Abstract

We analyze in depth the eigenmodes symmetry of the vectorial electromagnetic wave equation with discrete symmetry, using a recently developed maximal symmetrization and reduction scheme leading to an automatic technique which decomposes every mode into its most fundamental internal geometrical components carrying independent symmetries, the ultimately reduced component functions (URCFs). Using URCFs, geometrical properties of photonic crystal defect modes can be analyzed in great details. In particular we analytically identify the kind of modes that display non-vanishing transverse electric or transverse magnetic amplitude at the cavity center in $C_{2v}$, $C_{3v}$, $C_{4v}$, and $C_{6v}$ symmetries, and their degeneracies. We also build a postprocessing tool able to extract and identify URCFs out of the modes whether from experimental or numerical origin. In the latter case it is independent of the eigenmode computation method. In another variant the whole eigenmode computation can be systematically reduced to a minimal domain, without any need for applying specific non-trivial boundary conditions. The approach leads to strong analytical predictions which are illustrated for specific $H1$ and $L3$ cavities using the postprocessing tool on full three-dimensional computed modes. It not only constitutes an unprecedented check of the symmetry of the computational results, but it is shown to also deliver a deep geometrical and physical insight into the structure of the modes of photonic bandgap microcavities, which is of direct use for most modern applications in quantum photonics.

© 2010 Optical Society of America

Analysis of photonic crystals with defects using coupled-mode theory

Vladislav R. Shteeman, Inna Nusinsky, Eli Kapon, and Amos A. Hardy
J. Opt. Soc. Am. B 26(6) 1248-1255 (2009)

Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab

O. Painter, J. Vučković, and A. Scherer
J. Opt. Soc. Am. B 16(2) 275-285 (1999)

Frequency domain analysis of guided resonances and polarization selectivity in photonic crystal membranes

Jan Kupec, Uğur Akçakoca, and Bernd Witzigmann
J. Opt. Soc. Am. B 28(1) 69-78 (2011)

Classification of modes in suspended-membrane, 19-missing-hole photonic-crystal microcavities

Wan Kuang, Jiang R. Cao, Tian Yang, Sang-Jun Choi, Po-Tsung Lee, John D. O'Brien, and P. Daniel Dapkus
J. Opt. Soc. Am. B 22(5) 1092-1099 (2005)

Analysis of defect mode in a one-dimensional symmetric double-negative photonic crystal containing magnetized cold plasma defect

Alireza Aghajamali, Azadeh Zare, and Chien-Jang Wu
Appl. Opt. 54(29) 8602-8606 (2015)