Abstract

It has been proposed that dielectric structures with a periodic index of refraction could give rise to photonic band gaps for which propagation of electromagnetic waves is forbidden in the structure.¹ The interest has been focused on finding three-dimensionally (3D) periodic structures that would generate such band gaps.^2,3 However, an increasing interest in integrated optics, surface-emitting lasers, and two-dimensional transmission lines has prompted research on two-dimensionally (2D) periodic structures ^4-6 These structures have an important distinction with 3D periodic structures: in 3D structures, the band diagrams for transverse electric (TE) and transverse magnetic (TM) waves are very similar; many TE and TM bands are degenerate. However, in 2D periodic structures, TE and TM-waves have very different dispersion relations, which hinder the TE and TM gaps from overlapping.

© 1992 Optical Society of America