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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 13178–13186

An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane

Harald G. L. Schwefel and Christopher G. Poulton  »View Author Affiliations


Optics Express, Vol. 17, Issue 15, pp. 13178-13186 (2009)
http://dx.doi.org/10.1364/OE.17.013178


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Abstract

We present a numerically improved multipole formulation for the calculation of resonances of multiple disks located at arbitrary positions in a 2-d plane, and suitable for the accurate computation of the resonances of large numbers of disks and of high-wavenumber eigenstates. Using a simple reformulation of the field expansions and boundary conditions, we are able to transform the multipole formalism into a linear eigenvalue problem, for which fast and accurate methods are available. Observing that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family, we present a numerical algorithm to compute a range of multiple-disk resonances and field distributions using only two diagonalizations. This method can be applied to photonic molecules, photonic crystals, photonic crystal fibers, and random lasers.

© 2009 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.5750) Optical devices : Resonators
(140.3945) Lasers and laser optics : Microcavities
(230.4555) Optical devices : Coupled resonators

ToC Category:
Optical Devices

History
Original Manuscript: April 29, 2009
Revised Manuscript: June 30, 2009
Manuscript Accepted: June 30, 2009
Published: July 17, 2009

Citation
Harald G. Schwefel and Christopher G. Poulton, "An improved method for calculating resonances of multiple dielectric disks arbitrarily positioned in the plane," Opt. Express 17, 13178-13186 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-13178


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