Exact solution of Maxwell’s equations for optical interactions with a macroscopic random medium

Tseng, Snow H.; Greene, Jethro H.; Taflove, Allen; Maitland, Duncan J.; Backman, Vadim; Walsh, Joseph T.

doi:10.1364/ol.29.001393

Cited by 31 publications

(14 citation statements)

References 6 publications

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“…This yields an enormous decrease of computer resources relative to FDTD, and thereby permits using PSTD to directly model realistic three dimensional tissue regions having spans as large as hundreds of microns to millimeters. Within such a volume, PSTD can provide the complete near- and far-field interactions of hundreds, even thousands of arbitrarily complex biological structures with no simplifications other than the sub-wavelength discretization of the refractive index distribution (116-118). In particular, PSTD has been used to model light transport in media with the overall sizes up to a few hundreds of microns.…”

Section: Computational Methods In Optical Scatter Imaging and Specmentioning

confidence: 99%

Microscopic Imaging and Spectroscopy with Scattered Light

Boustany

Boppart

Backman

2010

Annu. Rev. Biomed. Eng.

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120

106

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Optical contrast based on elastic scattering interactions between light and matter can be used to probe cellular structure and dynamics, and image tissue architecture. The quantitative nature and high sensitivity of light scattering signals to subtle alterations in tissue morphology, as well as the ability to visualize unstained tissue in vivo, has recently generated significant interest in optical scatter based biosensing and imaging. Here we review the fundamental methodologies used to acquire and interpret optical scatter data. We report on recent findings in this field and present current advances in optical scatter techniques and computational methods. Cellular and tissue data enabled by current advances in optical scatter spectroscopy and imaging stand to impact a variety of biomedical applications including clinical tissue diagnosis, in vivo imaging, drug discovery and basic cell biology.

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Section: Computational Methods In Optical Scatter Imaging and Specmentioning

confidence: 99%

Microscopic Imaging and Spectroscopy with Scattered Light

Boustany

Boppart

Backman

2010

Annu. Rev. Biomed. Eng.

Self Cite

120

106

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“…Taflove and his research team, for instance, have combined the FDTD method with several classes of physics models. They have used the resulting FDTD simulators to model extremely low-frequency propagation within the Earth-ionosphere waveguide to identify potential precursors of earthquakes and to prospect for deep underground oil and ore deposits [61]; to model ultrahigh-speed wireless digital interconnects to investigate chip-to-chip data transfers at rates > 400 Gbits/sec [62]; to model optical ultramicroscopy; and to model bio-photonics to investigate the early-stage detection of epithelial cancers such as those found in the colon [63]. His team has also considered using rate equation models of multi-level atoms to achieve a self-consistent modeling of optical interactions with gain media in complex/random structures [64].…”

Section: Recent Cem Trendsmentioning

confidence: 99%

Antennas and Propagation in the Presence of Metamaterials and Other Complex Media: Computational Electromagnetic Advances and Challenges

Ziolkowski

2005

IEICE Transactions on Communications

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There have been significant advances in computational electromagnetics (CEM) in the last decade for a variety of antennas and propagation problems. Improvements in single frequency techniques including the finite element method (FEM), the fast mulitipole moment (FMM) method, and the method of moments (MoM) have led to significant simulation capabilities on basic computing platforms. Similar advances have occurred with time domain methods including finite difference time domain (FDTD) methods, time domain integral equation (TDIE) methods, and time domain finite element (TD-FEM) methods. Very complex radiating and scattering structures in the presence of complex materials have been modeled with many of these approaches. Many commercial products have been made available through the efforts of many individuals. The CEM simulators have enabled virtual EM test ranges that have led to dramatic improvements in our understanding of antennas and propagation in complex environments and to the realization of many of their important applications.

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“…Computing the scattering matrix would give one such example. A related and more sophisticated example would be simulations of the broad band wave packet propagation in random media [2]. To obtain a numerical solution of the initial-value problem in this case, the propagation must be carried out multiple times for every (random) state of the medium in order to perform the statistical averaging over the medium states.…”

Section: Introductionmentioning

confidence: 99%

Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

Borisov¹,

Shabanov²

2006

Journal of Computational Physics

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Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schrödinger equation i∂Ψ/∂t = HΨ, where H is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector Ψ composed of the electromagnetic fields and auxiliary matter fields describing the medium response. In this representation, the initial value problem is solved by applying the fundamental solution exp(−itH) to the initial field configuration. The Faber polynomial approximation of the fundamental solution is used to develop a numerical algorithm for propagation of broad band wave packets in passive media. The action of the Hamiltonian on the wave function Ψ is approximated by the Fourier grid pseudospectral method. The algorithm is global in time, meaning that the entire propagation can be carried out in just a few time steps. A typical time step is much larger than that in finite differencing schemes, ∆t F ≫ H −1 . The accuracy and stability of the algorithm is analyzed. The Faber propagation method is compared with the Lanczos-Arnoldi propagation method with an example of scattering of broad band laser pulses on a periodic grating made of a dielectric whose dispersive properties are described by the Rocard-Powels-Debye model. The Faber algorithm is shown to be more efficient. The Courant limit for time stepping, ∆t C ∼ H −1 , is exceeded at least in 3000 times in the Faber propagation scheme.

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Exact solution of Maxwell’s equations for optical interactions with a macroscopic random medium

Cited by 31 publications

References 6 publications

Microscopic Imaging and Spectroscopy with Scattered Light

Microscopic Imaging and Spectroscopy with Scattered Light

Antennas and Propagation in the Presence of Metamaterials and Other Complex Media: Computational Electromagnetic Advances and Challenges

Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

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