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FD-TD modeling of 2-D dielectric waveguides for propagation and scattering of femtosecond optical solitonsExperimentalists have produced all-optical switches capable of 100-fs responses. To adequately model such switches, nonlinear effects in optical materials (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work, the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) that solve only for the envelope of the optical pulses. In this paper, we present first-time calculations from the vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional systems of dielectric waveguides exhibiting the Kerr and Raman quantum effects. We use the finite-difference time-domain (FD-TD) method in an extension of our 1-D work. There, in a fundamental innovation, we treated the linear and nonlinear convolutions for the electric polarization as new dependent variables. By differentiating these convolutions in the time domain, we derived an equivalent system of coupled, nonlinear second-order ODE's. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in inhomogeneous nonlinear dispersive media. Backstorage in time is limited to only that needed by the time-integration algorithm for the ODE's, rather than that needed to store the time-history of the kernel functions of the convolutions (1000-10,000 time steps). Thus, a 2-D nonlinear optics model from Maxwell's equations is now feasible.
Document ID
19940015933
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Joseph, Rose
(Northwestern Univ. Evanston, IL., United States)
Goorjian, Peter
(NASA Ames Research Center Moffett Field, CA, United States)
Taflove, Allen
(Northwestern Univ. Evanston, IL., United States)
Date Acquired
September 6, 2013
Publication Date
January 1, 1993
Publication Information
Publication: JPL, Progress In Electromagnetics Research Symposium (PIERS)
Subject Category
Communications And Radar
Accession Number
94N20406
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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