Backscattering of electromagnetic waves by large-scale inhomogeneities in a periodically inhomogeneous medium

It is shown that backscattering of electromagnetic waves is possible in a periodically inhomogeneous medium by random inhomogeneities whose scale is greater than the wavelength. A small scattered field emerges in the case of appearance of the Bragg cavity when the periodic layer is a matching system for the incident wave. Scattering is effective even for inhomogeneities whose scale is much greater than the Fresnel radius of the inhomogeneous layer. The correlation radius of the scattered field can also be that large. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1230–1240, October, 1997.     

Scattering of a plane wave from a periodic random surface: a probabilistic approach

This paper deals with a probabilistic formulation of the wave scattering from a periodic random surface. When a plane wave is incident on a random surface described by a periodic stationary stochastic process, it is shown by a group-theoretic consideration that the scattered wave may have a stochastic Floquet form, i.e. a product of a periodic stationary random function and an exponential phase factor. Such a periodic stationary random function is then written by a harmonic series representation similar to a Fourier series, where Fourier coefficients are mutually correlated stationary processes instead of constants. The mutually correlated stationary processes are represented by Wiener - Hermite functional series with unknown coefficient functions called Wiener kernels. In case of a slightly rough surface and TE wave incidence, low-order Wiener kernels are determined from the boundary condition. Several statistical properties of the scattering are calculated and illustrated in figures.     

Lowering of the threshold of nonlinear wave interaction in plasma with periodic inhomogeneities

We show that an absolute instability corresponding to the induced double Mandelshtam-Brillouin scattering develops at smaller amplitude of the incident wave if periodic inhomogeneities exist in the plasma. The lowering of the instability threshold is related to the increase of the wave amplitudes in the Bragg resonator that is formed in the medium with periodic inhomogeneities. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 7, pp. 704–708, July 1999.     

Light scattering from a magnetically tunable dense random medium with dissipation: ferrofluid

We present a semi-phenomenological treatment of light transmission through and its reflection from a ferrofluid which we regard as a magnetically tunable system of dense random dielectric scatterers with dissipation. Partial spatial ordering is introduced by the application of a transverse magnetic field that superimposes a periodic modulation on the dielectric randomness. This causes Bragg scattering that effectively enhances the scattering due to the disorder alone, and thus reduces the elastic mean free path towards Anderson localization. A theoretical treatment, based on invariant imbedding, gives a simultaneous decrease of the transmission and the reflection without change of incident linear polarisation as the spatial order is tuned magnetically to the Bragg condition, namely the light wave vector being equal to half the Bragg vector (Q). Our experimental observations are in qualitative agreement with these results. We have also given expressions for the transit (sojourn) time of the light, and for the light energy stored in the random medium under a steady illumination. The ferrofluid thus provides an interesting physical realization of effectively a “Lossy Anderson-Bragg” (LAB) cavity with which to study the effect of interplay of the spatial disorder, partial order and the dissipation on light transport. Given current interests in the light propagation, optical limiting and the storage of light in ferrofluids, the present work seems topical.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Spatial modal control of two-dimensional photonic crystal Bragg lasers

We investigate the modal losses and field distributions of different order transverse modes supported by the photonic crystal Bragg structure using a transfer matrix method. We find that only the fundamental transverse mode has a single-lobed near field and far field and there exists a trade-off between ensuring lasing in the fundamental transverse mode and reducing the threshold. Employing these design principles, we experimentally demonstrate a large-area, edge-emitting, and single-mode semiconductor photonic crystal Bragg laser with a single-lobed, diffraction-limited far field under continuous wave condition.     

Radiative Transport in a Periodic Structure

We derive radiative transport equations for solutions of a Schrödinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, and the scattering part by the random fluctuations.     

Multiple focused-waves production by parametric mixing in a layer with hysteretic quadratic nonlinearity

Nonlinear scattering of a weak probe wave by a strong pump wave in a layer with nonlinearity hysteresis is analysed. It is demonstrated that a spherical probe wave from a point source after nonlinear process of difference frequency excitation is scattered in several foci. Different foci correspond to different frequencies of the transformed wave spectrum. In the case of a plane pump wave and under the condition that nonlinear scattering proceeds without acoustic mode conversion wave front reversal is possible. To achieve wave front reversal in a layer with hysteretic quadratic nonlinearity the pump wave should have a frequency equal to the frequency of the probe wave or to any of its subharmonics.     

Diffraction and scattering of TM plane waves from a binary periodic random surface

This paper deals with the diffraction and scattering of a TM plane wave from a binary periodic random surface generated by a stationary binary sequence using the stochastic functional approach. The scattered wave is represented by a product of an exponential phase factor and a periodic stationary process. Such a periodic stationary process is regarded as a stochastic functional of the binary sequence and is expressed by an orthogonal binary functional expansion with band-limited binary kernels. Then, hierarchical equations for the binary kernels are derived from the boundary condition without approximation. We point out that binary kernels obtained by a single scattering approximation diverge unphysically when the periodic random surface is zero on average, thus the effects of multiple scattering should be taken into account. The expressions of such binary kernels are obtained using the multiply renormalizing approximation. Then, statistical properties such as differential scattering cross-section and the optical theorem are numerically calculated with the first two order binary kernels and illustrated in the figures. It is found that the incoherent Wood's anomaly appears in the angular distribution of scattering even when the surface has zero average.     

Continuous‐wave vertically emitting photonic crystal terahertz laser

Compact semiconductor light sources with high performance continuous‐wave (CW) and single mode operation are highly demanded for many applications in the terahertz (THz) frequency range. Distributed feedback (DFB) and photonic crystal (PhC) quantum cascade (QC) lasers are amongst the leading candidates in this field. Absorbing boundary condition is a commonly used method to control the optical performance of a laser in double‐metal confinement. However, this approach increases the total loss in the device and results in a large threshold current density, limiting the CW maximum output power and operating temperature. In this letter, a robust surface emitting continuous‐wave terahertz QC laser is realized in a two‐dimensional PhC structure by a second order Bragg grating extractor that simultaneously provides the boundary condition necessary for mode selection. This results in a 3.12 THz single mode CW operation with a 3 mW output power and a maximum operation temperature (T_max) of 100 K. Also, a highly collimated far‐field pattern is demonstrated, which is an important step towards real world applications.     

利用超格子模型对布拉格光纤的研究

为了研究布拉格光纤的模式特征和传输特性,提出了超格子模型,利用傅里叶级数表示光纤横向折射率分布,利用平面波展开法分析布拉格光纤的能带结构,基于厄米-主斯函数的局域正交函数展开法,从全矢量耦合波动方程出发,得到关于模式传播常量和电场展开系数的本征方程,从而分析布拉格光纤的模式特征。以高折射率芯布拉格光纤为例,实现了该算法,得到基模与二次模的横向电场分布、基模色散曲线和模式双折射。基模的模式双折射可用于衡量算法的精度,结果表明该算法精度较高。超格子模型不仅可以用于研究高折射率芯布拉格光纤,而且同样可以研究低折射率区域导光的布拉格光纤。     

Wave scattering from a periodic random surface generated by a stationary binary sequence

This paper studies the scattering of a TE plane wave from a periodic random surface generated by a stochastic binary sequence using a stochastic functional method. The scattered wave is first expressed as a product of an exponential phase factor and a periodic stationary process. The periodic stationary process is then expressed by a harmonic series representation, that is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence and they are represented by orthogonal binary functional expansions with band-limited binary kernels. The binary kernels are determined up to the second order from the boundary condition. Then, several statistical properties of the scattering are calculated numerically and illustrated in figures. It is found that, in the binary case, the second-order scattering cross section has a subtractive term and becomes much smaller than the first-order one.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

湍流边界层激励下高速列车车窗参数研究*

高速列车运行过程中,由于结构表面的不平整性产生的湍流边界层激励（TBL）对车厢内部的声场环境产生了一定的影响。采用非相关壁面平面波技术（UWPWs）将随机激励（TBL）转化为一组壁面平面波,利用该激励模型模拟获取了TBL激励下高速列车车窗表面的壁面压力,并将其加载到车窗有限元结构上构建了TBL激励下高速列车车窗模型。分别调查了空腔厚度、双侧玻璃厚度比以及空腔阻尼损耗因子三个参数对车窗声振特性的影响。结果表明：当空腔厚度为20mm,双侧玻璃厚度比为9:5,空腔阻尼损耗因子为0.05时,分别为各自参数下调查工况中的最优解。基于参数调查的结果对车窗结构进行了优化,优化后车窗结构的速度级响应在分析频段内较之前有了显著的削弱,辐射声功率级整体下降了2.8dB。     

外部加环肋有限长圆柱壳体声散射

为了深入理解双层加肋圆柱壳体的声散射机理,专门研究了两层壳体之间环肋的声散射。仅考虑模型的刚性散射,采用Kirchhoff近似推导了单个环肋的反向散射声场的解析解,并推广到等间距的环肋散射,结合圆柱壳刚性散射得到外部加周期性环肋的圆柱壳体的散射声场近似解。同时,利用图形声学方法(GRACO)对模型的目标强度进行数值计算。理论与实验的结果表明,刚性散射在反向散射声场中起主要作用,周期性环肋引起的Bragg散射对散射声场有重要贡献,同时遮挡效应在实际情况下有较大作用。      

Quantization of electromagnetic field and analysis of Purcell effect based on formalism of scattering matrix

We have developed a rigorous self-consistent approach for the quantization of electromagnetic field in inhomogeneous structures. The approach is based on utilization of the scattering matrix of the system. Instead of the use of standard periodic Born-Karman boundary conditions, we use the quantization condition implying equating eigenvalues of the scattering matrix (S-matrix) of the system to unity (S-quantization). In the trivial case of uniform medium boundary condition for S-quantization is nothing but periodic boundary condition. S-quantization allows calculating modification of the spontaneous emission rate for arbitrary inhomogeneous structure and direction of the emitted radiation. S-quantization solves the long-standing problem coupled to normalization of the quasi-stationary electromagnetic modes. Examples of application of S-quantization for the calculation of spontaneous emission rate for the cases of Bragg reflector and microcavity are demonstrated.     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Vibro-acoustic response of orthogonally stiffened panels: The effects of finite dimensions

This paper investigates the effects of finite dimensions on the vibro-acoustic response of orthogonally stiffened panels. Three types of excitations are considered: acoustical excitation, point force excitation and random excitation by a turbulent boundary layer. In each case, a spatially windowed periodic model is compared with a Rayleigh-Ritz model where the modes of the un-stiffened panel are used as the basis functions. The latter model accounts for the reflected wave field generated at the boundaries by assuming that the panel is simply supported. On the contrary, the windowed periodic model only accounts for finiteness on sound radiation (the assumption of an infinite periodic structure is used to calculate the panel response). Numerical studies show that when the bending wavelength becomes comparable or smaller than the stiffener spacing, the periodic model is able to reproduce the results obtained with the Rayleigh-Ritz model. To complement the study, the developed models are compared with numerical simulations (finite element method) and with experimental results.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of a plane wave by one-dimensional dielectric random rough surfaces—study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of a one-dimensional dielectric random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the diffraction amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The results of a Gaussian random process with a Gaussian roughness spectrum are compared to published experimental and numerical data. Comparisons are conclusive.