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Analysis Of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps, Armando Bazzani, Christopher Frye, Massimo Giovannozzi, Cédric Hernalsteens
Analysis Of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps, Armando Bazzani, Christopher Frye, Massimo Giovannozzi, Cédric Hernalsteens
Faculty Bibliography 2010s
Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinear resonances and slow time variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These …
The Heisenberg Relation - Mathematical Formulations, Richard V. Kadison, Zhe Liu
The Heisenberg Relation - Mathematical Formulations, Richard V. Kadison, Zhe Liu
Faculty Bibliography 2010s
We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Attractive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Attractive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation (NLS) modeling attractive Bose-Einstein condensates (BECs) in a small potential are obtained via a form of nonlinear perturbation. The focus here is on perturbations to the bright soliton solutions due to small potentials which either confine or repel the BECs: under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of the bright solitons. Importantly, we do not need to assume that the nonlinearity is small, as we perform a sort of nonlinear perturbation by allowing the zeroth-order perturbation term to be governed by a …
Stationary Solutions For The 2+1 Nonlinear Schrodinger Equation Modeling Bose-Einstein Condensates In Radial Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 2+1 Nonlinear Schrodinger Equation Modeling Bose-Einstein Condensates In Radial Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 2 + 1 cubic nonlinear Schrodinger equation modeling Bose-Einstein condensates (BEC) in a small potential are obtained via a form of perturbation. In particular, perturbations due to small potentials which either confine or repel the BECs are studied, and under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of radial BEC solutions. Numerical results are also provided for regimes where perturbative results break down (i.e., the large-potential regime). Both repulsive and attractive BECs are considered under this framework. Solutions for many specific confining potentials of physical relevance to experiments on BECs …
A Squeeze-Like Operator Approach To Position-Dependent Mass In Quantum Mechanics, Héctor M. Moya-Cessa, Francisco Soto-Eguibar, Demetrios N. Christodoulides
A Squeeze-Like Operator Approach To Position-Dependent Mass In Quantum Mechanics, Héctor M. Moya-Cessa, Francisco Soto-Eguibar, Demetrios N. Christodoulides
Faculty Bibliography 2010s
We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schrodinger equation may then be applied to find the respective eigenvalues and eigenfunctions. As an example, we consider a position-dependent-mass that leads to the integrable Morse potential and therefore to well-known solutions.
Continuous And Discrete Schrodinger Systems With Parity-Time-Symmetric Nonlinearities, Amarendra K. Sarma, Mohammad-Ali Miri, Ziad H. Musslimani, Demetrios N. Christodoulides
Continuous And Discrete Schrodinger Systems With Parity-Time-Symmetric Nonlinearities, Amarendra K. Sarma, Mohammad-Ali Miri, Ziad H. Musslimani, Demetrios N. Christodoulides
Faculty Bibliography 2010s
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a discretized version of this PT-nonlinear Schrodinger equation on a lattice. When only two elements are involved, by obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry-breaking conditions. This arrangement is unique in the sense that the exceptional points are …
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Repulsive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Repulsive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder
Faculty Bibliography 2010s
Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation modeling repulsive Bose-Einstein condensates (BEC) in a small potential are obtained through a form of nonlinear perturbation. In particular, for sufficiently small potentials, we determine the perturbation theory of stationary solutions, by use of an expansion in Jacobi elliptic functions. This idea was explored before in order to obtain exact solutions [Bronski, Carr, Deconinck, and Kutz, Phys. Rev. Lett. 86, 1402 (2001)], where the potential itself was fixed to be a Jacobi elliptic function, thereby reducing the nonlinear ODE into an algebraic equation, (which could be easily solved). However, …
Scaling Laws And Accurate Small-Amplitude Stationary Solution For The Motion Of A Planar Vortex Filament In The Cartesian Form Of The Local Induction Approximation, Robert A. Van Gorder
Scaling Laws And Accurate Small-Amplitude Stationary Solution For The Motion Of A Planar Vortex Filament In The Cartesian Form Of The Local Induction Approximation, Robert A. Van Gorder
Faculty Bibliography 2010s
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrodinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and …
Unifying Model Of Driven Polymer Translocation, T. Ikonen, A. Bhattacharya, T. Ala-Nissila, W. Sung
Unifying Model Of Driven Polymer Translocation, T. Ikonen, A. Bhattacharya, T. Ala-Nissila, W. Sung
Faculty Bibliography 2010s
We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by …
Spectral Analysis Of Certain Schrodinger Operators, Mourad E.H. Ismail, Erik Koelink
Spectral Analysis Of Certain Schrodinger Operators, Mourad E.H. Ismail, Erik Koelink
Faculty Bibliography 2010s
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages].
Orthogonal Basic Hypergeometric Laurent Polynomials, Mourad E.H. Ismail
Orthogonal Basic Hypergeometric Laurent Polynomials, Mourad E.H. Ismail
Faculty Bibliography 2010s
The Askey-Wilson polynomials are orthogonal polynomials in x = cos theta, which are given as a terminating (4)phi(3) basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z = e(i theta), which are given as a sum of two terminating (4)phi(3)'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single (4)phi(3)'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke …
Unstaggered-Staggered Solitons In Two-Component Discrete Nonlinear Schrodinger Lattices, Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
Unstaggered-Staggered Solitons In Two-Component Discrete Nonlinear Schrodinger Lattices, Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
Faculty Bibliography 2010s
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrodinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite …
Exact Solution For The Self-Induced Motion Of A Vortex Filament In The Arc-Length Representation Of The Local Induction Approximation, Robert A. Van Gorder
Exact Solution For The Self-Induced Motion Of A Vortex Filament In The Arc-Length Representation Of The Local Induction Approximation, Robert A. Van Gorder
Faculty Bibliography 2010s
We review two formulations of the fully nonlinear local induction equation approximating the self-induced motion of the vortex filament (in the local induction approximation), corresponding to the Cartesian and arc-length coordinate systems. The arc-length representation put forth by Umeki [Theor. Comput. Fluid Dyn. 24, 383 (2010)] results in a type of 1 + 1 derivative nonlinear Schrodinger (NLS) equation describing the motion of such a vortex filament. We obtain exact stationary solutions to this derivative NLS equation; such exact solutions are a rarity. These solutions are periodic in space and we determine the nonlinear dependence of the period on the …
Morphologies From Slippery Ballistic Deposition Model: A Bottom-Up Approach For Nanofabrication, Anthony Robledo, Christopher N. Grabill, Stephen M. Kuebler, Aniruddha Dutta, Helge Heinrich, Aniket Bhattacharya
Morphologies From Slippery Ballistic Deposition Model: A Bottom-Up Approach For Nanofabrication, Anthony Robledo, Christopher N. Grabill, Stephen M. Kuebler, Aniruddha Dutta, Helge Heinrich, Aniket Bhattacharya
Faculty Bibliography 2010s
We report pattern formation using a slippery ballistic deposition (SBD) model where growth germinates from a single site or from sites distributed periodically on a lattice. By changing the sticking probability p(s) and choosing systems with different lattice constants and symmetries, we demonstrate that a variety of patterns can be generated. These patterns can be further used as scaffolds for nanofabrication. We also demonstrate that by choosing a lateral sticking probability p(l) at the base that is different than p(s), one can control both the early and late time morphologies originating from a seed. Furthermore, we indicate a possible generalization …
Dispersion Relation On The Kerr Constant Of A Polymer-Stabilized Optically Isotropic Liquid Crystal, Meizi Jiao, Jin Yan, Shin-Tson Wu
Dispersion Relation On The Kerr Constant Of A Polymer-Stabilized Optically Isotropic Liquid Crystal, Meizi Jiao, Jin Yan, Shin-Tson Wu
Faculty Bibliography 2010s
The dispersion relation on the Kerr constant (K) of a polymer-stabilized isotropic phase (PSIP) liquid-crystal (LC) composite is investigated. Our experimental results show that K decreases as the wavelength (lambda) increases. The single-band birefringence dispersion model is used to fit the lambda K values of the PSIP LC composite. Very good agreement between the experiment and physical model is obtained.
Polymer Translocation Induced By A Bad Solvent, Christopher Lörscher, Tapio Ala-Nissila, Aniket Bhattacharya
Polymer Translocation Induced By A Bad Solvent, Christopher Lörscher, Tapio Ala-Nissila, Aniket Bhattacharya
Faculty Bibliography 2010s
We study polymer translocation through a nanopore subject to conformational differences created by putting two different solvents at the cis and trans compartments using Langevin dynamics in three dimensions (3D). Initially a fraction of the chain is placed in a good solvent at the cis side and the rest of the chain at the trans side is immersed in a bad solvent where it forms a globule. We study several aspects of the translocating chain as a function of the strength of the interaction epsilon/k(B)T for the bad solvent, where the temperature T is kept below the Theta temperature for …
Out-Of-Equilibrium Characteristics Of A Forced Translocating Chain Through A Nanopore, Aniket Bhattacharya, Kurt Binder
Out-Of-Equilibrium Characteristics Of A Forced Translocating Chain Through A Nanopore, Aniket Bhattacharya, Kurt Binder
Faculty Bibliography 2010s
Polymer translocation through a nanopore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the cis and the trans side separately either as a function of the time during the translocation process or as as function of the monomer index m inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the …
Scale-Dependent Anisotropic Polarizability In Mesoscopic Structures, David Haefner, Sergey Sukhov, Aristide Dorgariu
Scale-Dependent Anisotropic Polarizability In Mesoscopic Structures, David Haefner, Sergey Sukhov, Aristide Dorgariu
Faculty Bibliography 2010s
Optical properties of inhomogeneous materials are, in general, scale dependent. We show that, when observed at mesoscopic scales, the local anisotropic polarizabilities depend on the volume of interaction, which may be limited by either the excitation field or material dimensions. We demonstrate the existence of a specific interaction length scale corresponding to the maximum degree of local anisotropy and discuss its relation to the detailed morphology of a disordered medium. Probing these mesoscopic scales provides information about the local structure and allows characterizing material systems that otherwise may appear similar.
Dynamics Of Entanglement Between A Quantum Dot Spin Qubit And A Photon Qubit Inside A Semiconductor High-Q Nanocavity, Hubert Pascal Seigneur, Gabriel Gonzalez, Michael Niklaus Leuenberger, Winston Vaughan Schoenfeld
Dynamics Of Entanglement Between A Quantum Dot Spin Qubit And A Photon Qubit Inside A Semiconductor High-Q Nanocavity, Hubert Pascal Seigneur, Gabriel Gonzalez, Michael Niklaus Leuenberger, Winston Vaughan Schoenfeld
Faculty Bibliography 2010s
We investigate in this paper the dynamics of entanglement between a QD spin qubit and a single photon qubit inside a quantum network node, as well as its robustness against various decoherence processes. First, the entanglement dynamics is considered without decoherence. In the small detuning regime (Delta = 78 mu eV), there are three different conditions for maximum entanglement, which occur after 71, 93, and 116 picoseconds of interaction time. In the large detuning regime (Delta = 1.5 meV), there is only one peak for maximum entanglement occurring at 625 picoseconds. Second, the entanglement dynamics is considered with decoherence by …
Two-Dimensional Blasius Viscous Flow Of A Power-Law Fluid Over A Semi-Infinite Flat Plane, Robert A. Van Gorder
Two-Dimensional Blasius Viscous Flow Of A Power-Law Fluid Over A Semi-Infinite Flat Plane, Robert A. Van Gorder
Faculty Bibliography 2010s
Analytic results are obtained for the similarity equation governing the two-dimensional Blasius viscous flow of a power-law fluid over a semi-infinite flat plane via Taylor series for small values of the independent similarity variable. Then, an analytic perturbative procedure is used to determine an approximate solution that exhibits the correct asymptotic behavior. This perturbation method allows for the computation of the shear stress at the wall, something which is impossible with a Taylor series approach. It is found that the perturbation solutions converge sufficiently rapidly; indeed, a first order approximation gives qualitatively accurate results. Furthermore, we employ the perturbation method …
Delta-Expansion Method For Nonlinear Stochastic Differential Equations Describing Wave Propagation In A Random Medium, Robert A. Van Gorder
Delta-Expansion Method For Nonlinear Stochastic Differential Equations Describing Wave Propagation In A Random Medium, Robert A. Van Gorder
Faculty Bibliography 2010s
We apply the delta-expansion method to nonlinear stochastic differential equations describing wave propagation in a random medium. In particular, we focus our attention on a model describing a nonlinear wave propagating in a turbulent atmosphere which has random variations in the refractive index (we take these variations to be stochastic). The method allows us to construct much more reasonable perturbation solutions with relatively few terms (compared to standard "small-parameter" perturbation methods) due to more accurate linearization used in constructing the initial approximation. We demonstrate that the method allows one to compute effective wave numbers more precisely than other methods applied …
Wave Functions And Energy Spectra For The Hydrogenic Atom In R-3 X M, Robert A. Van Gorder
Wave Functions And Energy Spectra For The Hydrogenic Atom In R-3 X M, Robert A. Van Gorder
Faculty Bibliography 2010s
We consider the hydrogenic atom in a space of the form R-3 x M, where M may be a generalized manifold obeying certain properties. We separate the solution to the governing time-independent Schrodinger equation into a component over R-3 and a component over M. Upon obtaining a solution to the relevant eigenvalue problems, we recover both the wave functions and energy spectrum for the hydrogenic atom over R-3 x M. We consider some specific examples of M, including the fairly simple D-dimensional torus T D and the more complicated Kahler conifold K in order to illustrate the method. In the …
Buckling Instability Of Lipid Tubules With Multibilayer Walls Under Local Radial Indentation, Yue Zhao, Linan An, Jiyu Fang
Buckling Instability Of Lipid Tubules With Multibilayer Walls Under Local Radial Indentation, Yue Zhao, Linan An, Jiyu Fang
Faculty Bibliography 2000s
The mechanical behavior of self-assembled lipid tubules is an important property which determines their suitability for technological applications. We study the instability of multibilayer lipid tubules (with wall thickness t and external radius R(ext)) beyond elastic response under local radial atomic force microscopy indentations. A discontinuity in force-distance curves associated with the buckling instability of lipid tubules is observed. The critical force at which lipid tubules undergo a buckling transition linearly scales as t/R(ext). In addition, a reduced critical buckling force is found to extend a distance of similar to 1 mu m from the end of lipid tubules.
Coupled Dipole Method For Modeling Optical Properties Of Large-Scale Random Media, S. Sukhov, D. Haefner, A. Dogariu
Coupled Dipole Method For Modeling Optical Properties Of Large-Scale Random Media, S. Sukhov, D. Haefner, A. Dogariu
Faculty Bibliography 2000s
We present an extension of the coupled dipole approximation technique to model optical properties of large-scale slabs of homogeneous and inhomogeneous materials. This method is based on a modification of the Green's function to take into account the interaction between dipoles located at arbitrary distances within the slab. This method allows modeling of various aspects of the structural morphology of composite materials, including component size and spatial distribution as well as surface roughness effects. Our procedure provides an adequate description of far-field optical properties such as the specular and diffuse reflection of light.
Elastic Modulus Of Viral Nanotubes, Yue Zhao, Zhibin Ge, Jiyu Fang
Elastic Modulus Of Viral Nanotubes, Yue Zhao, Zhibin Ge, Jiyu Fang
Faculty Bibliography 2000s
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5 nm indentation depths and Hertz theory in 1.5 nm indentation depths. The derived radial Young's modulus of TMV nanotubes is 0.92 +/- 0.15 GPa from finite-element analysis and 1.0 +/- 0.2 GPa from the Hertz model, which are comparable with the reported axial Young's modulus of 1.1 GPa [Falvo et al., Biophys. …
Self-Bending Of Dark And Gray Photorefractive Solitons, M. I. Carvalho, M. Facão, D. N. Christodoulides
Self-Bending Of Dark And Gray Photorefractive Solitons, M. I. Carvalho, M. Facão, D. N. Christodoulides
Faculty Bibliography 2000s
We investigate the effects of diffusion on the evolution of steady-state dark and gray spatial solitons in biased photorefractive media. Numerical integration of the nonlinear propagation equation shows that the soliton beams experience a modification of their initial trajectory, as well as a variation of their minimum intensity. This process is further studied using perturbation analysis, which predicts that the center of the optical beam moves along a parabolic trajectory and, moreover, that its minimum intensity varies linearly with the propagation distance, either increasing or decreasing depending on the sign of the initial transverse velocity. Relevant examples are provided.
Power-Law Eigenvalue Density, Scaling, And Critical Random-Matrix Ensembles, K. A. Muttalib, Mourand E. H. Ismail
Power-Law Eigenvalue Density, Scaling, And Critical Random-Matrix Ensembles, K. A. Muttalib, Mourand E. H. Ismail
Faculty Bibliography 2000s
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a scaling appropriate for such power-law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.
Polarization-Induced Spectral Changes On Propagation Of Stochastic Electromagnetic Beams, Jixiong Pu, Olga Korotkova, Emil Wolf
Polarization-Induced Spectral Changes On Propagation Of Stochastic Electromagnetic Beams, Jixiong Pu, Olga Korotkova, Emil Wolf
Faculty Bibliography 2000s
It was shown some years ago that the spectrum of a stochastic scalar field depends not only on the source spectrum but also on the degree of coherence of the source. In this paper we show that there are electromagnetic fields for which not only the state of coherence of the source, but also its degree of polarization affect the spectrum of the radiated field. We illustrate the analysis by diagrams which show the far-zone spectra of some stochastic electromagnetic beams generated by sources of different states of coherence and different degrees of polarization. The spectra of the radiated field …
Optical Breathers In Nonlinear Anisotropic And Dispersive Media, G. T. Adamashvili, D. J. Kaup
Optical Breathers In Nonlinear Anisotropic And Dispersive Media, G. T. Adamashvili, D. J. Kaup
Faculty Bibliography 2000s
Anisotropic crystals containing impurity atoms, when the principal optical axis of the uniaxial crystal and the vector of electrical dipole moment of the impurity atoms are perpendicular to each other and are directed along different crystallographic axes, are shown to have three different mechanisms of the formation of breathers depending on the direction of the wave propagation and on the symmetry of the medium. Explicit analytic expressions for the parameters of breathers and the effective nonlinear susceptibilities for extraordinary waves are obtained. All uniaxial crystals with quadratic susceptibilities can be divided into three different groups, according to the crystal classes. …
Near-Field Characterization Of Effective Optical Interfaces, A. Apostol, D. Haefner, A. Dogariu
Near-Field Characterization Of Effective Optical Interfaces, A. Apostol, D. Haefner, A. Dogariu
Faculty Bibliography 2000s
The properties of many heterogeneous media depend on both the surface roughness and the local variations of the optical properties. An effective optical interface is usually invoked to describe the characteristics of such media. Using approaches specific to near-field optics, the two influences can be decoupled and a quantitative assessment of their contributions can be performed. It is also shown that a discrete random-walk model can be used to determine the magnitude of the dielectric constant fluctuations at subwavelength scales which, in turn, describe the morphology of optically inhomogeneous media.