method is found effective for evaluation of the areas with good properties and of the effect of the absorbers. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 89(1): 1–10, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20255

On a linear theory of an FEL amplifier with an axisymmetric electron beam

The paper touches upon the questions of the linear theory of an FEL amplifier with an axisymmetric electron beam. An FEL model is discussed wherein diffraction effects, space charge fields and energy spread of electrons in the beam are taken into account. The rigorous solutions of the eigenvalue problem have been found for the stepped and bounded parabolic electron beam profiles. The multilayer approximation method has been used to solve the eigenvalue problem for the beams with an arbitrary gradient profile of current density. For the stepped electron beam profile the initial problem is solved analytically with the Laplace transform technique and in the case of the arbitrary gradient profile with the numerical solution of the self-consistent field equations. The optimum conditions of the external radiation field focusing on the electron beam have been obtained.

Mode theory of FEL oscillator with the open plane Fabry-Perot resonator, helical undulator and axisymmetric electron beam

This paper presents an analytic method of finding the eigenvalue problem solution for the FEL oscillator with the open plane Fabry-Perot resonator. The method is based on the self-consistent solution of Maxwell's equations and the kinetic equation. To take into account diffraction effects we apply the impedance boundary conditions of resonance type at the open resonator ends. As an example of using the general approach we consider the systems with axial symmetry. The rigorous solution of the eigenvalue problem is found for the case when the electron beam has a bounded parabolic profile. The multilayer approximation method is used when the electron beam has an arbitrary gradient profile.

Quasi-optical theory of FEL amplifier with planar waveguide

The analytical results of the FEL amplifier theory in the framework of the “sheet electron beam-planar waveguide-planar undulator” model are presented. Rigorous solutions of the eigenvalue problem for the sheet homogeneous electron beam and the sheet electron beam with the bounded parabolic profile are obtained. Transcendental eigenvalue equations are investigated, and distributions of field amplitude of active waveguide modes have been found. The asymptotic behavior of the rigorous solutions is studied. A multilayer approximation method is proposed to solve the eigenvalue problem when the electron beam has an arbitrary gradient profile. The numerical results are compared with the analytical rigorous solutions for the beam with the bounded parabolic profile.

Mode theory of plane Fabry-Pérot resonator with inhomogeneous active medium

A new method of the eigenvalue problem solution for a resonator with inhomogeneous active medium is given. The approach is based on Maxwell's wave equation and impedance boundary conditions of resonance-type at open resonator ends. A resonator equipped with mirrors in the form of infinite long strips is studied as an example. A rigorous solutions for the cases of stepped and bounded parabolic active medium profiles are obtained. Transcendental eigenvalue equations are investigated, distributions of field amplitude of active resonator modes are found. Asymptotic behavior of rigorous solutions is investigated. A multilayer approximation method is proposed for the eigenvalue problem solution for a resonator with an arbitrary gradient profile of active medium. The testing of this method was carried out with the rigorous solutions for the bounded parabolic profile.

Mode theory of FEL amplifier with gradient profile of electron beam

The paper touches upon the analytical treatment of a FEL amplifier with the gradient profile of an electron beam. An exact solution of the eigenvalue problem for an electron beam with Epstein profile is found. The dispersion relation is derived and the dependence of its roots on the problem parameters is analyzed. The distributions of the mode fields are found, the asymptotic behavior of the exact solutions is investigated. A multilayer approximation method of the eigenvalue problem solution is proposed for the electron beams with an arbitrary gradient profile when one fails to find the exact solutions in terms of the known functions. Testing of this method was carried out with exact solutions for a beam with Epstein profile. As an example of an application, the multilayer approximation method is used for the eigenvalue problem investigation in the case of an electron beam with gaussian profile.

Numerical analysis of planar arbitrarily anisotropic diffused optical waveguides using finite-element method

The finite-element method for light propagation in planar anisotropic diffused optical waveguides with arbitrary permittivity tensor is presented. The validity of the method is confirmed by comparing numerical results with the results of the well known multilayer-approximation method.

Compensation of Intermodal Dispersion by Splicing Two Graded-Index Multimode Fibers

The deviations from the group delays expected for the optimum power-law index profile are numerically calculated for several types of undesired fibers using a scalar multilayer approximation method. This paper shows the way two fibers are selected from among undesired fibers so that the fiber spliced to each other becomes broad band.

Some comments on the analysis of electromagnetic fields in inhomogeneous media

AbstractAmong the principal approaches to electromagnetic field analysis in an homogeneous medium are numerical methods. The homogeneous multilayer approximation used in numerical methods is invalid when there is wave equation singularity. This paper demonstrates that the finite difference method is equivalent to the homogeneous multilayer approximation methods when the number of subdivision is increased; further, it is shown that finite difference methods also can be invalid. To analyze electromagnetic fields in the medium for which the wave equation contains a singularity, we propose here an inhomogeneous multilayer approximation method (a piecewise linear approximation) based on the power series solutions. A technique is presented for improving the homogeneous multilayer approximation method and the finite difference method by using the results of piecewise linear approximations. We further propose a modified multilayer approximation method by combining advantages of various methods. The principal features of the modified multilayer approximation method are as follows: 1) Calculations are possible even when the wave equation has several singularities; 2) the method is applicable to the structure with arbitrary medium profile; 3) the solution near the singularities can be obtained relatively easily; 4) a desired degree of accuracy can be obtained by increasing the number of subsections; and 5) no extensive mathematical background is required.The modified multilayer approximation method is used to analyze the reflection of a plane wave from an inhomogeneous plasma slab. Presented in graphical manner are the power reflection coefficient, the energy absorption, the electromagnetic field distribution inside the slab and the power flow.

Numerical Analysis of Pulse Broadening in Graded Index Optical Fibers

A scalar multilayer approximation method for calculating the impulse response of multimode optical fibers from measured refractive-index profiles is described. A comparison is made between shapes of measured pulses and calculated pulses.

Reflection of electromagnetic waves by a multistream plasma slab and some comments on the multilayer approximation method

Reflection of electromagnetic waves by a multistream plasma slab and some comments on the multilayer approximation method