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A POLYNOMIAL CHAOS METHOD FOR DISPERSIVE ELECTROMAGNETICS

Abstract

Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell’s equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.

Material Code

PBM_fnrzb

Reference

[1] R. A. Albanese, J. W. Penn, and R. L. Medina. Short-rise-time microwave pulse propagation through dispersive biological media. J. Opt. Soc. Amer. A, 6:1441–1446, 1989. [2] M. Armentrout and N. L. Gibson. Electromagnetic relaxation time distribution inverse problems in the time-domain. In WAVES International Conference Proceedings, 2011. [3] H Banks and V Bokil. A computational and statistical framework for multidimensional domain acoustooptic material interrogation. Quarterly of Applied Mathematics, 63(1):156–200, 2005. [4] H. T. Banks, M. W. Buksas, and T. Lin. Electromagnetic Material Interrogation Using Conductive Interfaces and Acoustic Wavefronts, volume FR21 of Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 2000. [5] H. T. Banks and N. L. Gibson. Well-posedness in Maxwell systems with distributions of polarization relaxation parameters. Appl. Math. Let., 18(4):423–430, 2005. [6] H. T. Banks and N. L. Gibson. Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters. Quarterly of Appl. Math., 64(4):749–795, 2006. [7] HT Banks, Nathan L Gibson, and William P Winfree. Gap detection with electromagnetic terahertz signals. Nonlinear Analysis: Real World Applications, 6(2):381–416, 2005.

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