Band gap studies of triangular 2D photonic crystals with varying pore roundness

Photonic crystals (PCs) are theoretically studied in order to correlate the structural parameters with the resulting electro-magnetic behaviour. Two-dimensional (2D) PCs of dielectric media are routinely assumed to be formed by circular rods or pores, respectively. Main topics of the paper are band gap modifications (TM- and TE-polarization) for pores of deteriorating roundness, approximated by ellipses of varying eccentricity. On the basis of Maxwellʹs equations and a ‘plane wave expansion’, band structures are computed for triangular 2D lattices of air columns in silicon. The results are compared with calculations for circular air columns of varying filling factors.