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Title: Efficient modeling of photonic crystals with local Hermite polynomials

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This generalmore » method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.« less
Authors:
;  [1] ;  [2] ;  [3]
  1. Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609 (United States)
  2. Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824 (United States)
  3. Departments of Physics and Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609 (United States)
Publication Date:
OSTI Identifier:
22273582
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Applied Physics; Journal Volume: 115; Journal Issue: 15; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 77 NANOSCIENCE AND NANOTECHNOLOGY; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; COMPOSITE MATERIALS; COMPUTERIZED SIMULATION; CRYSTALS; DIELECTRIC MATERIALS; EIGENFUNCTIONS; FIELD EMISSION; HERMITE POLYNOMIALS; INTEGRATED CIRCUITS; INTERPOLATION; QUANTUM WELLS; VARIATIONAL METHODS; WAVE PROPAGATION