TABLE OF CONTENTS This chapter is dedicated to periodic structures that are geometrically more complex than 2D photonic crystals, but not as complex as full 3D photonic crystals. In particular, we consider the optical properties of photonic crystal fibers, optically induced photonic lattices, and photonic crystal slabs.
First, we consider electromagnetic modes that propagate along the direction of continuous translational symmetry 
of a 2D photonic crystal (Fig. 7.1(a)). In this case, modes carry electromagnetic energy along the direction, and, therefore, can be considered as modes of an optical fiber extended in the direction and having a periodic dielectric profile in its cross-section. Fibers of this type are called photonic crystal fibers. From Section 2.4.5, it follows that fiber modes can be labeled with a conserved wave vector of the form 
, where k t is a transverse Bloch wave vector, and k z ? 0. To analyze the modes of a photonic crystal fiber with periodic cross-section, we will employ the general form of a plane-wave expansion method presented in Section 6.2.
k z, where k z ? 0, and k t is a transverse Bloch wave vector confined to a fiber cross-section. (b) A defect in a 2D photonic crystal lattice can localize light, while still guiding the light along...
