Modified geometric optics: Accounting for exponentially small scattered fields

We propose a modified geometrical-optics approximation (MGO). It is based on the solution of the Helmholtz equation in the form of a series in which the main term describes the zero-order geometrical-optics approximation. The proposed method allows one to take into account an exponentially small backscattering in smoothly inhomogeneous media and thus improves the geometrical-optics approximation. In the case of forward scattering, the solution obtained is reduced to the conventional geometrical-optics series over negative powers of the wavenumber. We estimate the backscattering using the perturbation technique for rays and determine the conditions under which the backscattered field agrees with the Born approximation of scattering theory. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 2, pp. 106–114, January 2000.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the 'wings' of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

Abstract

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the ‘wings’ of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method. Based on the plane-wave angular spectrum expansion and Fresnel approximation, the analytical expressions of the reflected field, internal field as well as transmitted field in each region are obtained. Through numerical simulations, the intensity distributions of the incident beam, reflected beam, internal beam as well as transmitted beam are presented at oblique incidence. Besides, we also compare the intensity distributions of the geometrical-optics beam field, the first order beam mode field and the actual beam field, which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab. Meanwhile, the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated. Finally, the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail. The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.     

Fast transient capacitance measurements for implanted deep levels in silicon

The present diffraction problem is solved by means of a perturbation calculus in the transition conditions and by repeated application of the method of steepest descent to two-dimensional Fourier integrals. We obtain a reflection coefficient for the rough surface resulting in a geometrical-optics approximation for the space wave field strength. In the case of a periodic roughness profile the application of the method of steepest descent in the transform space can be avoided and we get the electromagnetic field through differentiation of the Bromwich potentials. The numerical results of the two methods are discussed in the case of a one-dimensional cosine profile. We show that the influence of the earth's roughness increases with increasing receiver heights and fixed receiver distance. On the other hand, we point out that the geometric optical approach is a rather good approximation for the space wave field strength.     

Laser ray tracing and power deposition on an unstructured three-dimensional grid

A scheme is presented for laser beam evolution and power deposition on three-dimensional unstructured grids composed of hexahedra, prisms, pyramids, and tetrahedra. The geometrical-optics approximation to the electromagnetic wave equation is used to follow propagation of a collection of discrete rays used to represent the beam(s). Ray trajectory equations are integrated using a method that is second order in time, exact for a constant electron-density gradient, and capable of dealing with density discontinuities that arise in certain hydrodynamics formulations. Power deposition by inverse-bremsstrahlung is modeled with a scheme based on Gaussian quadrature to accommodate a deposition rate whose spatial variation is highly nonuniform. Comparisons with analytic results are given for a density ramp in three dimensions, and a "quadratic-well" density trough in two dimensions.     

Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method

Normal incidence of a plane electromagnetic wave on a periodical structure can be simulated by the finite-difference time-domain method using a single unit cell with periodical boundary conditions imposed on its borders. For the oblique wave incidence, the boundary conditions would contain time delays and thus are difficult to implement in the time-domain method. We propose a method of oblique incidence simulation, based on an iterative algorithm. The accuracy of this method is demonstrated by comparing it with the layer Korringa-Kohn-Rostoker frequency-domain method for calculation of transmission spectra of a monolayered photonic crystal.     

Influence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface

This paper is concerned with the backscattering of HF radio waves from the rough sea surface, which have propagated through the ionosphere with random large-scale irregularities.

For the sake of simplicity, it is assumed in calculations that the rough sea surface is a perfectly conducting surface with the known Philips power spectrum of irregularities. Ionospheric irregularities of a random medium that are isotropic and single-scale ones, with a Gaussian spectrum, are considered within the limits of the hypothesis of frozen-in irregularities.

Within the first approximation of perturbation theory, using, as the incident wave and the Green function, their geometrical-optics approximations, we obtained the expression for the backscattering spectrum of the ionospheric chirp radio signal with a Gaussian envelope. The expression involves the parameters of the receive-transmit antenna, the signal, the propagation medium, and of the scattering surface. Numerical simulation was used to investigate the influence of all the above-mentioned parameters on the backscattering spectrum. It is shown that travel of ionospheric irregularities has the largest influence on the scattering spectrum, the signal parameters mainly determine the size of the scattering area in the range, and the form of the coherent integration window determines the form of the received signal and can distort it.     

Influence of ionospheric irregularities on the form of radio signal scattering spectrum in over-the-horizon radar sounding of the rough sea surface

Abstract

This paper is concerned with the backscattering of HF radio waves from the rough sea surface, which have propagated through the ionosphere with random large-scale irregularities.

For the sake of simplicity, it is assumed in calculations that the rough sea surface is a perfectly conducting surface with the known Philips power spectrum of irregularities. Ionospheric irregularities of a random medium that are isotropic and single-scale ones, with a Gaussian spectrum, are considered within the limits of the hypothesis of frozen-in irregularities.

Within the first approximation of perturbation theory, using, as the incident wave and the Green function, their geometrical-optics approximations, we obtained the expression for the backscattering spectrum of the ionospheric chirp radio signal with a Gaussian envelope. The expression involves the parameters of the receive–transmit antenna, the signal, the propagation medium, and of the scattering surface. Numerical simulation was used to investigate the influence of all the above-mentioned parameters on the backscattering spectrum. It is shown that travel of ionospheric irregularities has the largest influence on the scattering spectrum, the signal parameters mainly determine the size of the scattering area in the range, and the form of the coherent integration window determines the form of the received signal and can distort it.     

Geometrical optics of lightguides with an oblique input end-face

The geometrical-optics relations between meridional rays of incidence and maximum aperture have been derived for the general case of a lightguide with an oblique input end-face. It is shown that the maximum angles of incidence are asymmetrical with respect to both the axis of the lightguide and the normal to the input end-face. A numerical comparison shows that for a light-guide with an oblique input end-face, in the meridional ray case, a greater or smaller angle of aperture may result, depending on the cutting angle, compared with that for a lightguide input end-face perpendicular to the optical axis. A greater angle of aperture is especially important since it means an improvement in the launching efficiency of incoherent light sources. Moreover, the maximum angle of aperture has been derived for the generalized light guide in which successive total internal reflections at the cladding/surroundings interface have been taken into account.     

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.     

A comparison of the results of a numerical simulation and an approximate calculation of the statistical characteristics of radio waves in a layer with random inhomogeneities of dielectric permittivity

We consider the formation algorithm for a random inhomogeneity field of dielectric permittivity of a medium that is used in simulations of the statistical characteristics of a wave that has propagated through a randomly inhomogeneous layer. We carry out a comparison of the statistical characteristics of a geometrical-optics wave, obtained via a numerical simulation, with the results of calculations of these characteristics by approximate formulae obtained using perturbation theory. It is pointed out that the applicability limits of the perturbation method, when solving geometrical-optics equations in a randomly inhomogeneous medium, depend on the formulation (one- or two-point) of the trajectory problem. It is shown that a calculation of the spatial correlation function of the field can be carried out using the perturbation method, even in the case of relatively strong fluctuations of dielectric permittivity. This is due to the fact that, in the region where this function differs markedly from zero, the correlation function of the eikonal obtained by the perturbation method is sufficiently accurate, and amplitude fluctuations are small.     

大角度斜入射情况下的猫眼效应激光反射特性

基于角谱衍射理论,采用2维离散傅里叶变换和将双衍射孔径进行投影合并的方法,推导了斜入射情况下猫眼效应反射光的衍射传输过程,通过数值计算分析了入射角和衍射距离对衍射光场分布的影响规律,并实验验证了入射角的影响规律。结果表明,这种方法能够准确描述大角度入射时的反射光衍射光场分布,入射角对其衍射光场分布模式的影响相当于增大了衍射距离。依据入射角与衍射光场分布模式之间的对应关系,可对猫眼目标进行参数识别研究。     

High-frequency field intensity along focal point of a long metallic parabolic reflector coated by a magnetized plasma layer using oblique incidence

Theoretical analysis of the electromagnetic field distribution in the focal region of a long metallic parabolic reflector that has its surface covered with a magnetized plasma layer is derived. The incident wave is considered to be with a general oblique incidence for both parallel and perpendicular polarizations. The electromagnetic field intensity expressions along the focal region are obtained accurately using Maslov's method. The effects of plasma thickness on the reflected and transmitted field distributions are investigated. The effects of other physical parameters such as the angle of incidence and the plasma and cyclotron frequencies on the transmitted fieldintensity distribution along the focal region are also studied. The results obtained by Maslov's method and Kirchhoff's approximation are found to be in a good agreement.     

Effects of barrier penetration on energy spectrum and wave functions in the path integral formalism

We present a systematic approximation scheme for the non-relativistic Green function in the path integral representation which takes into account barrier penetration effects on the energy spectrum and wave functions for potentials having several minima. The method is applied to the cases of a symmetric potential with two minima and to a periodic potential. The energy spectrum is shown to agree with the usual WKB results. For the first mentioned case we also determine the wave functions in the classically allowed and forbidden regions from the residues of the Green function. They agree with those obtained in the standard WKB approximation.     

Frequency upshifting of electromagnetic radiation via obliqueincidence on an ionization front

Frequency upshifting of electromagnetic radiation impinging on a relativistically moving ionization front is theoretically investigated. Unlike previous works in this field treating the case of normal incidence and qualitatively similar case of oblique incidence of a transverse electric polarized wave, oblique incidence of a transverse magnetic polarized wave on the front is considered. The peculiarities of the case under consideration are connected with the generation of Langmuir waves behind the front and Brewster's phenomenon. We present a complete analysis of the incident wave transformation including analysis of the frequencies and amplitudes of the waves excited ahead of and behind the front. Special emphasis is made on energy transformation in the case when a wave packet is incident on the front. In particular, we show that even for negligible angles of incidence, energy losses via transformation into Langmuir waves may be very high (up to ~60%). In general, generation of Langmuir waves may play a significant role in the plasma-based radiation sources with relativistic ionization fronts     

Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits

We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution.     

Determination of embedded layer properties using adaptive time-frequency domain analysis

A general model for determination of the complete set of acoustical and geometrical properties of an isotropic layer embedded between isotropic or anisotropic multilayered solids is developed. These properties include density, longitudinal and shear elastic moduli, layer thickness, and loss factors, simultaneously determined from two measurements, one at normal and one at oblique incidence. The inversion model is an extension of the method proposed by Lavrentyev and Rokhlin [J. Acoust. Soc. Am. 102, 3467 (1997)] which is applicable to thick substrates. In this new method, the inversion model mimics an experiment by using the same time-domain gating of the signal reflected from the embedded layer. This allows application of this method to layered solids when reflections from different layers overlap in the time domain. The sensitivity of the method, its stability against data scatter, and the effect of the oblique incident angle are evaluated. The effect of plane-wave approximation versus beam approximation in the inverse algorithm is discussed. Experimental results are given to demonstrate examples of adhesive layer property reconstruction.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Numerical implementation of complex geometrical optics

We propose a numerical scheme for calculation of the wave field, based on the geometrical-optics method generalized for complex values. The main advantage of the complex-value method is a possibility to take into account diffraction effects using only the ordinary differential equations of the geometrical optics. This allows one to significantly reduce the amount of computations and, hence, computation time. The efficiency of this algorithm is illustrated by two numerical examples that allow comparison with the known analytical solutions: the plane-wave field behind the caustic in the linearly inhomogeneous layer and the field of a Gaussian beam in a homogeneous medium. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 630–637, July, 2000.