Abstract

An efficient numerical method is developed for the modal analysis of two-dimensional photonic crystal waveguides (PCWs). Using the Dirichlet-to-Neumann (DtN) map of the supercell, the waveguide modes are solved from an eigenvalue problem formulated on two boundaries of the supercell, leading to significantly smaller matrices when it is discretized. The eigenvalue problem is linear even when the medium is dispersive. The DtN map of a domain is an operator that maps the wave field on the boundary of the domain to the normal derivative of the field. The DtN map of the supercell can be efficiently calculated by merging the DtN maps of the ordinary and defect unit cells.

© 2007 Optical Society of America

Computing Photonic Crystal Defect Modes by Dirichlet-to-Neumann Maps

Shaojie Li and Ya Yan Lu
Opt. Express 15(22) 14454-14466 (2007)

Efficient analysis of photonic crystal devices by Dirichlet-to-Neumann maps

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Opt. Express 16(22) 17383-17399 (2008)

Modeling two-dimensional anisotropic photonic crystals by Dirichlet-to-Neumann maps

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J. Opt. Soc. Am. A 26(7) 1606-1614 (2009)

Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells

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Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice

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