Efficient modeling of photonic crystals with local Hermite polynomials

Journal Article · Mon Apr 21 00:00:00 EDT 2014 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.4871459· OSTI ID:22273582

Boucher, C. R.; Li, Zehao ^[1]; Albrecht, J. D. ^[2]; Ram-Mohan, L. R. ^[3]

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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)

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 general 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.

• OSTI ID: 22273582
• Journal Information: Journal of Applied Physics, Vol. 115, Issue 15; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

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