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Allen Taflove

Publications and source records attributed to Allen Taflove.

5 recordsLinked to original sources
arXiv2020

d'Alembert Digitized: A Wave Pulse Method for Visualizing Electromagnetic Waves in Matter and for Deriving the Finite Difference Time Domain Method for Numerically Solving Maxwell's Equations

An alternative way of visualizing electromagnetic waves in matter and of deriving the Finite Difference Time Domain method (FDTD) for simulating Maxwell's equations for one dimensional systems is presented. The method uses d'Alembert's splitting of waves into forward and backward pulses of arbitrary shape and allows for grid spacing and material properties that vary with position. Constant velocity of waves in dispersionless dielectric materials, partial reflection and transmission at boundaries between materials with different indices of refraction, and partial reflection, transmission, and attenuation through conducting materials are derived without recourse to exponential functions, trigonometric functions, or complex numbers. Placing d'Alembert's method on a grid is shown to be equivalent to FDTD and allows for a simple and visual proof that FDTD is exact for dielectrics when the ratio of the spatial and temporal grid spacing is the wave speed, a straightforward way to incorporate reflectionless boundary conditions, and a derivation that FDTD retains second order accuracy when the grid spacing varies with position and the material parameters make sudden jumps across layer boundaries.

physics.optics↗
arXiv2015

Reflection statistics of weakly disordered optical medium when its mean refractive index is different from an outside medium

Based on the difference between mean background of an optical sample refractive index n_0 and an outside medium, n_out, different than n_0, we study the reflection statistics of a one-dimensional weakly disordered optical medium with refractive index n(x)=n_0+dn(x). Considering dn(x) as color noise with the exponential spatial correlation decay length l_c and k as the incident wave vector, our results show that for the small correlation length limit, i.e. k*l_c<1, the average value of reflectance, r, follows a form that is similar to that of the matched refractive-index case n_0=n_out, i.e., proportional to l_c. However, the standard deviation of r is proven to be std(r(dn,l_c)) proportional to sqrt( l_c), which is different from the matched case. Applications to light scattering from layered media and biological cells are discussed

physics.optics↗
arXiv2008

FDTD Simulation of Thermal Noise in Open Cavities

A numerical model based on the finite-difference time-domain (FDTD) method is developed to simulate thermal noise in open cavities owing to output coupling. The absorbing boundary of the FDTD grid is treated as a blackbody, whose thermal radiation penetrates the cavity in the grid. The calculated amount of thermal noise in a one-dimensional dielectric cavity recovers the standard result of the quantum Langevin equation in the Markovian regime. Our FDTD simulation also demonstrates that in the non-Markovian regime the buildup of the intracavity noise field depends on the ratio of the cavity photon lifetime to the coherence time of thermal radiation. The advantage of our numerical method is that the thermal noise is introduced in the time domain without prior knowledge of cavity modes.

physics.optics↗
arXiv2004

Field and intensity correlations in amplifying random media

We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble averaged correlation functions due to existence of lasing realizations. We introduce conditional average for correlation functions by omitting the divergent realizations. Our numerical simulation reveals that amplification does not affect local spatial correlation. The nonlocal intensity correlations are strongly magnified due to selective enhancement of the contributions from long propagation paths. We also show that by increasing gain, the average mode linewidth can be made smaller than the average mode spacing. This implies that light transport through a diffusive random system with gain could exhibit some similarities to that through a localized passive system, owing to dominant influence of the resonant modes with narrow width.

cond-mat.dis-nn↗