Two-dimensional hexagonal photonic crystals can be recorded using the simple superimposition of two interference patterns rotated by 60 masculine. Such process generates high contrast masks, however, it generates elliptical cross section structures instead of cylinders. We study the PBG properties of the experimentally feasible geometries, using this technique and we demonstrate that the effect of this asymmetric shape is a reduction in the PBG map area, for TE polarization, in comparison with cylindrical structures. On the other hand, it appears a PBG for TM polarization.
The Cell Method, a new efficient numerical method suitable for working with periodic structures having anisotropic inhomogeneous media with curved shapes, is proposed in order to calculate the band gap of 2D photonic crystals for in-plane propagation of TM and TE waves. Moreover some numerical comparisons with other numerical methods will be provided.
Finite-element analysis in time and frequency domains using perfectly matched layers and isoparametric curvilinear elements for finite-size photonic-crystal (PC) cavities is presented in this paper. The time-domain approach includes current sources, the full band scheme, and the slowly varying envelope approximation; consequently, bigger time steps can be used independent of the size of the elements. The resonant frequency, quality factor, effective modal area, and field distribution for each mode can be obtained in a single simulation. A strategy to compute the higher resonant modes by using only a quarter of the cavity and adequate boundary conditions is also presented.
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