A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

  • Authors:

  • Carl A. Bauer;Gregory R. Werner;John R. Cary

  • Affiliations:

  • Department of Physics and the Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309, USA;Department of Physics and the Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309, USA;Department of Physics and the Center for Integrated Plasma Studies, University of Colorado, Boulder, CO 80309, USA and Tech-X Corporation, Boulder, CO 80303, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardson extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.