Arnold D. Kim

Characterization of space-time focusing in time-reversed random fields

This paper proposes various metrics to characterize space-time focusing resulting from application of time reversal techniques in richly scattering media. The concept and goals of time reversal are presented. Pertinent metrics describing both the time and space focusing effects are outlined. Two examples based on a model of discrete and continuous scattering media are used to illustrate how the proposed metrics vary as a function of various system and channel parameters, such as the bandwidth, delay and angle spreads, number of antennas, etc.

Transport theory for light propagation in biological tissue.

We study light propagation in biological tissue using the radiative transport equation. The Greens function is the fundamental solution to the radiative transport equation from which all other solutions can be computed. We compute the Greens function as an expansion in plane-wave modes. We calculate these plane-wave modes numerically using the discrete-ordinate method. When scattering is sharply peaked, calculating the plane-wave modes for the transport equation is difficult. For that case we replace it with the Fokker-Planck equation since the latter gives a good approximation to the transport equation and requires less work to solve. We calculate the plane-wave modes for the Fokker-Planck equation numerically using a finite-difference approximation. The method of computing the Greens function for it is the same as for the transport equation. We demonstrate the use of the Greens function for the transport and Fokker-Planck equations by computing the point-spread function in a half-space composed of a uniform scattering and absorbing medium.

Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation

The generation of uniform soliton pulse trains by additive pulse mode locking has been experimentally demonstrated in a birefringent fiber laser with a passive polarizer. Numerical simulations of pulse propagation around such a fiber loop are presented which reveal that this mode-locking scheme does not result in strictly uniform pulse trains. Rather, the train of output pulses exhibits periodic fluctuations in intensity and polarization. A model for the pulse dynamics is developed which shows that these fluctuations depend on the strength of the fiber birefringence and the alignment of the polarizer with the fast- and slow-polarization axes of the fiber. It is also shown that increased uniformity of pulse trains is achieved with near alignment of the polarizer with the slow axis of the birefringence.

Chebyshev Spectral Methods for Radiative Transfer

We study the performance of Chebyshev spectral methods for time-dependent radiative transfer equations. Starting with a method for one-dimensional problems in homogeneous media, we show that the modifications needed to consider more general problems such as inhomogeneous media, polarization, and higher dimensions are straightforward. In this method, we approximate the spatial dependence of the intensity by an expansion of Chebyshev polynomials. This yields a coupled system of integro-differential equations for the expansion coefficients that depend on angle and time. Next, we approximate the integral operation on the angle variables using a Gaussian quadrature rule resulting in a coupled system of differential equations with respect to time. Using a second-order finite difference approximation, we discretize the time variable. We solve the resultant system of equations with an efficient algorithm that makes Chebyshev spectral methods competitive with other methods for radiative transfer equations.

Spatial Focusing and Intersymbol Interference in Multiple-Input–Single-Output Time Reversal Communication Systems

In this paper, we study a multiple-input-single-output (MISO) underwater communication system that applies time reversal (TR) to transmit signals so that they focus spatially and compress temporally on the intended receiver. Our simulations model an underwater acoustic channel as a waveguide, and we investigate the cases of a waveguide both with and without random inhomogeneities. We investigate physical TR metrics and communications related performance indicators. The results of our simulations show that spatial focusing depends strongly on the delay spread ( DS ) , as has been seen in experiments. This physical property of TR could be exploited in communication systems where signal coherence is desired only at the receiver location. However, in the simulations, we find that while spatial compression increases with DS in a robust way (i.e., even when inhomogeneities exist), time compression does not increase with DS. Moreover, physical measures of the temporal compression (temporal peak-to-sidelobe ratio) do not improve with waveguide inhomogeneities. Nevertheless, TR reduces intersymbol interference (ISI) at the receiver as DS increases for both types of waveguides, which is an important effect for efficient, high-speed communication. In addition to TR, preequalization at the transmitter can ideally eliminate ISI without significantly affecting spatial compression. However, this preequalization causes a reduction of received power, which may be acceptable when the signal-to-noise ratio (SNR) at the receiver is high.

Beam propagation in sharply peaked forward scattering media

We calculate the radiance of a light beam propagating in a uniformly scattering and absorbing slab and determine the point-spread function. We do this by solving numerically the governing radiative transport equation by use of plane-wave mode expansions. When scattering is sharply peaked in the forward direction and it becomes difficult to solve the radiative transport equation, we replace it with either the Fokker-Planck or the Leakeas-Larsen equation. We also solve these equations by using plane-wave mode expansions. Numerical results show that these two equations agree with the radiative transport equation for large anisotropy factors. The agreement improves as the optical thickness increases.

Nonlinear Dynamics of Mode-locking Optical Fiber Ring Lasers

We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature of the governing equations. Pulse-train uniformity is achieved in three parameter regimes in which the amplitude and the chirp decouple from the polarization and the phase. Alignment of the polarizer either near the slow or the fast axis of the fiber is sufficient to establish this stable mode locking.

Light propagation in tissues with forward-peaked and large-angle scattering

We study light propagation in tissues using the theory of radiative transport. In particular, we study the case in which there is both forward-peaked and large-angle scattering. Because this combination of the forward-peaked and large-angle scattering makes it difficult to solve the radiative transport equation, we present a method to construct approximations to study this problem. The delta-Eddington and Fokker-Planck approximations are special cases of this general framework. Using this approximation method, we derive two new approximations: the Fokker-Planck-Eddington approximation and the generalized Fokker-Planck-Eddington approximation. By computing the transmittance and reflectance of light by a slab we study the performance of these approximations.

Radiative transport theory for optical molecular imaging

We study the inverse fluorescent source problem for optical molecular imaging. In particular, we recover key properties of a fluorescent source inside a halfspace composed of a uniform absorbing and scattering medium from angularly resolved measurements at the boundary plane. We use the radiative transport equation to model the multiple scattering of light in tissues. Using Greens function, given as an analytical expansion in plane wave solutions, we subtract contributions from the measured angular data due to surface sources yielding a quantity that depends only on the interior fluorescent source. We analyse this reduced problem and obtain explicit solutions for a point source and a voxel source. Using the point source and voxel source solutions, we estimate the location, size and total strength of a general source. We perform numerical studies to validate this theory as well as investigate modelling errors due to incorrectly assumed optical properties of the medium.

Deriving Kubelka–Munk theory from radiative transport

We derive Kubelka-Munk (KM) theory systematically from the radiative transport equation (RTE) by analyzing the system of equations resulting from applying the double spherical harmonics method of order one and transforming that system into one governing the positive- and negative-going fluxes. Through this derivation, we establish the theoretical basis of KM theory, identify all parameters, and determine its range of validity. Moreover, we are able to generalize KM theory to take into account general boundary sources and nonhomogeneous terms, for example. The generalized Kubelka-Munk (gKM) equations are also much more accurate at approximating the solution of the RTE. We validate this theory through comparison with numerical solutions of the RTE.