Optical theorem detectors for active scatterers

We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

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.     

On optical properties of nonspherical inhomogeneous particles

To solve the problem of light scattering by multilayer scatterers of an arbitrary axisymmetric shape, a separation of variables method that involves special scalar potentials and their expansions in spherical functions is developed. The approach is shown to yield highly exact results even for particles that have 100 layers or more. A graphic library that illustrates the optical properties of layered and homogeneous (with an effective refractive index) spheroids, spheres, and Chebyshev particles of various shapes and sizes (about 650 figures) is created and is put on the Internet. It is noted that the linear polarization of radiation transmitted forward through a polydisperse medium containing partially oriented nonspherical porous particles strongly depends on the structure of scatterers. It is shown that the difference between the degrees of polarization of layered and corresponding homogeneous scatterers can exceed 200–300%.     

Contribution of multiple scattering to the dielectric constant of a randomly inhomogeneous medium

Within the statistical theory of multiple scattering of light in random media, the dielectric constant of a suspension is represented as a diagram series in scattering orders and concentration of particles. The contributions of double and triple scattering events are determined. The extinction length and the transport mean free path in highly concentrated suspensions calculated with the use of the optical theorem are in good agreement with the available data. It is shown that the two-particle Born approximation, combined with the Mie form factor and the Percus-Yevick structure factor, is not adequate for systems with a high concentration of scatterers. A contribution to the optical parameters is found that is missing in the above approximation.     

Analyzing the coda from correlating scattered surface waves

The accuracy of scattered Rayleigh waves estimated using an interferometric method is investigated. Summing the cross correlations of the wave fields measured all around the scatterers yields the Green's function between two excitation points. This accounts for the direct wave and the scattered field (coda). The correlations themselves provide insights into the location of the scatterers, as well as which scatterer is responsible for particular parts of the coda. Furthermore, these measurements confirm a constant-time arrival in the correlations, not part of the Green's function, but which has previously been derived as a result of the generalized optical theorem.     

Splitting of a surface plasmon polariton beam by chains of nanoparticles

The operation of a micro-optical beam splitter for surface plasmon polaritons (SPP’s) formed by lined up scatterers is modeled and studied in the framework of a vectorial dipolar approach for multiple SPP scattering by equivalent non-spherical nanoparticles. It is shown that the inclusion of anisotropic polarizability of individual scatterer in the vectorial dipolar model of multiple SPP scattering allows one to obtain, in some cases, quantitative agreement between modeling and experimental results. As an example, we apply this approach to model an SPP beam-splitter formed by a chain of spheroidal particles. The dependencies of the splitting efficiency on the shape of particles, the incidence angle and the waist of an incident SPP Gaussian beam are considered. It is found that the efficiency is very sensitive to the shape of scatterers and the angle of SPP beam incidence. Comparison of numerical results with experimental data shows good agreement with respect to the particle shape and incident angular dependences. PACS 02.70.-c; 71.36.+c; 78.68.+m     

How exact are simplified scalar approaches to optical fields in oxide-confined stripe-geometry diode lasers?

Optical model, scalar or vectorial one, describing behaviour of an optical field within a diode-laser cavity, is one of the most important parts of modelling of a diode-laser operation. As compared to more accurate vectorial optical approaches, scalar ones are known to be less exact but simultaneously they need much less computation time. Besides, they have been sometimes found to be surprisingly exact even beyond their confirmed range of validity. Therefore, in this paper, real validity limits of their application have been determined by comparing their simplified results with more exact results obtained with the aid of vectorial models. The analysis comprises a comparison of an application of the most popular scalar approach to optical properties of diode lasers, i.e., the effective index method, and the vectorial method of lines for the standard 1.3-μm GaAs-based stripe-geometry diode laser. The scalar model has been found to be quite exact in the case of a determination of the effective refractive index, i.e., the wavelength of emitted radiation, whereas its exactness in the lasing threshold analysis is much worse, especially in the case of higher-order modes. Our analysis is concluded with a determination of the regions where both models give satisfactorily close results.     

Modeling of a surface plasmon polariton interferometer

We model the operation of a micro-optical interferometer for surface plasmon polaritons (SPPs) that comprises an SPP beam-splitter formed by equivalent scatterers lined up and equally spaced. The numerical calculations are carried out by using a relatively simple vectorial dipolar model for multiple SPP scattering [Phys. Rev. B 67 (2003) 165405]. The SPP beam-splitter is simulated elucidating the influence of system parameters, such as the angle of SPP beam incidence, scattering particle size, and inter-particle distance, on the splitting efficiency and phase difference between the transmitted and reflected beams. It is found that the splitting efficiency is very sensitive to the size of scatterers and angle of incidence. Comparing our simulations with experimental data available in the literature, we conclude that this approach can be used, with certain limitations, for modelling of SPP components assembled of individual scatterers, e.g., beam-splitters and interferometers, and suggest further improvements of the model used.     

Scattering from anisotropic particles: A challenge for the optical theorem?

The optical theorem is a very general law of scattering theory that has been discussed almost exclusively for spherically symmetric scatterers. In this work we present the extension to the case of anisotropic scatterers, by treating explicitly the problem within the Rayleigh-Gans approximation. Working formulas for the fluctuating components of the forward-scattering amplitude S _VV(0) and S _VH(0) are given, and a paradox concerning the applicability of the optical theorem is solved. While the S _VH(0) cannot interfere with the incoming vertical polarized beam, we show that S _VV(0) fluctuates around a non-zero average so to compensate at any instant for the integrated scattered intensity at both polarizations. The results are relevant for the design and interpretation of experiments of dynamic depolarized light scattering in the forward direction.     

An “optical” theorem for acoustic scattering by baffled flexible surfaces

The classical optical theorem for scattering by compact obstacles is a forward scattering theorem. That is, the total cross section of the obstacle is proportional to the imaginary part of the far field directivity factor evaluated in the forward scattering direction. An analogous theorem is derived in this paper for the scattering of acoustic waves by baffled membranes and plates. In this “optical” theorem the directivity factor is evaluated in the direction of the specularly reflected wave, so that it is a reflected scattering theorem.     

Cancellation of spurious arrivals in Green's function retrieval of multiple scattered waves

The Green's function for wave propagation can be extracted by cross-correlating field fluctuations excited on a closed surface that surrounds the employed receivers. This study treats an acoustic multiple scattering medium with discrete scatterers and shows that for a given source the cross-correlation of waves propagating along most combinations of scattering paths gives unphysical arrivals. Because theory predicts that the true Green's function is retrieved, such unphysical arrivals must cancel after integration over all sources. This cancellation occurs because the scattering amplitude of each scatterer satisfies the generalized optical theorem. The cross-correlation of scattered waves with themselves does not lead to the correct retrieval of scattered waves, because the cross-terms between the direct and scattered waves is essential.     

Validity of Scalar Approaches to Radiation Modes of the GaAs-Based 1.3-μm Diode Lasers Designed for the Optical–Fibre Communication

The work presents a comparison between results of optical simulations based on the scalar and vectorial models applied to both stripe – geometry Fabry-Perot (FPL) as well as vertical-cavity surface-emitting (VCSEL) diode lasers designed for the 1.3-μm optical–fibre communication. As compared to vectorial optical approaches, scalar ones are known to be less exact but simultaneously they need as many as approximately 100 times shorter computation time, which favours those models in many applications. Therefore, vectorial models should be applied only in cases of confirmed faulty performance of scalar ones. While the Effective Index Method and the Effective Frequency Method have been chosen as scalar approaches to FPLs and VCSELs, respectively, simulations, the Method of Lines has been used in both cases as a vectorial one. Scalar models have been found to be quite exact in the case of a determination of the effective refractive index and wavelength of emitted radiation, whereas their exactness in the lasing threshold analysis is much worse, especially in the case of higher-order modes. Our analysis is concluded with the determination of the regions where both models give satisfactorily close results.     

一种近似矢量衍射模型在衍射微光学元件分析中的应用

标量衍射理论形式简洁，有很高实用性，但是在衍射微光学元件分析中显得模型粗糙，准确度下降。严格矢量衍射理论由于计算复杂，非常耗费时间和资源，因此也不是一种很有效的设计工具。 我们在本文中运用了一种简单的近似矢量衍射模型分析了几种典型衍射微光学元件衍射性能，此衍射模型采用了标量衍射理论和近似近场模型的结合。 TE和TM两种偏振模式均运用此近似矢量衍射模型进行了分析，我们发现此衍射模型可以得到比标量衍射理论更准确的结果，而与严格电磁场理论相比，它占用很少的计算时间。     

On the electronic structure of liquid metals

We consider the electronic structure of liquid metals as a problem of multiple scattering. The total scattering operator is developed in terms of the reaction operators of a single scattering event, having a ‘standing wave’ boundary condition. This method has several advantages with respect to the approach where the total scattering operator is developed in terms of the scattering operators of a single scattering. Since the reaction operators are hermitian, the occurring perturbation expansions have a real perturbation parameter, which is more easily handled. Furthermore, if in the expansion of the total scattering operator, only terms up to the second order are maintained, this approximate expression satisfies already the ‘optical theorem’, just as the exact total scattering operator. Finally, spurious damping terms are eliminated at the outset. For very dense systems we obtain practically non-attenuated waves and this can be understood as if the damping due to a single scattering event is compensated by the reaction of the surrounding scatterers.     

Wave propagation in a disordered array of monopole scatterers

We study scalar wave propagation in a disordered static array of spherical scatterers. Due to a hard core repulsion the scatterers do not overlap. The wave is scattered by a δ-function potential at the center of each of the spheres. To this monopole model we apply the previously developed cluster expansion for the self-energy. We find the root of the dispersion equation for the coherent wave for a range of volume fraction⁵. It turns out that the monopole model develops an instability when the scattering is too strong.     

Propagation of guided waves through weak penetrable scatterers

The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed.     

Vectorial Hermite--Laguerre--Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh--Sommerfeld integrals, the free-space propagation expressions for vectorial Hermite--Laguerre--Gaussian (HLG) beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.     

Nonparaxial propagation of a vectorial apertured off-axis Lorentz beam

Based on the vectorial Rayleigh--Sommerfeld integral formula and the complex Gaussian expansion of the hard-edge aperture function, an analytical propagation expression for a nonparaxial vectorial off-axis Lorentz beam passing through a rectangular aperture is derived. The unapertured case, the far field expression and the scalar paraxial result are also presented as special cases of the general formulae, respectively. Some numerical examples are also given to show the propagation characteristics of a nonparaxial vectorial off-axis Lorentz beam through a rectangular aperture. It is indicated that the f parameter, the off-axis displacement and the truncation parameter all play an important role in determining nonparaxial propagation behaviour.