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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 4 — Feb. 25, 2013
  • pp: 4072–4092

The finite element method applied to the study of two-dimensional photonic crystals and resonant cavities

Imanol Andonegui and Angel J. Garcia-Adeva  »View Author Affiliations


Optics Express, Vol. 21, Issue 4, pp. 4072-4092 (2013)
http://dx.doi.org/10.1364/OE.21.004072


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Abstract

A critical assessment of the finite element (FE) method for studying two-dimensional dielectric photonic crystals is made. Photonic band structures, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals are calculated by using the FE (real-space) method and the plane wave expansion or the finite difference time domain (FDTD) methods and a comparison is established between those results. It is found that, contrarily to popular belief, the FE method (FEM) not only reproduces extremely well the results obtained with the standard plane wave method with regards to the eigenvalue analysis (photonic band structure and density of states calculations) but it also allows to study very easily the time-harmonic propagation of electromagnetic fields in finite clusters of arbitrary complexity and, thus, to calculate their transmission coefficients in a simple way. Moreover, the advantages of using this real space method in the context of point defect cluster quality factor calculations are also stressed by comparing the results obtained with this method with those obtained with the FDTD one. As a result of this study, FEM comes out as an stable, robust, rigorous, and reliable tool to study light propagation and confinement in both periodic and aperiodic dielectric photonic crystals and clusters.

© 2013 OSA

OCIS Codes
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(140.3945) Lasers and laser optics : Microcavities
(160.5293) Materials : Photonic bandgap materials
(160.5298) Materials : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: November 28, 2012
Revised Manuscript: January 4, 2013
Manuscript Accepted: January 15, 2013
Published: February 11, 2013

Citation
Imanol Andonegui and Angel J. Garcia-Adeva, "The finite element method applied to the study of two-dimensional photonic crystals and resonant cavities," Opt. Express 21, 4072-4092 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4072


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