Vadim A. Markel

Coupled-dipole Approach to Scattering of Light from a One-dimensional Periodic Dipole Structure

Abstract The coupled-dipole approximation is used to study theoretically the scattering of light from an infinite linear one-dimensional chain of monomers interacting via dipole fields. It is shown that if the distance between monomers is much less then λ, the shift of optical resonances is governed by only interaction in the near-zone, and the spectral width of resonances, on the contrary, by interaction in all zones (near, intermediate and far-zone). The condition under which the developed theory yields correct depolarization coefficients of a dielectric cylinder in a quasi-static case is found. The extinction cross-section is calculated as a function of driving frequency.

Divergence of dipole sums and the nature of non-Lorentzian exponentially narrow resonances in one-dimensional periodic arrays of nanospheres

The origin and properties of non-Lorentzian spectral lines in linear chains of nanospheres are discussed. The lines are shown to be super-exponentially narrow with the characteristic width exp[−C(h/a)3] where C is a numerical constant, h the spacing between the nanospheres in the chain and a the sphere radius. The fine structure of these spectral lines is also investigated.

Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas.

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. Inversion formulas based on the Fourier-Laplace transform are used to establish the existence and uniqueness of solutions to this problem in planar, cylindrical, and spherical geometries.

Imaging complex structures with diffuse light.

We use diffuse optical tomography to quantitatively reconstruct images of complex phantoms with millimeter sized features located centimeters deep within a highly-scattering medium. A non-contact instrument was employed to collect large data sets consisting of greater than 10(7) source-detector pairs. Images were reconstructed using a fast image reconstruction algorithm based on an analytic solution to the inverse scattering problem for diffuse light.

Propogation of Surface Plasmons in Ordered and Disordered Chains of Metal Nanospheres

We describe two types of surface plasmons in ordered and disordered chains. The second kind is mediated by far-field interaction and is affected by Ohmic and radiative losses much less than the first kind.

Inverse problem in optical diffusion tomography. II. Role of boundary conditions

We consider the inverse problem of reconstructing the absorption and diffusion coefficients of an inhomogeneous highly scattering medium probed by diffuse light. The role of boundary conditions in the derivation of Fourier-Laplace inversion formulas is considered. Boundary conditions of a general mixed type are discussed, with purely absorbing and purely reflecting boundaries obtained as limiting cases. Four different geometries are considered with boundary conditions imposed on a single plane and on two parallel planes and on a cylindrical and on a spherical surface.

Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition

We continue our study of the inverse scattering problem for diffuse light. In particular, we derive inversion formulas for this problem that are based on the functional singular-value decomposition of the linearized forward-scattering operator in the slab, cylindrical, and spherical geometries. Computer simulations are used to illustrate our results in model systems.

Modified spherical harmonics method for solving the radiative transport equation

A new effective approach to solving the three-dimensional radiative transport equation with an arbitrary phase function is proposed. The solution depends on eigenvectors and eigenvalues of several symmetrical tridiagonal matrices of infinite size. The matrices must be truncated and diagonalized numerically. Then, given eigenvectors and eigenvalues of these matrices, the dependence of the solution on position and direction is found analytically. The approach is based on expanding the angular part of the specific intensity in q-dependent spherical functions for each spatial Fourier component characterized by the vector q. Apart from the truncation of the matrices, no other approximations are made.

Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10(8) source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly scattering medium containing absorbing inhomogeneities.

Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas.

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.