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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 28, Iss. 8 — Aug. 1, 2011
  • pp: 1951–1958

Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions

Tobias Stollenwerk, Dmitry N. Chigrin, and Johann Kroha  »View Author Affiliations


JOSA B, Vol. 28, Issue 8, pp. 1951-1958 (2011)
http://dx.doi.org/10.1364/JOSAB.28.001951


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Abstract

Wannier function expansions are well suited for the description of photonic-crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the efficiency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two-dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based stochastic methods. Besides the commonly used second moment (SM) locality measure, we introduce a new locality measure, namely, the integrated modulus (IM) of the Wannier function. We show numerically that, in contrast to the SM criterion, the IM criterion leads to an optimization problem with a single extremum, thus allowing for fast and efficient construction of maximally localized Wannier functions using local optimization techniques. We also present an analytical formula for the initial choice of Bloch phases, which, under certain conditions, represents the global maximum of the IM criterion and, thus, further increases the optimization efficiency in the general case.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.3120) Optical devices : Integrated optics devices
(250.5300) Optoelectronics : Photonic integrated circuits
(230.5298) Optical devices : Photonic crystals

ToC Category:
Optical Devices

History
Original Manuscript: March 28, 2011
Revised Manuscript: June 8, 2011
Manuscript Accepted: June 21, 2011
Published: July 18, 2011

Citation
Tobias Stollenwerk, Dmitry N. Chigrin, and Johann Kroha, "Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions," J. Opt. Soc. Am. B 28, 1951-1958 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-8-1951

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