Abstract
A study is carried out to investigate the possible enhancement of photonic crystal (PC) microcavity performance induced by geometrical and permittivity variations in relation to localization of the associated evanescent Bloch wave. The study is focused on PCs of hexagonally packed dielectric rods. A numerical scheme formulated on the basis of Green's function method with multipole expansion approximation is employed to exhibit explicitly the exponential growth curves of the spontaneous emission rate ($F$) and quality factor ($Q$) of the cavity with respect to increasing number of surrounding layers ($N$), which are characterized by their growth rates ${k}_{F}$. While the same exponential growth pattern is found for PCs with different rod parameters, the associated growth rates do show distinct and significant differences, implying that an appropriate choice of the rod parameters may produce a large performance enhancement for the microcavity or achieve the same performance with a largely reduced surrounding layer number. Meanwhile, the corresponding spatial decay constants of the evanescent Bloch waves, represented by its smallest Im($k$) in the photonic gap, are calculated by means of the extended plane-wave expansion method. The resulting smallest values of Im($k$) show their strong correlation with ${k}_{F}$ as characterized by their linear relation. The study further demonstrates that a judicious choice of the defect rod parameters may also give rise to a remarkable performance enhancement of the microcavity, even at a reduced number of surrounding rod layers. Remarkably, the [${k}_{F},\mathrm{Im}(k)$] values of all PCs considered are located on the same linear correlation line.
Published Version
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