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Author(s): Iurov, A; Huang, D; Gumbs, G; Pan, W; Maradudin, AA | Abstract: The effects of induced optical polarization by Dirac electrons in graphene on the hybridization of radiative and evanescent fields are found. Such effects result in a localized polarization field which significantly modifies an incident surface-plasmon-polariton (SPP) field. This yields a high sensitivity to local dielectric environments and provides an investigative tool for molecules or proteins selectively bound with carbons. A scattering matrix is utilized with varied frequencies in the vicinity of the surface-plasmon (SP) resonance for the increase, decrease, and even a full suppression of the polarization field, which enables accurate effective-medium theories to be constructed for Maxwell-equation finite-difference time-domain methods. Moreover, double peaks in the absorption spectra for hybrid SP and graphene-plasmon modes are significant only with a large conductor plasma frequency, but are overshadowed by a round SPP peak at a small plasma frequency as the graphene is placed close to the conductor surface. These resonant absorptions facilitate polariton-only excitations, leading to polariton condensation for a threshold-free laser.

It is shown that the phenomenon of self-induced transparency can occur when a coherently excited propagating phonon mode has a frequency that is equal to the difference between the frequencies of two flat phonon branches. The nonlinear coupling is due to cubic anharmonicity. Using a quantum kinetic-type approach, the Maxwell-Bloch equations are derived for such systems. Including third-order correlations in this approach, the intrinsic damping of parametrically excited two-phonon oscillations is investigated, that lead to phonon squeezing. In addition, we analyze the resonant interaction of a coherently driven phonon mode with one flat branch of the phonon dispersion relation.

By using a finite-difference time-domain numerical method based on the numerical simulation of the excitation of an isolated eigenstate at a specific frequency by using an oscillating dipole embedded in a two-dimensional photonic crystal we have calculated both the eigenfrequencies and eigenfunctions of the localized defect modes induced by defect cylinders placed at the center or in interstitial positions within an otherwise perfect two-dimensional photonic crystal consisting of dielectric cylinders arrayed in a triangular lattice. In the case of a substitutional defect cylinder we have imposed boundary conditions appropriate to the irreducible representations of the ${C}_{6v}$ point group, and in addition to fully symmetric localized states of ${A}_{1}$ symmetry we have also found localized modes possessing ${A}_{2},$ ${B}_{1},$ and ${B}_{2}$ symmetry, and doubly degenerate modes of ${E}_{1}$ and ${E}_{2}$ symmetry. For defect rods placed in interstitial positions we have found localized modes that belong to the irreducible representations ${A}_{1},$ ${A}_{2},$ ${B}_{1},$ and ${B}_{2}$ of the ${C}_{2v}$ point group. We have also studied the effects of the geometrical and material parameters on the eigenfrequencies and eigenfunctions of the defect modes by varying the dielectric strength and/or radius of the defect rods. We have shown that the calculated eigenfrequencies obtained for a substitutional defect rod within the triangular lattice with lattice constant a whose radius ${r}_{d}$ is in the interval $0l{r}_{d}l0.5a$ are in good quantitative agreement with both the nondegenerate and degenerate modes obtained by the supercell method by Feng and Arakawa [Jpn. J. Appl. Phys. Part 2 36, 120(1997)].

The attenuation of Rayleigh waves due to their interaction with resonating structures randomly distributed on the surface of a semi-infinite elastic medium is calculated along with the Rayleigh wave frequency. The resonating structures are modeled by single oscillators coupled to the displacement field at the surface of the elastic medium. Using the coherent potential approximation, the dependence of the frequency and damping constant of the Rayleigh waves on wave vectors are determined for various values of the concentration of oscillators on the surface.

We consider the scattering of monochromatic and polychromatic light from a randomly rough dielectric film deposited on a planar, perfectly conducting surface. Setting up scattering integral equations with the image Green's-function technique, we develop improved Monte Carlo simulations and use them to investigate the as yet unstudied evolution of frequency and angular spectra of the scattered light on propagation from the near to the far zone. In the monochromatic case, we illustrate the disappearance of the evanescent component and the formation of coherent enhanced backscattering and satellite peaks with increasing distance from the surface. In the polychromatic case, we find that the scattering of light from a rough surface produces significant spectral changes, which tend to increase on propagation from the near to the far zone. Coherent features in the intensity of the scattered light (such as satellite peaks), whose angular positions are frequency dependent, are found to cause very pronounced spectral changes in the scattered radiation. Since the existence and intensity of these coherent features are determined by the shape of the power spectrum of the surface roughness, and by the spectrum of guided or surface waves in the scattering system, we conclude that the frequency spectrum of the scattered light in different zones provides rich and physically meaningful information about the scattering system.

A diagrammatic perturbation theory approach, based on a scalar wave treatment, is used to study the scattering of light of frequency \ensuremath{\omega} from a volume disordered dielectric medium. The dielectric medium is described by a position-dependent dielectric constant of the form $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})=\ensuremath{\epsilon}(\ensuremath{\omega})+\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r}),$ where $\ensuremath{\epsilon}(\ensuremath{\omega})$ does not depend on $\stackrel{\ensuremath{\rightarrow}}{r},$ and $\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})$ is a zero-mean Gaussian random process defined by $〈\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r})\ensuremath{\delta}\ensuremath{\epsilon}({r}^{\ensuremath{'}})〉={\ensuremath{\sigma}}^{2}\mathrm{exp}(\ensuremath{-}|\stackrel{\ensuremath{\rightarrow}}{r}\ensuremath{-}{r}^{\ensuremath{'}}{|}^{2}{/a}^{2}),$ where the angle brackets denote an average over the ensemble of realizations of $\ensuremath{\delta}\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{r}),$ a is the correlation length of the disorder, and $\ensuremath{\sigma}$ is the root mean square deviation of the dielectric constant from its average value $\ensuremath{\epsilon}(\ensuremath{\omega}).$ The speckle correlation function $C(\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k}|{q}^{\ensuremath{'}},{k}^{\ensuremath{'}})=〈[I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})\ensuremath{-}〈I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})〉][I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})\ensuremath{-}〈I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})]〉$ where $I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})$ is proportional to the differential-scattering coefficient for the scattering of light of incident wave vector $\stackrel{\ensuremath{\rightarrow}}{k}$ into light of wave vector $\stackrel{\ensuremath{\rightarrow}}{q}$ is computed. In these calculations the contributions associated with both ladder and maximally crossed diagrams are summed in a Feynman diagram treatment of the speckle correlator, in the approximation that only s-wave-scattering terms are retained. Results are presented for the differential-scattering coefficient of light scattered from the disordered medium, which displays the phenomenon of enhanced backscattering, and for the correlator C in the approximation where ${C=C}^{(1)}{+C}^{(10)}{+C}^{(1.5)}.$ The contribution ${C}^{(1)}$ is proportional to $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{-}{q}^{\ensuremath{'}}+{k}^{\ensuremath{'}})$ and describes the memory and time-reversed memory effects. ${C}^{(10)}$ is proportional to $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{k}+{q}^{\ensuremath{'}}\ensuremath{-}{k}^{\ensuremath{'}}),$ while ${C}^{(1.5)}$ is unrestricted in its dependence on $\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k},{q}^{\ensuremath{'}},{k}^{\ensuremath{'}}.$ The latter two contributions have recently been treated in the scattering of light from randomly rough surfaces, but have not been previously treated in the scattering of light by volume disordered media. A number of peaks associated with resonant processes are observed in ${C}^{(1.5)}$ considered as a function of the wave vectors of the incident and scattered light.

By using a finite-difference time-domain numerical method based on introducing an oscillating dipole at a proper position in a two-dimensional photonic crystal consisting of an array of dielectric cylinders, we numerically solve the inhomogeneous wave equation discretized in both space and time to calculate the eigenfrequency and the eigenfunction of a localized defect mode. We study the spatial distribution of the electric field and the radiated power associated with the defect modes produced by introducing a defect cylinder into an otherwise periodic two-dimensional triangular photonic crystal. We have obtained excellent agreement for the defect mode of ${A}_{1}$ symmetry created by removing a single cylinder from the center of the region of cylinders arrayed in a triangular lattice with the experimental result of Smith et al. [J. Opt. Soc. Am. B 10, 314 (1993)]. We have also examined systems in which defect states are introduced by varying the radius of a single cylinder and when both the dielectric strength and the radius of the defect cylinder are changed. The calculated values of the donor and acceptor levels associated with the exponentially decaying defect modes of ${A}_{1}$ symmetry induced by changing the radius are in good quantitative agreement with the nondegenerate donor and acceptor levels obtained by the supercell method within the plane-wave approach reported recently by Feng et al. [Jpn. J. Appl. Phys. 36, 120 (1997)].

A kinetic theory of the instability of homogeneous alloy growth with respect to fluctuations of alloy composition is developed. The growth mechanism studied is the step-flow growth of an alloy from the vapor on a surface vicinal to the (001) surface of a cubic substrate. The epitaxial growth implies that the adsorbed atoms migrate on the surface during the growth of each monolayer, and that their motion is ``frozen'' after the completion of the monolayer. ``Frozen'' fluctuations of alloy composition in all completed monolayers create, via a composition-dependent lattice parameter, an elastic strain that influences the migration of adatoms of the growing monolayer. The migration consists of diffusion- and strain-induced drift in an effective potential. For temperatures lower than a certain critical temperature ${T}_{c},$ strain-induced drift dominates diffusion and results in the kinetic instability of the homogeneous alloy growth. In an approximation linear in the fluctuation amplitude, the instability means the exponential increase of the fluctuation amplitude with the thickness of the epitaxial film. It is shown that the critical temperature of the kinetic instability ${T}_{c}$ increases with the increase of elastic effects. The wave vector ${\mathbf{k}}_{c}$ of the most unstable mode of composition fluctuations is determined by the interplay of the anisotropic elastic interaction and the anisotropic diffusion of the adatoms on a stepped vicinal surface. The direction of the wave vector ${\mathbf{k}}_{c}$ differs from the lowest-stiffness direction of the crystal. Regions in k space of both stable and unstable modes are found by model calculations.

We present an approach that allows calculating photonic band structures of electromagnetic waves propagating in periodic systems containing dispersive and highly absorptive materials characterized by a dielectric function, which is frequency dependent and has a non-negligible imaginary part. This method, which provides a complementary approach to that of the transfer-matrix method, is based on the use of a position-dependent dielectric function and the plane-wave technique. The use of the complex form of the dielectric function transforms Maxwell's equations into a generalized nonlinear eigenvalue problem. At low filling fractions of the dispersive and absorptive component (f\ensuremath{\leqslant}1%), the generalized eigenvalue problem is reduced to a problem of solving sets of simultaneous nonlinear equations which correspond to the diagonal terms of the matrix equation in the plane-wave representation, with the nondiagonal elements taken into account perturbatively. The resulting complex band structure yields, in addition to the dispersion curves, the attenuation of each mode as it propagates through the system. We first consider a model system represented by a one-dimensional (1D) periodic array of alternating layers of vacuum, and a metal characterized by the complex frequency-dependent dielectric function. To calculate the photonic band structure of this system we employ, in addition to the transfer-matrix method and our perturbative plane-wave approach, a standard linearization technique which solves the general nonlinear eigenvalue problem by the diagonalization of an equivalent, enlarged, matrix. We then apply both our perturbative plane-wave approach and the linearization scheme to obtain the photonic band structures of an infinite array of parallel, infinitely long metallic rods whose intersections with a perpendicular plane form a simple square lattice. The interesting features associated with the presence of dissipation displayed by the photonic band structures, such as an asymmetric behavior of the absorption coefficient and the lifetime of each electromagnetic wave for wave vectors near the Brillouin-zone boundaries, the splitting of the lifetimes of degenerate modes, and the different dependences of the real and imaginary parts of the complex photonic band structure on the polarization of the electromagnetic waves in 2D systems, are discussed.

By the use of the plane-wave method, we calculate the photonic band structure for electromagnetic waves of E and H polarization propagating in a system consisting of an infinite array of identical, infinitely long, parallel cylinders of circular cross section, embedded in vacuum, whose intersections with a perpendicular plane form a square or triangular lattice. The cylinders are fabricated from GaAs, which represents a cubic, polar crystal material, containing two atoms in a primitive unit cell, for which the dielectric function has the form \ensuremath{\epsilon}(\ensuremath{\omega})=${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$ (${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}^{2g}$-${\mathrm{\ensuremath{\omega}}}^{2}$ )/(${\mathrm{\ensuremath{\omega}}}_{\mathrm{T}}^{2g}$-${\mathrm{\ensuremath{\omega}}}^{2}$ ), where ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$ is the optical frequency dielectric constant, while ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathrm{T}}$ are the frequencies of the longitudinal optical and transverse optical vibration modes of infinite wavelength, respectively. For electromagnetic waves of both polarizations the problem of obtaining the photonic band structure is reduced to the solution of a generalized eigenvalue problem. In comparison with the dispersion curves of electromagnetic waves in vacuum, the photonic band structures are the most significantly affected by the particular form of the dielectric function we have assumed for frequencies in the vicinity of the polariton gap ${\mathrm{\ensuremath{\omega}}}_{\mathrm{T}}$ ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ . For small filling fractions of the GaAs cylinders the photonic band structure for each polarization, except within the frequency range of the polariton gap, is a slightly perturbed version of the dispersion curves of electromagnetic waves in vacuum. For higher values of the filling fraction the dispersion curves deviate substantially from the dispersion curves of electromagnetic waves in vacuum within a broader frequency range, and in the case of E polarization, the photonic band structures reveal the existence of absolute band gaps. As the most striking feature, the calculated photonic band structures yield additional, nearly dispersionless bands that for waves of both polarizations occur at and below ${\mathrm{\ensuremath{\omega}}}_{\mathrm{T}}$ and in the case of H polarization occur also within the frequency range ${\mathrm{\ensuremath{\omega}}}_{\mathrm{T}}$ ${\mathrm{\ensuremath{\omega}}}_{\mathrm{L}}$ where \ensuremath{\epsilon}(\ensuremath{\omega}) is negative. The results for H polarization and small filling fractions of the GaAs cylinders are reproduced by an approach in which the zeros of a determinant are sought. A possible origin of the flat bands obtained in this polarization by both approaches is discussed.

The reduced Rayleigh equation for the scattering of a surface plasmon polariton incident normally on a one-dimensional ridge or groove on an otherwise planar metal surface is solved by a purely numerical approach. The solution is used to calculate the reflectivity and transmissivity of the surface plasmon polariton and its conversion into volume electromagnetic waves in the vacuum above the metal surface. The results obtained are compared with those of earlier calculations of these quantities.

In this paper we present a critical comparison of calculations of phonon-dispersion curves for aluminum, based on pseudopotential and empirical force-constant methods. The former method is based on both perturbative and nonperturbative evaluations of the total energy of the crystal. In the perturbative approach the total energy is evaluated to second order in the electron-ion interaction with a local pseudopotential. In the nonperturbative approach the electron-ion interaction is treated exactly using a nonlocal ab initio pseudopotential. In the empirical force-constant method the total energy is represented by a sum of two-body and three-body terms, the latter being restricted to interactions among triplets of nearest neighbors and of nearest and next-nearest neighbors

The spectral shape of the displacement correlation function of a quantum chain of atoms interacting through a nearest-neighbor potential is approached at all temperatures and wave vectors by the evaluation of the related frequency moments. The latter ones have been obtained, until the sixth one, by using an effective potential derived by a variational approach to the path-integral formulation of the quantum statistical mechanics. This method allows us to reduce the computation of quantum averages of time-independent functions to classical-like space integrals, so that all the tools developed for classical calculations can be again applied. Explicit results for the Lennard-Jones potential are presented and tested against extensive quantum path-integral Monte Carlo simulations, where an improved Trotter extrapolation procedure is also used. The good agreement between the two calculations confirms the apparent strong simplification introduced by the variational method in the evaluation of the quantum averages when the quantum coupling can be treated semiclassically. The reconstruction of the dynamical behavior of the system through the knowledge of a sufficient number of moments appears realistic. Explicit spectral shapes of Lennard-Jones chains are given, showing the relevance of the quantum effects.

By the use of a position-dependent dielectric constant and the plane-wave method, we have calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic array of parallel dielectric rods of circular cross section, whose intersections with a perpendicular plane form a triangular lattice. The rods are embedded in a background medium with a different dielectric constant. The electromagnetic waves are assumed to propagate in a plane perpendicular to the rods, and two polarizations of the waves are considered. Absolute gaps in the resulting band structures are found for waves of both polarizations, and the dependence of the widths of these gaps on the ratio of the dielectric constants of the rods and of the background, and on the fraction of the total volume occupied by the rods, is investigated.

Crystalline nitrous oxide is used as a prototype system for analyzing the dynamics of bound states in orientationally disordered materials and to study the combined effects of anharmonicity and disorder. In that system a frozen-in disorder occurs with respect to head-tail arrangements of the molecules. When the resonance dipole-dipole intermolecular interactions are predominant, the disorder is of Ising type for the vibron states, but in the harmonic approximation the eigenstates are still given in terms of Bloch waves. It is shown that an intramolecular cubic anharmonicity breaks down the translational invariance of the harmonic Hamiltonian. This anharmonic term is enhanced by a quasiresonance between the ${\ensuremath{\nu}}_{1}$ intramolecular mode and the overtone 2${\ensuremath{\nu}}_{2}$ (Fermi resonance) and leads to two hybrid bound states ${\ensuremath{\nu}}^{+}$ and ${\ensuremath{\nu}}^{\mathrm{\ensuremath{-}}}$. The usual solutions for this Fermi-resonance problem in ordered crystals are no longer valid and we discuss a perturbative approach for the disordered configurations. Assuming that the ${\mathrm{N}}_{2}$O crystal is totally disordered, expressions for the polarized Raman band shapes of the two bound states ${\ensuremath{\nu}}^{+}$ and ${\ensuremath{\nu}}^{\mathrm{\ensuremath{-}}}$ are obtained. The Raman response of the bound states mainly reflects the density of states. However, the assumption of a partially coherent part in the Raman intensity is necessary to obtain a good agreement with the experimental data.

A theoretical study is presented of the reflection of acoustic waves from a surface of a semi-infinite elastic medium covered by a random distribution of resonating structures. The latter are modeled by single oscillators coupled to the displacement field at the surface of the elastic medium. The incoherent part of the differential reflection coefficient of this system has been calculated using the coherent potential approximation that has been extended to account for effects of weak localization. When certain resonance conditions are satisfied, a strong enhancement of the backscattering peak has been found in the incoherent scattering of acoustic waves.

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on the dimensionality of inhomogeneities modulating the period of the superlattice are studied. The cases of one- and three-dimensional modulations, as well as modulation by a mixture of inhomogeneities of both of these dimensionalities, are considered. The correlation function of the superlattice K(r) has the form of a product of the same periodic function and a decreasing function that is significantly different for these different cases. For r→∞, the decreasing function goes to zero for the one-dimensional inhomogeneities and to a nonzero asymptote for the three-dimensional ones. Consequently, the transition from the disordered to ordered states is accompanied in the three-dimensional case not only by an increase of the correlation radius as in the one-dimensional case, but also by a change in the relationship between the volumes of the superlattices with finite and infinite correlation radii. The decreasing part of the correlation function for the mixture of inhomogeneities of different dimensionalities has the form of a product of the decreasing parts of the correlation functions of the components of the mixture. This leads to the nonadditivity of the contributions of the components of different dimensionalities to the resulting modification of the parameters of the wave spectrum that are due to the inhomogeneities (the damping of waves for the mixture of these components is smaller than the sum of the dampings of the components, the maximum gap in the spectrum corresponds to the simultaneous presence of both components, and so on).

By the use of the homogeneous form of the reduced Rayleigh equation for the electric field above and on the rough surface of a metal in contact with a vacuum, we have obtained the dispersion relation for surface-plasmon polaritons propagating across such an interface. This dispersion relation is exact within the domain of validity of the Rayleigh hypothesis upon which it is based. It is applied to a two-dimensional vacuum-metal interface formed from a periodic array of hemiellipsoids on the planar surface of the same metal. Nonperturbative numerical solutions of the resulting dispersion relation are obtained for wave vectors along the boundary of the irreducible element of the first Brillouin zone for a square and a triangular array of the hemiellipsoids. Absolute band gaps in the frequency spectrum, where the density of states vanishes, are found, and the dependence of the position and width of these gaps on various geometrical parameters of each array is investigated. We also study the influence of radiative damping and ohmic losses on the dispersion curves. Our theoretical results are compared with existing experimental data.

We study the scattering of an electromagnetic wave from a cylinder of infinite length fabricated from a combined split-ring resonator (SRR) and thin metal wire medium that is characterized by an effective frequency-dependent permittivity ∈ e f f (ω) and permeability μ e f f (ω) that can both be negative in a certain frequency region, and thus constitutes a left-handed (LH) metamaterial. We evaluate the scattering width of the cylinder in terms of the most general form of the Mie coefficients a n ,b n that takes into account the magnetic effects through the effective refractive index neff(ω)= √∈ e f f (ω) √μ e f f (ω). Incident waves of both E polarization (where the electric field is parallel to the axis of the cylinder) and H polarization (where the magnetic field is parallel to the axis of the cylinder) are considered. We find that in the case when the magnetic field is perpendicular to the plane of the SRR, the scattering width as a function of the frequency of the incident wave reveals the resonances of the Mie coefficients a n and b n , for both E- and H-polarized incident waves These peaks occur in the frequency range where the effective refractive index is negative, and they arise from modes that propagate with a negative group velocity. This behavior is consistent with the results of transfer-matrix calculations and transmission experiments on two-dimensional LH metamaterials, which show that the medium becomes transparent to the electromagnetic radiation in this frequency region.

To describe a partially randomized multilayer structure with arbitrary thicknesses of the interfaces between layers, we introduce a model in which the dependence of a material parameter along the axis of such a superlattice is described by a Jacobian elliptic sine function with a random spatial modulation of its period. Both one- and three-dimensional inhomogeneities of the period are considered. We develop the correlation function for this model, and investigate the dispersion law and damping of averaged waves in this superlattice. The dependencies of the widths of the gaps in the spectrum and the damping at the boundaries of all odd Brillouin zones, on the thicknesses of the interfaces, and on the dimensionality, intensity, and correlation wave number of the inhomogeneities are found. It is shown that experimental investigations of the widths of the gaps and damping for several Brillouin zones could permit, in principle determining all parameters of the superlattice as well as the parameters of the inhomogeneities from these spectral characteristics.

Two computer simulation studies of the speckle correlations in the light scattered from a volume disordered dielectric medium consisting of a random array of dielectric spheres are made. In both studies light is treated in the scalar wave approximation, and the wavelength of the light is taken to be much greater than the radius of the dielectric spheres. In one study, the scattering medium is formed by placing dielectric spheres of radius R and dielectric constant $\ensuremath{\epsilon}$ randomly in space. The spheres occupy space uniformly, under the provision that no two spheres overlap. In a second study, the scattering medium is formed by placing dielectric spheres of radius R and dielectric constant $\ensuremath{\epsilon}$ randomly on the vertices of a simple cubic lattice so that a fixed fraction of the vertices is occupied by the spheres. The lattice constant of the simple cubic lattice is taken to be of the order of magnitude of the wavelength of light in vacuum. In both studies the the volume filling fraction is the same, and the region outside the spheres is vacuum. The field equations are integrated numerically to determine the scattered fields, and these fields are used to calculate the speckle correlation function defined by $C(\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k}|{q}^{\ensuremath{'}},{k}^{\ensuremath{'}})=〈[I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})\ensuremath{-}〈I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})〉][I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})\ensuremath{-}〈I({q}^{\ensuremath{'}}|{k}^{\ensuremath{'}})]〉.$ Here $I(\stackrel{\ensuremath{\rightarrow}}{q}|\stackrel{\ensuremath{\rightarrow}}{k})$ is proportional to the differential scattering coefficient for the elastic scattering of light of wave vector $\stackrel{\ensuremath{\rightarrow}}{k}$ into light of wave vector $\stackrel{\ensuremath{\rightarrow}}{q},$ and $〈〉$ indicates an average over an ensemble of random systems. Results are presented for $C(\stackrel{\ensuremath{\rightarrow}}{q},\stackrel{\ensuremath{\rightarrow}}{k}|{q}^{\ensuremath{'}},{k}^{\ensuremath{'}})$ with particular attention paid to regions of $\stackrel{\ensuremath{\rightarrow}}{k}$ space in which either the ${C}^{(1)}$ or ${C}^{(10)}$ contributions dominate the correlator.

We study by numerical simulations the scattering of $s$-polarized light from a rough dielectric film deposited on the planar surface of a semi-infinite perfect conductor. The dielectric film is allowed to be either active or passive, situations that we model by assigning negative and positive values, respectively, to the imaginary part $\epsilon_2$ of the dielectric constant of the film. We study the reflectance ${\cal R}$ and the total scattered energy ${\cal U}$ for the system as functions of both $\epsilon_2$ and the angle of incidence of the light. Furthermore, the positions and widths of the enhanced backscattering and satellite peaks are discussed. It is found that these peaks become narrower and higher when the amplification of the system is increased, and that their widths scale linearly with $\epsilon_2$. The positions of the backscattering peaks are found to be independent of $\epsilon_2$, while we find a weak dependence on this quantity in the positions of the satellite peaks., Comment: Revtex, 9 pages, 9 figures