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.     

随机激光器中准态腔的阈值与其局域化程度的关系

基于光波在有限随机介质中的局域化理论，利用有限时域差分法数值求解Maxwell方程 组，研究了随机介质中的激光现象，分析了准态模的放大与其 空间局域性的关系. 通过研究二维非增益随机介质中光波的局域化，确定了准态模的空间分 布和频谱特征. 通过引入增益，研究了准态模的放大过程和阈值特性. 结果表明空间局域化 强的准态模在增益介质中被优先放大，且有较低的阈值. 关键词： 随机激光器 准态模 随机介质中的光学特性     

本征态的局域化与增益介质中局域态的放大

用时域有限差分方法(FDTD)模拟了二维增益、非增益随机介质中的光学现象。在非增益介质中，观察到了局域态空间分布及其频率特征。在增益介质中，观察到局域态的放大过程。模拟结果显示非增益介质中的局域态相当于传统激光腔的腔模，随机激光是由局域态谐振产生的。     

磁各向异性介质中的平面电磁波

讨论了磁各向异性理想介质中平面电磁波的一般特性,继而推证了这种介质中平面波的对偶关系,导出了磁晶体中的“菲涅耳方程”,并利用此方程分析了这种理想介质中的平面波的结构、传播及其偏振特性．     

二维各向同性异向介质负折射特性仿真验证

提出了一种工作在C波段的二维各向同性异向介质，相比于以往的二维异向介质，它除了具有二维各向同性的优点外，还具有带宽更宽，单元结构的尺寸更小，构造也更简单的特点.通过分别仿真验证异向介质的双负特性和负折射特性最终肯定上述异向介质的存在. 关键词： 各向同性异向介质 宽频带 小单元 双负特性     

随机介质介电常量的涨落与光波的空间分布

采用随机介质统计模型和时域有限差分方法模拟了二维随机介质中光场的空间分布及其同介电常量涨落的关系。模拟中,散射微粒随机地分布在均匀介质中以增加光子在介质中滞留时间。不同随机强度α,形成不同空间结构的随机介质。通过小心地调节入射光波长,得到了不同随机介质中的场强分布。结果表明,随机介质介电常量的涨落导致在介质的某些区域形成一些特殊结构。这些结构延长了光子在其中的滞留时间,产生了光波的局域态,起到了光腔的作用,使得随机介质在抽运激励下能够产生激光辐射。这样的光腔在介质中是随机分布的,其数量与分布特征与介电常量涨落的强弱有关。     

平面波在横向各向同性均匀介质中的传播

导出均匀各向异性介质当中具有横向各向同性性质的一类介质中平面波的严格解,给出了慢度曲面的三维分布图形,研究了属于这类介质的单向纤维增强复合材料中声波的传播规律。平面波的特征用慢度矢量、波矢量、偏振矢量和群速度等物理量来刻画．由于引入了描述介质各向异性特性的方向矢量,各物理量最终以与座标系无关的形式来表达,因而具有普遍的适用性。     

二维随机激光器的模式选择及阈值与饱和特性

基于将Maxwell方程与四能级原子系统速率方程相结合而建立起随机激光时域理论，并利用有限时域差分法，研究了二维随机介质中激光模式的输出特性与介质尺寸、外形及抽运速率等参数的关系.结果表明，与传统激光模式相似，随机激光模式的强度随抽运速率的变化不仅具有阈值特性，而且具有饱和特性.基于模式特性对介质及抽运参数的依赖关系，提出了二维随机激光器的选模方式，在很大程度上不同于传统激光器的选模方式. 关键词： 随机激光器 模式选择 无序介质中的光学特性     

同材质颗粒不同填充密度的随机介质中光场的空间分布

用时域有限差分法研究了同一材质的颗粒在不同填充密度下的随机介质中光局域化问题. 依据随机介质激光的实验参数,模拟了颗粒填充密度不同的随机介质中光场的空间分布. 结果表明：当散射颗粒的散射平均自由程与波长相当时,随机介质中的光场分布呈现局域化的特征,而且随着颗粒填充密度增大,光场的局域化程度增强. 因此,在同样的抽运激励下,颗粒填充密度越大的随机增益介质越容易产生激光辐射. 数值模拟结果与实验定性符合. 关键词： 随机激光 时域有限差分法 颗粒填充密度 局域化     

由光子晶体局域模对称关系分析其简并性

使用平面波展开法计算了二维正方格子介质柱光子晶体在改变中央介质柱半径的情况下谐振腔的模式，根据所计算的局域模式场分布的对称关系，研究了二维光子晶体谐振腔模式的简并性.结果表明：具有C4v对称群光子晶体谐振腔，存在着二重简并偶极模和二重简并六极模，同时也存在非简并单极模和四极模，二重简并模的90°旋转态与其形成简并对.模式的简并与非简并可以直观地通过考察模式场分布的对称关系而得到.     

Transverse or off-axis localization of electromagnetic waves in random one- and two-dimensional dielectric systems which are periodic on average

We study the transverse or off-axis localization of electromagnetic waves for several different random dielectric systems which are periodic on average. Unlike previous scalar wave treatments of transverse localization, in the present work we present results based on a full vector treatment of the electromagnetic fields based on Maxwell's equations. In a first system, we consider a random semi-infinite array of slabs with plane waves or finite beams of electromagnetic waves obliquely incident on the slab surfaces. The localization of the fields in a region near the surface of illumination is studied as a function of the oblique angle of incidence. In a second system, an array of semi-infinite slabs with random thickness is considered with an incident finite beam of electromagnetic waves initially directed parallel to the slab surfaces. The spreading of the beam width is computed as it propagates through the array of semi-infinite slabs. In a final system, we consider a semi-infinite array of random dielectric rods (2D system) with obliquely incident plane waves. The localization length of the plane-wave fields is computed as a function of the oblique angle of incidence and as a function of the strength of the disorder of the dielectric medium. All the random media we consider, when averaged over their randomness, are periodic on average. The above systems are studied for both p- and s-polarizations of incident electromagnetic waves, and the difference in the transverse localization of the electromagnetic field for these two polarizations is determined.     

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.     

Reflection and transmission of plane waves at the interface between anisotropic random discrete media

The Maxwell equations are solved for a random discrete medium using the single-scattering approximation and the condition of immersion in a maximally packed medium. The reflection and transmission factors of plane waves at the interface between vacuum and a random discrete anisotropic medium are determined. The calculated and experimental results on reflection and transmission of plane waves near the edge of a forest as an example of natural anisotropy of a random discrete medium are compared.     

Scattering of a TM plane wave from periodic random surfaces

This paper deals with the scattering of a TM plane wave from conductive periodic random surfaces. By means of the stochastic functional approach, the scattered field is expressed in terms of a harmonic series representation, in which the coefficients are homogeneous random functions and are given by Wiener-Hermite expansions. An approximate solution for the Wiener kernels is obtained up to the second order. Several anomalies appear in the angular distribution of the incoherent scattering because of combinations of scattering due to surface randomness and diffraction due to surface periodicity. These are incoherent Wood's anomalies associated with guided surface waves propagating along the surface, enhanced backscattering and diffracted backscattering enhancement. The physical reasons for these anomalies and numerical results are discussed.     

Scattering from a slightly random, one-dimensional metal surface: 45° linearly polarized incidence, backscattering enhancement and degree of polarization

The scattering of an electromagnetic wave from a slightly random metal surface which supports the surface plasmon mode at optical frequencies is studied theoretically by means of a stochastic functional approach. In order to investigate the Stokes matrix or the state of polarizations, as well as the intensity of the scattered waves, the rough surface is assumed to be one dimensional, and is illuminated by a+45° linearly polarized plane electromagnetic (light) wave whose plane of incidence is perpendicular to the grooves of the surface. The stochastic wave fields are represented in terms of the Wiener-Hermite functionals, and the approximate solutions of the Wiener kernels are obtained for both TM- and TE-polarized components, from which the Stokes matrix elements can be determined. The dressed or perturbed plasmon mode in the presence of surface roughness is obtained by a mass operator involved in the solutions, and the enhanced backscattering closely related to the plasmon mode is studied in connection with the enhanced peak width and the mass operator for the dressed plasmon mode. The Stokes parameters and the degree of polarization are calculated numerically from various polarized components of the incoherent scattering distribution. To clarify the surface plasmon's association with the scattering characteristics, calculations are made for two kinds of random surfaces, a random surface with a centred Gaussian spectrum and a random grating with twin spectral peaks at the plasmon spatial frequency.     

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.     

Contribution to the statistical theory of wave localization in a two-layered medium

A very simple system of stochastic boundary-value wave equations that describes the interaction of two types of waves in a randomly inhomogeneous medium is studied. The statistics of the reflection and transmission coefficients for the incident and excited waves are discussed. It is shown that the excitation of waves is statistically equivalent to switching on damping for the initial incident waves which are localized in separate specific realizations. The parameters of the length of such localization are estimated in terms of the spectral density of the variations of the medium. It is also shown that for excited waves there is no dynamical localization, and the transmission coefficients for them are estimated. Zh. éksp. Teor. Fiz. 111, 2030–2043 (June 1997)     

Localization of Classical Waves II: Electromagnetic Waves

We consider electromagnetic waves in a medium described by a position dependent dielectric constant . We assume that is a random perturbation of a periodic function and that the periodic Maxwell operator has a gap in the spectrum, where . We prove the existence of localized waves, i.e., finite energy solutions of Maxwell's equations with the property that almost all of the wave's energy remains in a fixed bounded region of space at all times. Localization of electromagnetic waves is a consequence of Anderson localization for the self-adjoint operators . We prove that, in the random medium described by , the random operator exhibits Anderson localization inside the gap in the spectrum of . This is shown even in situations when the gap is totally filled by the spectrum of the random operator; we can prescribe random environments that ensure localization in almost the whole gap. Received: 1 July 1996 / Accepted: 15 August 1996     

Bands of Localized Electromagnetic Waves in 3D Random Media

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.