Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis.

By Steven G. Johnson, John D. Joannopoulos. Optics Express, 2001

3,264 citations recorded by the source corpus.

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 Delta 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.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/e4161851c183ab3c1c1f7836aedd7eb20ac24a90

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Citations in the corpus

Observation of soliton pulse compression in photonic crystal waveguides (2010, methodology): “Parameters are obtained directly from experimental measurements or calculated as required (A3eff) [35].”
Reduced Bloch mode expansion for periodic media band structure calculations (2008, methodology): “These include the plane-wave method (Ho et al. 1990; Leung & Liu 1990; Zhang & Satpathy 1990; Meade et al. 1993; Johnson & Joannopoulos 2001), the transfer matrix method (Pendry & MacKinnon 1992), the multiple scattering method (Leung & Qiu 1993; Wang et al. 1993), the finite-difference time-domain…”
Enhancement of light extraction from light emitting diodes (2011, neutral): “• Plane wave expansion method (PWEM) [471,694]”
S4 : A free electromagnetic solver for layered periodic structures (2012, methodology): “Subpixel averaging is widely used in the time-domain code Meep [37] as well as the mode-solver code MPB [38].”