Uniaxial and biaxial 2D photonic crystals
Abstract
We have studied the effective dielectric tensor ɛ_ij of 2D photonic crystals in the low-frequency limit. We prove analytically that a crystal composed of circular cylinders in a square lattice is uniaxial with the optical axis z being parallel to the cylinders. Such a result is also obtained numerically for square cylinders in a square lattice and for circular or triangular cylinders in a triangular lattice. The nonvanishing elements of ɛ_ij are ɛ_xx= ɛ_yy=[<1/ɛ(r)> + Tr B(G,G^')]-1, where the matrix B depends on crystal structure, and ɛ_zz = <ɛ(r)>. Numerical results for these elements were obtained, using matrix inversion, for the aforementioned 2D crystals. For more complex 2D crystals ɛ_xx neq ɛ_yy and the matrix B also depends on the direction of propagation of the wave; such crystals are biaxial. The calculation of ɛ_xx and ɛ_yy is underway.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 1998
- Bibcode:
- 1998APS..MAR.W2712K