Strong Permittivity Fluctuation Research Articles

Uniaxial Effective Permittivity of Anisotropic Bicontinuous Random Media Using NMM3D

In this letter, we generate anisotropic bicontinuous media with different vertical and horizontal correlation functions. With the computer-generated bicontinuous medium, we then use numerical solutions of Maxwell equations in 3-dimensions (NMM3D) to calculate the anisotropic effective permittivities and the effective propagation constants of V and H polarizations. The copolarization phase difference (CPD) of VV and HH is then derived. The CPDs have recently been applied to the retrieval of snow water equivalent, snow depth, and anisotropy. The NMM3D simulation results are also compared with the results of the strong permittivity fluctuations in the low frequency limit and compared against the Maxwell–Garnett mixing formula.

Solitons in a homogenized two-phase, isotropic, nonlinear, particulate composite medium

The strong permittivity fluctuation theory was employed to determine the effective linear relative permittivity and the effective nonlinear susceptibility of a two-phase, isotropic, nonlinear, particulate composite medium. Propagation in the homogenized composite medium obeys the complex Ginzburg–Landau equation, and therefore the medium can support the propagation of chirped solitons that are either Pereira–Stenflo (PS) bright solitons or Nozaki–Bekki (NB) dark solitons, when linear loss is counterbalanced by nonlinear gain. Soliton propagation depends on the volume fraction of the component phases as well as on the correlation length of the spatial fluctuation of the dielectric properties in the composite medium.

Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Permittivity Fluctuations

Most previous multiple-scattering theories for electromagnetic waves in strongly fluctuating media are limited by the assumption of statistical homogeneity of media. In the paper, a lossy electrically isotropic random medium is considered whose mean permittivity distribution, as well as the multipoint permittivity's moments are invariant under arbitrary rotations about and translations along a fixed symmetry axis, and are inhomogeneous in the radial direction. The goal of the paper is to calculate the effective permittivity operator (EPO) for such medium in the case of strong permittivity fluctuations. For this purpose, one has to eliminate the secular terms from the spectral representation of the-EPO in the basis set of waves suited to a statistically inhomogeneous medium. This is achieved via a renormalization approach which takes into proper account a delta function singularity of the spectral Green's function (rather than that of the spatial Green's function accounted for in the past) referring to a spatially inhomogeneous electrically anisotropic background medium. On this basis, the permittivity matrix of the background medium is explicitly found, a full perturbation series solution and a bilocal approximation for the EPO are derived, the macroscopic properties of the spatially dispersive effective medium are studied, and a perturbative solution for the propagation constants of guided modes of the mean field is obtained.

EFFECTIVE PERMITTIVITY OF A STATISTICALLY INHOMOGENEOUS MEDIUM WITH STRONG PERMITTIVITY FLUCTUATIONS - Abstract

Most previous multiple-scattering theories for electromagnetic waves in strongly fluctuating media are limited by the assumption of statistical homogeneity of media. In the paper, a lossy electrically isotropic random medium is considered whose mean permittivity distribution, as well as the multipoint permittivity's moments are invariant under arbitrary rotations about and translations along a fixed symmetry axis, and are inhomogeneous in the radial direction. The goal of the paper is to calculate the effective permittivity operator (EPO) for such medium in the case of strong permittivity fluctuations. For this purpose, one has to eliminate the secular terms from the spectral representation of the-EPO in the basis set of waves suited to a statistically inhomogeneous medium. This is achieved via a renormalization approach which takes into proper account a delta function singularity of the spectral Green's function (rather than that of the spatial Green's function accounted for in the past) referring to a spatially inhomogeneous electrically anisotropic background medium. On this basis, the permittivity matrix of the background medium is explicitly found, a full perturbation series solution and a bilocal approximation for the EPO are derived, the macroscopic properties of the spatially dispersive effective medium are studied, and a perturbative solution for the propagation constants of guided modes of the mean field is obtained.

Operator of Effective Permittivity of a Statistically Inhomogeneous Medium with Strong Fluctuations

The majority of known works on the theory of multiple scattering of electromagnetic waves in media with strong fluctuations are constrained by the assumption of statistical homogeneity of a medium. In this paper, we consider an isotropic lossy random medium, for which the principle value and multipole moments of the permittivity are invariant with respect to arbitrary rotations about a fixed symmetry axis and translations along the axis and are inhomogeneous in the radial direction. This paper is aimed at calculating the effective permittivity operator (EPO) for such a medium for the case of strong permittivity fluctuations.

Homogenisation of isotropic, cubically nonlinear, composite mediums by the strong–permittivity–fluctuation theory: third-order considerations

The third-order strong–permittivity–fluctuation theory (SPFT) is presented for an isotropic, cubically nonlinear, composite medium, under the long-wavelength approximation. The effective permittivity of the homogenised composite medium is thereby estimated. Convergence of the SPFT at the second-order level is demonstrated with respect to both the linear and nonlinear contributions to the effective permittivity. The nonlinear SPFT is found to be relatively insensitive to the choice of covariance function. The manifestation of nonlinearity enhancement is considered up to the level of the third-order SPFT.

Strong permittivity fluctuation theory of random media: Part I: Nonspherical scatterers

The strong permittivity fluctuation theory is applied to investigate the electromagnetic wave propagation in inhomogeneous media embedded with randomly positioned and randomly oriented nonspherical scatterers. Both bilocal approximation and low-frequency approximation are used to derive the random medium effective permittivities for the full space case. An isotropic model of random media is obtained due to the chosen geometry of scatterers as well as due to the chosen equal correlation lengths in two space directions. Using the given stochastic model, a first moment of random electromagnetic field can be directly computed. For the purposes of effective computation of permittivities, a FORTRAN 77 program is developed and approved. The developed random medium model was applied with success in sea ice investigation of its dielectric properties.

Application of strong permittivity fluctuation theory for isotropic, cubically nonlinear, composite mediums

A simple formula derived from the strong permittivity fluctuation theory (SPFT) is shown to provide a correction to the Bruggeman formalism for isotropic, cubically nonlinear, composite mediums by making use of the correlation length, a second-order statistic of the distribution of the two component material phases. The larger the correlation length, the larger are the differences between the estimates of the linear and the nonlinear dielectric properties of the homogenized composite medium provided by the two formalisms. The SPFT predicts attenuation and downgrades the possibility of nonlinearity enhancement, relative to the Bruggeman formalism.

Image reconstruction from TE scattering data using equation of strong permittivity fluctuation

Compared to the TM case, the inverse scattering problem for the TE incident field is more complicated due to its stronger nonlinearity. This work provides an effective method for the reconstruction of two-dimensional (2-D) inhomogeneous dielectric objects from TE scattering data. The algorithm applies the distorted Born iterative method to the integral equation of strong permittivity fluctuation to reconstruct scatterers with high-permittivity contrast. Numerical simulations are performed and the results show that the distorted Born iterative method (DBIM) for strong permittivity fluctuation (SPF-DBIM) converges faster and can obtain better reconstructions for objects with larger dimensions and higher contrasts in comparison with ordinary DBIM. A frequency hopping technique is also applied to further increase the contrast.

Extinction Properties of Dust Grains: A New Computational Technique

view Abstract Citations (23) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Extinction Properties of Dust Grains: A New Computational Technique Michel, B. ; Henning, Th. ; Stognienko, R. ; Rouleau, F. Abstract The Strong Permittivity Fluctuation Theory (SPFT) is a statistical approach to describe the optical properties of randomly oriented inhomogeneous dust grains. In contrast to most other methods that must calculate the extinction properties of individual particles and then sum the results to obtain ensemble averages, the SPFT starts with ensemble-averaged quantities from the very beginning. Therefore, the computation of the extinction has to be performed only once for a given ensemble. This makes this method especially suitable for astrophysical applications in which grain alignment is not required. We use the SPFT in bilocal approximation (BA) to calculate the orientationally and positionally averaged extinction cross section of dust agglomerates. In the BA, the average extinction cross section of a statistical ensemble of grains depends only on the complex refractive index of the constituent particles, and on the value and spatial correlation of the local density (filling factor) of the material. The BA is tested for the case of agglomerates of spherical grains by comparing its predictions to those of the discrete dipole approximation (DDA) and the generalized Mie theory (GMT), which embodies an exact solution of Maxwell's equations. We find that the BA works well for all size parameters tested (up to 0.6, taking the radius of the individual constituent spheres). We find a very good agreement between the BA, DDA, and GMT for a moderate refractive index (nref = 1.7 + 0.7i, typical of soot or "dirty" silicate cosmic dust analogs in the visual). For a somewhat larger refractive index (nref = 2.5 + 1.5i, typical of graphite in the UV), the BA is of comparable accuracy as the DDA. For the more extreme case of a quasimetallic refractive index (nref = 3.0 + 4.0i), the BA seems to be an inadequate approach. For this case, all methods are pushed to their limit. Publication: The Astrophysical Journal Pub Date: September 1996 DOI: 10.1086/177739 Bibcode: 1996ApJ...468..834M Keywords: ISM: DUST; EXTINCTION; METHODS: ANALYTICAL; METHODS: NUMERICAL full text sources ADS |

An electrothermodynamic model with distributed properties for effective permittivities of sea ice

This paper presents a model to calculate the temperature dependence of effective permittivities for sea ice, a heterogeneous medium containing multiphase scatterers. With the strong permittivity fluctuation approach the model accounts for the electrodynamic scattering effect together with the quasi‐static characteristics of multiple species and subspecies of inhomogeneities with distributed orientations, sizes, and shapes. Because of a preferential direction in the orientation distribution, the medium is effectively anisotropic. The size distribution is described with a probability density function in terms of normalized volumetric sizes. Scatterer shapes are nonuniform and have a general ellipsoidal form characterized by arbitrary axial ratios of correlation lengths which are related to physical geometries of the scatterers. In this formulation, sea ice consisting of solid ice, liquid brine, and gaseous inclusions is modeled to derive effective permittivities with thermodynamic phase redistribution and structural metamorphism. Theoretical results are in good agreement with experimental data at the C band frequency of 4.8 GHz for saline ice undergoing warming and cooling cycles. A competitive effect between the increase of liquid brine and the shape rounding of ellipsoidal scatterers at increasing temperatures explains the trend observed in measured data. Sensitivities of effective permittivities to structural and physical parameters characterizing sea ice are also studied.

Statistical method to calculate extinction by small irregularly shaped particles

A statistical approach is presented for calculation of the extinction of light by small, irregularly shaped particles in the framework of the strong-permittivity fluctuations theory. To this end the Dyson equation in the bilocal approximation is solved. The method, which is applicable even for particles with large optical constants, is used in the determination of the extinction cross section of interstellar dust particles in the visible and infrared region. The particles are assumed to be aggregates of the ballistic particle cluster aggregation type. A strong enhancement of the extinction in the far infrared is found. For moderate optical constants the results agree with Bruggeman’s effective-medium theory.

Polarimetric scattering from layered media with multiple species of scatterers

Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies‐layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost‐covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.

Scattering from Randomly Oriented Scatterers with Strong Permittivity Fluctuations

Strong permittivity fluctuation theory is used to solve the problem of scattering from a medium composed of completely randomly oriented scatterers under the low frequency limit. Based on Finkel'berg's approach [2,3], Gaussian statistics is not assumed for the renormalized scattering sources. The effective permittivity is obtained under the low frequency limit and the result is shown to be isotropic due to no preferred direction in the orientation of the scatterers. Numerical results of the effective permittivity are illustrated for oblate and prolate spheroidal scatterers and compared with the results for spherical scatterers. The results derived are shown to be consistent with the discrete scatterer theory. The effective permittivity of random medium embedded with nonspherical scatterers shows a higher imaginary part than that of spherical scatterer case with equal correlation volume. Under the distorted Born approximation, the polarimetric covariance matrix for the backscattered electric field is calculated for the half-space randomly oriented scatterers. The nonspherical geometry of the scatterers shows significant effects on the cross-polarized backscattering returns σhv and the correlation coefficient p between HH and VV returns. The polarimetric backscattering scattering coefficients can provide useful information in distinguishing the geometry of scatterers.

Scattering of electromagnetic waves from random media with strong permittivity fluctuations

All previous random media theories that have been applied to microwave remote sensing applications are only valid for cases of weak fluctuations of dielectric constant. By taking into proper account the singularity of the dyadic Green's function in the renormalization method, the low‐frequency limit of vector electromagnetic wave scattering from a random medium with large variance of permittivity function is studied. The strong fluctuation random theory is then applied to a ‘discrete scatterer’ problem in which the permittivity can assume only two values. It is then shown that the results of the strong fluctuation theory are consistent with those derived from discrete scatterer theory for all values of dielectric constants of the scatterers. Numerical results of the effective permittivity are illustrated for random media with isotropic and anisotropic correlation functions. It is shown that the results of the weak fluctuations theory differ significantly from those of the strong fluctuation theory. The second moment of the field in the backscattering direction is calculated using the distorted Born approximation and illustrated using parameters typically encountered in microwave remote sensing of vegetation.

Application of Strong Fluctuation Random Medium Theory to Scattering from Vegetation-Like Half Space

A model for vegetation scatter is developed using the theory of electromagnetic wave propagation in random medium with strong permittivity fluctuations. In applying the strong fluctuation theory, the singularity of the dyadic Green's function is taken into account. Backscattering coefficients are computed using the distorted Born approximation and illustrated as a function of incidence angle, frequency and moisture content of the vegetation. The mixing formula of the de Loor [28] was used in estimating the permittivity of leaves. The correlation function of Fung and Fung [18], and Fung and Ulaby [19] is used for the random medium.

Application of First-Order Renormalization Method to Scattering from a Vegetation-Like Half-Space

A general theory is developed for scattering from an inhomogeneous half-space with strong permittivity fluctuations. Closed form bistatic scattering coefficients are obtained using the method of field renormalization for a vegetation-like medium characterized by a random permittivity function with a large variance and a cylindrically symmetric, fast-decaying correlation function. Multiple-scattering effects are accounted for to the same extent as in the first-order renormalization approach. Behaviors of the scatter model are illustrated by computing sample cases using Carlson's permittivity model for leaves. Cursory comparison between this theory and some recent data shows general agreements in both level and angular trends, indicating promise in the use of the developed scatter model for explaining vegetation scatter.

Dynamics of propagation of radiation through random media: Slow or fast, weak or strong permittivity fluctuations and coupling of modes

We propose a unified treatment for the description of the statistical properties of radiation propagating through random media (weakly or strongly inhomogeneous) with slow or fast, weak or strong permittivity fluctuations including the coupling of modes and lossy mechanism. The coupling of modes is described with the help of a diagonalization procedure of the Hamiltonian and it is particularly considerable in the case of strong fluctuations in strongly inhomogeneous media. The rotating terms between radiation and the reservoir system are also taken into account. The Heisenberg, master and Fokker-Planck equations are obtained and their solutions are used to derive the quantum antinormal characteristic function and the corresponding quasidistribution and to discuss the photocounting statistics of radiation.