OUT-OF-PLANE PROPAGATION OF ELECTROMAGNETIC-WAVES IN A 2-DIMENSIONAL PERIODIC DIELECTRIC MEDIUM

By the use of the plane wave method we have calculated the dispersion curves (photonic band structure) of electromagnetic waves propagating in a structure consisting of an infinite array of parallel, infinitely long, dielectric rods of arbitrary cross-section, characterized by a dielectric constant epsilon(a), embedded in a medium characterized by a dielectric constant epsilon(b), when the intersections of the axes o f the rods with a perpendicular plane form a two-dimensional Bravais l attice. In contrast with earlier calculations of the photonic band str uctures of two-dimensional, periodic, dielectric structures, in the pr esent work the electromagnetic waves are assumed to propagate out of t he plane perpendicular to the rods. In numerical calculations we study a triangular lattice of air cylinders in a dielectric medium, which h as recently been shown to possess a band gap common to waves of both E and H polarization for propagation in the plane perpendicular to the rods. The shifts of the edges of this absolute band gap as k3, the com ponent of the wave-vector of the electromagnetic waves parallel to the rods, is increased from zero are studied, as is the closing up of thi s gap. A new absolute band gap is found to open up below the first ban d as k3 is increased. Conclusions concerning the filtering behaviour o f two-dimensional, periodic, dielectric structures in the case of out- of-plane propagation of electromagnetic waves through them are drawn.