George Y. Panasyuk

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.

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.

Radiative transport equation in rotated reference frames

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function with the constraint that it depends only on the angle between the angular variables and . This assumption corresponds to spherically symmetric (on average) random medium constituents. Boundary conditions are considered in the slab and half-space geometries. The approach developed in this paper is spectral. It allows for the expansion of the solution to the RTE in terms of analytical functions of angular and spatial variables to relatively high orders. The coefficients of this expansion must be computed numerically. However, the computational complexity of this task is much smaller than in the standard method of spherical harmonics. The solutions obtained are especially convenient for solving inverse problems associated with radiative transfer.

The Green's function for the radiative transport equation in the slab geometry

The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined from the boundary conditions, must also be computed. The Greens function for the radiative transport equation is computed and the results are compared with diffusion approximation and Monte Carlo simulations. We find that the diffusion approximation is not quite correct inside the slab, even when the light emitted from the slab is well described by the diffusion approximation. The solutions we obtain are especially convenient for solving inverse problems associated with radiative transport.

Fluorescent optical tomography with large data sets

In recent years, optical tomography (OT) of highly scattering biological samples has increasingly relied on noncontact CCD-based imaging devices that can record extremely large data sets, with up to 10(9) independent measurements per sample. Reconstruction of such data sets requires fast algorithms. The latter have been developed and applied experimentally in our previous work to imaging of the intrinsic absorption coefficient of highly scattering media. However, it is widely recognized that the use of fluorescent contrast agents in OT has the potential to significantly enhance the technique. We show that the algorithms previously developed by us can be modified to reconstruct the concentration of fluorescent contrast agents.

Classical Theory of Optical Nonlinearity in Conducting Nanoparticles

We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field.

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian’s approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian’s approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable to or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespective of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. Lett. 100, 47402 (2008)].

Superresolution and corrections to the diffusion approximation in optical tomography

We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard integral equations of scattering theory within the diffusion approximation to the radiative transport equation.

Short-distance expansion for the electromagnetic half-space Green's tensor: general results and an application to radiative lifetime computations

We obtain a short-distance expansion for the half-space, frequency domain electromagnetic Greens tensor. The small parameter of the theory is , where ω is the frequency, 1 is the permittivity of the upper half-space, in which both the source and the point of observation are located, and which is assumed to be transparent, c is the speed of light in vacuum and is a characteristic length, defined as the distance from the point of observation to the reflected (with respect to the planar interface) position of the source. In the case when the lower half-space (the substrate) is characterized by a complex permittivity 2, we compute the expansion to third order. For the case when the substrate is a transparent dielectric, we compute the imaginary part of the Greens tensor to seventh order. The analytical calculations are verified numerically. The practical utility of the obtained expansion is demonstrated by computing the radiative lifetime of two electromagnetically interacting molecules in the vicinity of a transparent dielectric substrate. The computation is performed in the strong interaction regime when the quasi-particle pole approximation is inapplicable. In this regime, the integral representation for the half-space Greens tensor is difficult to use while its electrostatic limiting expression is grossly inadequate. However, the analytical expansion derived in this paper can be used directly and efficiently. The results of this study are also relevant to nano-optics and near-field imaging, especially when tomographic image reconstruction is involved.

Phaseless Three-Dimensional Optical Nanoimaging

We propose a method for optical nanoimaging in which the structure of a three-dimensional inhomogeneous medium may be recovered from far-field power measurements. Neither phase control of the illuminating field nor phase measurements of the scattered field are necessary. The method is based on the solution to the inverse scattering problem for a system consisting of a weakly-scattering dielectric sample and a strongly-scattering nanoparticle tip. Numerical simulations are used to illustrate the results.