## Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis

Optics Express, Vol. 8, Issue 3, pp. 173-190 (2001)

http://dx.doi.org/10.1364/OE.8.000173

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### Abstract

We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell’s equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that *O*(Δ*x*^{2}) convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.

© Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

**ToC Category:**

Focus Issue: Photonic bandgap calculations

**History**

Original Manuscript: November 17, 2000

Published: January 29, 2001

**Citation**

Steven Johnson and John Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express **8**, 173-190 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-3-173

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