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.     

Ultrasonic wave interaction with multidirectional composites: modeling and experiment

Phenomena of wave transmission through a multidirectional composite laminate immersed in a fluid have been investigated. Based on a recently-developed recursive stiffness matrix method time-domain beam models have been developed to simulate the problem. Experimental and theoretical results at frequency 2.25 MHz show that the transmission amplitude is highly dependent on lamina orientation and angle of incidence. Large transmission amplitude appears at small (<10 degrees) and large incident angles (45 degrees-60 degrees). At intermediate incident angles (16 degrees-40 degrees) the transmission amplitude is almost zero. At high frequency, the residue epoxy layers between each lamina become important and corresponding resonances may be observed. These transmission phenomena have been interpreted in terms of Floquet waves. It shows that the pass and stop bands of the three Floquet waves obtained from the unit cell stiffness matrix determine the transmission amplitude distribution in frequency, incident angle and rotation angle domains. The effect of random deviation of the laminated structure periodicity has also been assessed. At normal incidence, the variation of the thickness of the epoxy residual layer between composite lamina has little effect on the overall stop and pass band structures but introduces random reverberation and scattering in the pass bands. It is shown that for oblique incidence the transmittivity spectrum of a composite with random lamina lay-up converges with increase of randomness to that of a [0/-45/90/45]2s quasi-isotropic composite. Randomization of lamina lay-up produces a small effect in the transmittivity spectrum for a quasi-isotropic composite.     

Wave propagation in a random medium: The solution of the m-nth moment equation with different wavenumbers

The moment equation with different wavenumbers and different transverse coordinates for wave propagation in a random medium is a linear differential equation. It often appears in the study of problems related to wave propagation in a random medium. The differential equation can be converted into an integral equation by using Green's functions and the integral equation can be solved by iteration. The moment equation is solved by the method of successive scatters, too. The solution of the moment equation is a Dyson expansion. The physical implication of the successive solution of the moment equation with different wavenumbers is explained.     

Scattering of an electromagnetic wave from a slightly random dielectric surface: Yoneda peak and Brewster angle in incoherent scattering

Abstract

The scattering of an electromagnetic wave from a two-dimensional, slightly rough dielectric surface is studied based on the stochastic functional approach. It is shown that in the case of TM(p)-polarized incidence there exists a zero in the incoherent scattering at the angle we call the ‘Brewster scattering angle’, which depends on the incident angle in contrast to the Brewster angle of coherent reflection which is independent of the incident angle, that a ‘quasi-anomalous scattering’ can generally occur in the optically denser medium at the critical angle of total reflection in both TE(s)- and TM(p)-polarized incidence, regardless of which side of the random surface is illuminated, and that the Yoneda peak in the x-ray scattering can be interpreted as a special case of the quasi-anomalous scattering which becomes sharper when the relative refractive index becomes closer to unity as in the x-ray region. Cross-polarized scattering and enhanced backscattering due to the second-order effect are also calculated.     

Transport of broadband arbitrary radiation through a bleaching medium

A novel analytical treatment of the transport of broadband radiation arbitrarily directed through a bleaching medium is presented. The emphasis is on the principle features of photodecomposition (bleaching) wave formation. Considering radiation from a uniform planar source with stable radiative characteristics and media with a uniform initial distribution of the absorptive component, we show that this problem has an asymptotic stationary solution for a wave propagating through a medium characterized by a photodecomposition spectrum without any portion in which the absorption cross section continually runs down to zero.     

Coherent inelastic electron reflection from a random medium with a sharp boundary

The weak localization of electrons inelastically scattered in a random medium with a sharp boundary is considered. An inelastic electron collision is accompanied by the excitation of a single bulk plasmon. The coherence of electron scattering results from the interference of electron waves related to two possible realizations of the process in which an electron excites a bulk plasmon and undergoes high-angle elastic scattering by chaotically arranged force centers. The sharpness of the boundary means that the statistically averaged length scale and depth of the surface mocroroughnesses are much smaller than the decay length of the wave field of fast electrons in the medium. The same condition is also imposed on the tail size of the electron density of the medium in vacuum. The theory developed makes it possible to determine the bulk-plasmon generation intensity by measuring the ratio of the electron fluxes inelastically and elastically reflected from the surface of a random medium. For this purpose, one should find the dependence of the ratio of these fluxes on three angles, namely, the polar angle of incidence of electrons, the polar angle of electron exit from the medium, and the azimuth angle between the projections of the velocities of the incident (v) and escaping (v′) electrons on the surface plane. Optimum conditions for the detection of this specific azimuth dependence are theoretically grounded for the case where both electron collisions occur in the near-surface region.     

二维随机介质中柱面波传播及其局域性的随机泛函分析

分析了二维各向同性均匀随机介质中柱面波的传播特性及局域化现象.用随机泛函理论,在频域内将随机介电起伏展开成柱坐标系下的Wiener积分式,将波场表示为内外行柱面波的线性和,求解二维Helmholtz波动方程,得到随机介电起伏对柱面波幅度与相位调制的解析表达.由柱面波能量的空间分布验证了波的局域化现象,并求解局域化长度.二维随机介质中平面波按柱面波展开的波转换方程与非随机介质中的情形有相似的表达,但具有随机介电起伏对幅度和相位的调制,并给出数值模拟结果.     

Stochastic functional analysis of propagation and localisation of cylindrical waves in a two-dimensional random medium

Propagation and localisation of cylindrical waves in a two-dimensional (2D) isotropic and homogeneous random medium is studied using the stochastic functional approach. By expanding the random permittivity fluctuation in the form of a Wiener integral equation, and representing the wave fields by a linear combination of outgoing and incoming waves, the scalar Helmholtz equation is solved in the cylindrical coordinates system. An analytical expression of the cylindrical wave is derived and demonstrates the localisation phenomenon, as well as the wavenumber fluctuation in the random medium. Comparing with the waves in non-random medium, the wave transfer equation between plane wave and cylindrical wave in random medium shows an additional exponential factor to indicate the modulation effect owing to the medium randomness in both the amplitude and phase. Numerical simulations are presented to illustrate the functional dependence of the localisation phenomena.     

正常金属d_(x~2-y~2)+id_(xy)混合波超导结中的隧道谱

在Blonder-Tinkham-Klapwijk散射理论框架下,通过求解Bogoliubov-deGennes方程,计算正常金属dx2-y2+idxy混合波超导结中的准粒子输运系数和隧道谱。研究表明:隧道谱中的电导峰位置强烈地依赖电子的入射角、超导的晶轴方位和dxy波分量的强度。     

Oblique incidence properties of locally resonant sonic materials with resonance and Bragg scattering effects

A locally resonant sonic material (LRSM) is an elastic matrix containing a periodic arrangement of identical local resonators (LRs), which can reflect strongly near their natural frequencies, where the wavelength in the matrix is still much larger than the structural periodicity. Due to the periodic arrangement, an LRSM can also display a Bragg scattering effect, which is a characteristic of phononic crystals. A specific LRSM which possesses both local resonance and Bragg scattering effects is presented. Via the layered-multiple-scattering theory, the complex band structure and the transmittance of such LRSM are discussed in detail. Through the analysis of the refraction behavior at the boundary of the composite, we find that the transmittance performance of an LRSM for oblique incidence depends on the refraction of its boundary and the transmission behaviors of different wave modes inside the composite. As a result, it is better to use some low-speed materials (compared with the speed of waves in surrounding medium) as the LRSM matrix for designing sound blocking materials in underwater applications, since their acoustic properties are more robust to the incident angle. Finally, a gap-coupled LRSM with a broad sub-wavelength transmission gap is studied, whose acoustic performance is insensitive to the angle of incidence.     

Spectra of discontinuous noise waves

The article considers the problem of the transformation of the energy spectrum of an intense random wave in a nonlinear, nondisperse medium. It is assumed that at the inlet to the nonlinear medium there is given a random quasimonochromatic wave, and an investigation is made of the spectrum of a nonlinear wave at distances where the original continuous wave goes over into a sequence of sawtooth pulses with a random position of the discontinuity and with random amplitudes. In the work, an investigation was made of the dependence of the spectral characteristics of discontinuous noise waves on the statistics of the amplitude and phase of the input quasimonochromatic wave. The form of the spectrum of the wave is found at low frequencies, which appear due to the effect of the autodetection of the quasimonochromatic wave in a nonlinear medium. The effect of the viscosity of the medium on the form of the energy spectrum is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1627–1636, November, 1978.The authors are indebted to A. N. Malakhov and A. I. Saichev for their valuable evaluations.     

Freak waves in random oceanic sea states.

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schr?dinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

折射率梯度表面机理的研究

本文构建了一种折射率梯度表面,并利用几何光学法对其物理机理作了研究,发现这种折射率梯度表面可以实现入射波到正常反射波,异常反射波,以及介质波的转换.当入射点介质折射率大于某一阈值时,异常反射波束方向角正弦值与入射波束方向角正弦值存在线性关系,意味着平行入射的波经介质后将平行出射到空气;而当折射率梯度常数大于某一阈值时,任何方向入射的波在透射到介质后,将发生全反射,被束缚在介质中.总而言之,通过调节结构参数,可以实现对波束方向与强度的人工调控,从而提供了一种人工可控的全介质梯度表面的工程实现思路.     

Path integrals for wave intensity fluctuations in random media

Approximate expressions for the fourth order moment of a wave propagating in a random medium are derived by using the path integral formulation. These solutions allow the spectrum of intensity fluctuations of a multiply scattered wave to be found, and they are valid at all distances in the medium. The results obtained by path integral methods turn out to be the same as those obtained previously by solving the parabolic partial differential equation for the fourth moment. The spatial frequency spectra of intensity fluctuations are evaluated for a medium in which the irregularities have a single scale and also for one in which there is a range of scale sizes.     

Vector solitary optical beam control with mixed type I–type II second-harmonic generation

The four vector equations, appropriate to a mixed type I–type II second-harmonic generation, in a thin planar waveguide, made from a second-order non-linear material, are solved, both approximately and exactly. The solutions are then used to generate possible applications. In this investigation, both the fundamental and the second-harmonic waves have two transverse field components. It is shown that, by controlling the ratio of the components of the fundamental wave, one component of the second-harmonic wave can be rigorously controlled, and even switched off. The ratio of the harmonic field components depends strongly upon the polarization angle of the fundamental wave, with the extinction angle depending strongly upon the phase mismatch parameter. In a second application, an aperture is placed at the output and it is shown that if approximate stationary states are used as an input to a quadratically non-linear medium, then varying the angle of incidence of two input beams produces an excellent output control. A numerical demonstration is given in which a switch from 80% of the input energy arriving at the output port to less than 3% is readily achievable.     

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

Abstract

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.     

Parametric Doppler effect in the case of oblique incidence in a medium with a plasma dispersion law

The parametric Doppler effect that occurs upon reflection of a plane monochromatic wave obliquely incident on an inhomogeneity of the refractive index moving in a medium with a frequency dispersion (homogeneous wave regimes) is analyzed. For a plasma-type frequency dispersion, the dependences of the frequency and angle of reflection on the frequency of the incident wave and on the angle of incidence are found.     

Quantization of electromagnetic field in quadratic continuous nonlinear absorptive dielectrics

This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.     

基于组合Wollaston棱镜成像光谱仪的视场扩大原理分析

论述了视场扩大型成像光谱仪的核心部件——组合Wollaston棱镜的结构和分光机理;应用波法线追迹法分析了光在任意方位入射面内,以任意角入射时组合Wollaston棱镜中的波矢传播规律;推导出了光在棱镜中的传播方向及出射点坐标;给出了传播过程中e光和o光之间光程差的理论表达式;采用计算机模拟,给出了光程差随入射角和入射面方位角的变化曲线;在此基础上对组合Wollaston棱镜扩大光谱仪视场的原理进行了深入分析和讨论.上述研究对偏振干涉成像光谱技术的理论研究与技术创新,对自行设计的稳态大视场偏振干涉成像光谱 关键词： Wollaston棱镜 偏振干涉成像光谱仪 波法线追迹法 视场扩大原理