Non-perturbative approach to high-index-contrast variations in electromagnetic systems

Lars Henning Rindorf, Niels Asger Mortensen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.
Original languageEnglish
JournalOptics Communications
Volume261
Issue number1
Pages (from-to)181-186
ISSN0030-4018
Publication statusPublished - 2006

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