Low-frequency limit for 2D photonic band structures
Abstract
We calculate analytically the effective dielectric constant ɛ_eff for periodic arrys of dielectric cylinders in the low frequency limit.For the electric field parallel to the cylinders (E-polarization) ɛ_eff=bar ɛ=fɛa + (1-f)ɛ _b, where ɛa (ɛ_b) is the dielectric constant of the cylinders (background) and f is the filling fraction. Thus for the E mode, ɛ_eff is independent of the direction of propagation and it represents the ordinary wave in the 2D photonic crystal. The extraordinary wave corresponds to the H-polarized mode, with H parallel to the cylinders. This mode exhibits anisotropy and ɛ_eff depends on the direction of the Bloch vector k. We show that the anisotropy increases drastically for the structures where the symmetry of the crystal lattice is broken by the "atoms". For example, for the hexagonal array of cylinders with square cross-section the anisotropy can be as large as 32% for f=0.85. In the limit ɛa arrow∞ (metallic cylinders) we do not obtain the result that the ɛ_eff calculated from the electrostatic and quasistatic approaches differ. Such a difference has been reported(N.A. Nicorovici et al), Phys. Rev. Lett. 75, 1507 (1995). and was mistakenly explained by the noncommutation of the two limits karrow 0 and ɛ_aarrow∞.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 1997
- Bibcode:
- 1997APS..MAR.I1807A