Spectral Changes of Light and Scattering Phenomena

In the last few years renewed attention has been paid to the study of light scattering from random media. This is due to the recent discovery of a phenomenon that dynamic light scattering from a fluctuating random medium may produce shifts of spectral lines, even when the source and the scattering medium are at rest relative to the observer. It has also been demonstrated that a similar phenomenon may occur in static light scattering from spatially random media without dynamic fluctuations. By the well-known analogy between the processes of scattering and radiation, these phenomena in scattering are found to be closely related to the correlation-induced spectral changes in the coherence theory which are often referred to as the Wolf effect. In this paper some recent developments are reviewed on research regarding the phenomena of changes in the spectrum of light induced by scattering from random media. Emphasis is placed on a number of up-to-date attempts for elucidating the effects of multiple scattering on these phenomena.This review was presented as an invited paper at the Symposium on Spectral Effects in Collective Phenomena organized as a satellite meeting of the Seventh Rochester Conference on Coherence and Quantum Optics, June 7–10 1995 (Rochester, NY).     

光通过纳米颗粒随机散射体透射光强的计算及分析

光通过随机散射体后透射光强的估算,对于提取散射体内部无法直接测量或者无法直接观察的信息至关重要。在分析平行光束通过纳米圆形颗粒随机散射体出射面上光强组成的基础上推导了透射光强的计算公式,并指出多重散射理论、一阶多重散射理论和朗伯-比尔定律在一定近似程度上可以相对精确地估算透射光强。这三种方法的估算结果之间会出现四种相对关系。根据这些相对关系,分析了光在散射体内部传输时散射过程的特征以及各种散射过程对出射面光强的贡献大小。     

Broken time‐reversal symmetry scattering at the Anderson transition

We study numerically the statistical properties of some scattering quantities for the Power‐law Banded Random Matrix model at criticality in the absence of time‐reversal symmetry, with a small number of single‐channel leads attached to it. We focus on the average scattering matrix elements, the conductance probability distribution, and the shot noise power as a function of the effective bandwidth b of the model. We find a smooth transition from insulating‐ to metallic‐like behavior in the scattering properties of the model by increasing b. We contrast our results with existing random matrix theory predictions.     

Interference effect in scattering loss of high-index-contrast planar waveguides caused by boundary reflections

We present theoretical and experimental results on an interference effect caused by boundary reflections on the optical scattering loss in high-index-contrast planar waveguides. Analytical expressions for the polarization-dependent scattering loss are derived using a surface Green's function. For high-index-contrast waveguides of submicrometer dimensions a significant deviation from accepted theory arises, including scattering loss suppression owing to a thin-film interference effect. Our theoretical predictions are confirmed by loss measurements on silicon-on-insulator channel waveguides.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Higher order processes in random Raman lasing

Random Raman lasers offer a unique opportunity to study many exciting dynamics of light propagation in turbid media. One of the most notable features observed to exist in the recently discovered random Raman laser is the presence of higher order stimulated Raman scattering processes. The higher order Stokes generation likely comes from photons that have the longest pathlengths, thus have the most gain. This makes these photons particularly likely to offer interesting insight into wave propagation effects such as coherent backscattering and optical Anderson localization. In this work, we use Monte Carlo simulations to investigate how these higher order processes occur and what properties they are expected to exhibit when considering only transport equation dynamics. This knowledge will allow us to look for deviations from this theory in future experiments to determine whether wavelike properties play an active role in random Raman lasing.     

Reggeon, Pomeron and Glueball, Odderon-Hadron-Hadron Interaction at High Energies - From Regge Theory to Quantum Chromodynamics

Based on analysis of scattering matrix S, and its properties such as analyticity, unitarity, Lorentz invariance, and crossing symmetry relation, the Regge theory was proposed to describe hadron-hadron scattering at high energies before the advent of QCD, and correspondingly a Reggeon concept was born as a mediator of strongly interaction. This theory serves as a successful approach and has explained a great number of experimental data successfully, which proves that the Regge theory can be regarded as a basic theory of hadron interaction at high energies and its validity in many applications. However, as new experimental data come out, we have some difficulties in explaining the data. The new experimental total cross section violates the predictions of Regge theory, which shows that Regge formalism is limited in its applications to high energy data. To understand new experimental measurements, a new exchange theory was consequently born and its mediator is called Pomeron, which has vacuum quantum numbers. The new theory named as Pomeron exchange theory which reproduces the new experimental data of diffractive processes successfully. There are two exchange mediators： Reggeon and Pomeron. Reggeon exchange theory can only produce data at the relatively lower energy region, while Pomeron exchange theory fits the data only at higher-energy region, separately. In order to explain the data in the whole energy region, we propose a Reggeon-Pomeron model to describe high-energy hadron- hadron scattering and other diffractive processes. Although the Reggeon-Pomeron model is successful in describing high-energy hadron-hadron interaction in the whole energy region, it is a phenomenological model. After the advent of QCD, people try to reveal the mystery of the phenomenological theory from QCD since hadron-hadron processes is a strong interaction, which is believed to be described by QCD. According to this point of view, we study the QCD nature of Reggeon and Pomeron. We claim that the Reggeon exchange is an exchange of mult     

Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement

The present paper deals with the electromagnetic (EM) scattering from a perfectly conductive, random surface by means of the stochastic functional approach and aims to study the backscattering enhancement associated with co-polarized and cross-polarized scattering. The treatment is based on the stochastic functional theory where the random EM field is represented in terms of a Wiener-Hermite functional of the homogeneous Gaussian random surface. To obtain more precise solutions than the previous works (Nakayama J et al 1981 Radio Sci. 16 831-53), we first establish the reciprocal theorem for vector Wiener kernels which describe the stochastic functional representation of the EM field and, using this, we derive the reciprocal relations for the co-polarized and cross-polarized scattering distribution relative to TE and TM polarizations of incident wave. Solutions for the vector Wiener kernels up to the second are obtained so precisely as to satisfy the reciprocal relations and are expressed in terms of generating matrices, so that complex EM scattering processes described by the vector Wiener kernels are given dear physical interpretations. Compact operator representations are introduced to reformulate the hierarchical kernel equations, the mass operator equation and higher-order kernel solutions. It is shown that the second vector Wiener kernel physically describes a 'dressed double-scattering' process, similar to the scalar theory (Ogura H and Takahashi N 1995 Waves Random Media 5 223-42), and that the 'dressed double scattering', which involves anomalous scattering in the intermediate scattering processes, creates the backscattering enhancement in both co- and cross-polarized scattering for both TE and TM wave incidence.     

随机激光器的理论与研究现状

综述了随机激光器的最新理论与实验进展，对光散射理论、环形腔理论、环形波导理论等各种随机激光理论的内容、应用范围及其差异等进行了重点分析和评述，并介绍了一些随机激光器的重要实验。讨论了随机激光器未来的发展，并描述了随机激光器潜在的应用前景。     

超宽频带THz脉冲在随机散射介质中传播的理论研究

研究了超宽频带THz脉冲入射到散射介质中时其透射脉冲的时空特性.根据Mie理论计算出随机散射介质的散射系数和各向异性因子,用时间分辨Monte Carlo方法模拟了超宽频带的THz脉冲在随机散射介质中的传播,研究了在不同散射颗粒半径,不同频宽的THz入射脉冲对透射脉冲的影响和散射对成像分辨率的影响.结果表明:散射会降低THz脉冲在随机散射介质中的成像分辨率,散射颗粒越小,散射介质越厚,其成像分辨率越差.     

Random lasing in porous scattering medium

The spectrum behavior evolution and the threshold of random lasing depending on the way of photon walk randomization in an active random medium were investigated. The following three ways of photon walk randomization were implemented: multiple light scattering by corundum and silica particles embedded into a solid polymer solution of dye (astrafloxin), multiple light reflection at sub-millimeter extensive air pores (mean diameter 200 μm) produced in the medium, and the combined action of both these effects. The most effective lasing is observed in the case of an active medium with air pores and scattering particles in the interpore space. Such a combined porous scattering medium acts as a network of dielectric waveguides transmitting effectively the random light. This spatial structure of the random active medium significantly increases the photon path in the medium, thereby promoting photon multiplication due to stimulated emission. In this combined medium the random lasing reveals the narrowest spectrum, the lowest threshold, and the highest density of spectral energy in the spectrum maximum.     

Scattering from an abruptly terminated planar metamaterial waveguide

We use a variational method to study the problem of reflection of a guided mode from an abruptly terminated planar dielectric waveguide made of a metamaterial. The theory is illustrated by problems of abruptly terminated three-layer waveguides with piecewise-constant and variable permittivity profiles. Differences in the scattering characteristics for systems with metamaterials and conventional media are discussed.     

Superfluid state of coherent light in nonlinear waveguides

We establish the photonic superfluid theory in waveguides made of self-defocussing polar crystals. In quantum theory it is shown that photons can sense an attractive effective interaction by exchange of virtual optical phonons. Such an interaction leads to the photonic superfluid state, in which a propagating photon pair consists of a combination of two photons with opposite transverse wave vector and spins. The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations. The traveling-wave superfluid state has the squeezing property and the soliton effect.     

Resonance widths in open microwave cavities studied by harmonic inversion

From the measurement of a reflection spectrum of an open microwave cavity, the poles of the scattering matrix in the complex plane have been determined. The resonances have been extracted by means of the harmonic inversion method. By this, it became possible to resolve the resonances in a regime where the linewidths exceed the mean level spacing up to a factor of 10, a value inaccessible in experiments up to now. The obtained experimental distributions of linewidths were found to be in perfect agreement with predictions from random matrix theory when wall absorption and fluctuations caused by couplings to additional channels are considered.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.     

Singular value distribution of the propagation matrix in random scattering media

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.