Microwave verification of a numerical optimization of fourier gratings

A recent holographic technique makes it possible to manufacture a new kind of grating, the “Fourier grating”, whose profile is given by a superposition of a fundamental and a finite number of harmonics. A local theoretical optimization shows that this type of grating can have an efficiency better, than that of the echelette, for a broad wavelength range. In this paper, we show the validity of this theoretical prediction by an experimental verification in the microwave region.     

Convergence of solutions to the rough-surface scattering problem

A new formulation of the rough-surface scattering problem is obtained that is closely linked to the Kirchhoff approximation. The governing equation is cast into a form amenable to solution by the method of successive approximations. The domain of convergence of this solution is established and is shown to apply also to the odd-ordered operator expansion, small-slope approximation and perturbation theory provided that the slope of the scattering surface is everywhere less than unity. The analysis is performed for scattering from one-dimensional pressure-release surfaces. Numerical examples are presented for sinusoidal and echelette gratings.     

Convergence of solutions to the rough-surface scattering problem

Abstract

A new formulation of the rough-surface scattering problem is obtained that is closely linked to the Kirchhoff approximation. The governing equation is cast into a form amenable to solution by the method of successive approximations. The domain of convergence of this solution is established and is shown to apply also to the odd-ordered operator expansion, small-slope approximation and perturbation theory provided that the slope of the scattering surface is everywhere less than unity. The analysis is performed for scattering from one-dimensional pressure-release surfaces. Numerical examples are presented for sinusoidal and echelette gratings.     

Principe d'un spectrometre a reseau a transmission constante

An unusual use of the echelette grating (incident wavevector is not perpendicular to the grooves) seems to allow the construction of a spectrometer (or monochromator) the high transmission of which does not depend on the wavelength.     

An iterative solution of the rough-surface scattering problem

Abstract

An iterative solution to the problem of scattering from a one-dimensional rough surface is obtained for the Dirichlet boundary condition. The advantages of this method are that bounds for convergence of the solution can be established and that the solution may readily be iterated to sufficiently high order in the interaction to examine the rate at which it converges. Absolute convergence of the iterative solution is also a sufficient condition for the convergence of the operator expansion method for surfaces on which the slope is everywhere less than unity. A numerical example of scattering from an echelette grating is considered, and bounds for convergence established. It is found that for scattering from such surfaces the rate at which the iterative solution converges decreases as the surface slope is increased. Corresponding results are found for the operator expansion method.     

Gyrotrons with echelette resonators

We consider gyrotrons with echelette resonators formed by diffraction gratings on the inner surface of a cone with the ribs perpendicular to the cone axis. The Q-factor of the operating cavity mode is controlled by the choice of grating parameters. Selective properties of the resonator are determined by the frequency dependence of the antireflection coefficient. Such resonators have a higher selectivity and more effective coupling with the output waveguide than cylindrical resonators, which allows gyrotron power to be increased. Echelette resonators can be used in gyrotrons at higher cyclotron harmonics owing to their higher selectivity without fear of exciting lower harmonics. Starting currents and efficiency of a gyrotron with an echelette resonator are found. Experimental studies of gyrotrons with echelette resonators confirmed the possibility to rarefy considerably the gyrotron oscillation spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, p. 691–698, June, 1996.This paper was supported in part by the International Science Foundation under Project No.R8Y300 (Theoretical and Experimental Study of Echelette-type Resonators for High-Power Gyrotrons) and the Russian Foundation for Fundamental Research under Grant No.93-02-15423.     

Atom diffraction from magnetic gratings in the thin phase-grating approximation

The problem of atom diffraction from a reflecting magnetic diffraction grating is solved in the thin phase-grating approximation. The general problem for scalar diffraction is modelled using a semi-classical method in which the grating potential is separated into a reflecting term and a diffracting term. The trajectory of the atom in the reflecting potential is solved classically and the atom wave function in the diffracting potential found by integrating the phase change along the classical trajectory. The diffraction orders are obtained after Fourier transforming the result. This can be done independently of the grating potential resulting in a general formula for the diffraction efficiencies. The general result is applied to the problem of atom diffraction from a magnetic grating. Several approximations are required to reduce the problem to a form amenable to analytic solution. The results are compared with an accurate numerical method. Received 1st February 2001 and Received in final form 8 March 2001     

基于遗传算法的不等间距阵优化方法*

阵元数一定情况下,针对不等间距拖线阵高频信号处理存在的空间增益和无栅瓣兼容问题,提出一种基于遗传算法的不等间距拖线阵阵型优化方法。该方法以频带交互下最大旁瓣级最小作为约束因子,通过模拟生物自然进化过程搜索全局最优解,得到优化后的阵元位置。优化后阵型在保证低频信号处理空间增益不变情况下,实现对高频信号高空间增益、无栅瓣处理。计算机仿真结果表明：相比未优化阵型,在高频信号处理方面,优化后阵型在无栅瓣情况下,空间增益提升值近似理论值提升值;在低频信号处理方面,优化后阵型具有相同的空间增益。为实际不等间距拖线阵阵型优化和应用提供了一种思路。     

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets. Received 13 June 2000 and Received in final form 15 December 2000     

Simple grating synthesis algorithm

Many authors (including this one) have suggested that the problem of synthesizing a grating from its reflection spectrum is significantly more difficult than the direct problem of obtaining the spectrum from the grating. Fortunately, this view is mistaken. One can synthesize a grating from any reflection spectrum by direct solution of the standard coupled-mode equations while simultaneously evaluating a simple integral to obtain the grating strength. This approach has the advantage of being based on a well-understood set of equations, making it amenable to physical interpretation, mathematical approximation, and generalization.     

High-frequency asymptotics of wave field diffracted by plane angular sector. I

The problem of plane-wave diffraction by an angular sector is examined. It is assumed that the wave process is described by the Helmholtz equation and that the Dirichlet or Neumann boundary conditions are satisfied on the sector. An exact solution of the problem is constructed in the form of a Sommerfeld integral, which is convenient for study of the problem in a high-frequency approximation.     

高频强场中Kramers-Henneberger变换在狄拉克方程中的应用

在强激光场中,通过Kramers-Henneberger(KH)变换和高频近似可以将狄拉克方程的求解从一个含时问题转换成一个稳态问题来研究。以氢原子为例,详细研究了相对论框架下该稳态问题中的有效库仑势的特点,并和非相对论框架下的结果进行了比较。研究发现,由于相对论有效质量的引入,有效库仑势的分布范围并不像非相对论条件下随着激光场强度的增强单调变大,而是增加到一定值后不再变化。另外,通过比较偶极近似和非偶极近似下有效库仑势的分布,发现对高频强场,偶极近似不再适用。     

Attenuated thick hologram gratings. Part I: Diffraction efficiency

In this paper volume hologram reconstruction is considered as an electromagnetic scattering problem that leads to a characteristic integral equation. Our main attempt is the calculation of diffraction efficiency for attenuated gratings, that is compared with those of unattenuated gratings, to point out the influence of grating attenuation. In this respect the solution in the first Born approximation is found to be sufficient for diffraction efficiency calculations of attenuated gratings.     

High-frequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach

The problem of diffraction of a high-frequency plane wave by a strip with ideal boundary conditions is considered for the case of oblique incidence. The study is based on the parabolic approximation, which is used to construct an expression for the directional pattern in terms of single quadratures. A similar result is obtained using the embedding formula. It is shown that the derived expression approximates the classical Michaeli result. A proof of the optical theorem for the parabolic problem is presented.     

On high-frequency scattering by a strip at nearly grazing incidence

The problem of diffraction by an absolutely soft segment is considered in the high-frequency approximation. The asymptotic field decomposition is obtained, which makes it possible to trace the transition from classical asymptotics valid for grazing incidence to geometrical optics asymptotics, which describes scattering at a finite (not small) angle.     

On the high-frequency limit of the second-order small-slope approximation

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.     

High-frequency modulation of light in diffraction by the Bragg grating with a refractive index traveling wave

The diffraction by a Bragg grating with high-frequency modulation of the refractive index of the medium is analyzed theoretically. The effect of the grating parameters and parameters of an rf signal on the efficiency of modulation of optical signals at frequencies above 10 GHz is investigated.     

On the high-frequency limit of the second-order small-slope approximation

Abstract

Small-slope approximation (SSA) is a scattering theory that is supposed to unify both the small-perturbation model and the Kirchhoff approximation (KA). We study and compute the second-order small-slope approximation (SSA2) in a high-frequency approximation (SSA2-hf) that makes it proportional to the first-order term, with a roughness-independent factor. For the 3D electromagnetic problem we show analytically that SSA2-hf actually meets KA in the case of perfectly conducting surfaces. This no longer holds in the dielectric case but we give numerical evidence that the two methods remain extremely close to each other for moderate scattering angles. We discuss the potential applications of SSA2-hf and give some 2D numerical comparison with rigorous computations.     

Image aberrations in an acousto-optical tunable filter

The problem of deformation of images due to diffraction from 3D diffraction gratings (in particular, the grating formed by an acoustic wave in an acousto-optical filter) is considered. For the first time, the exact solution is obtained without using the small birefringence approximation. The form of aberrations induced by main types of acousto-optical filters is analyzed and illustrated by calculations.