Waveguiding power of photonic crystal slabs

We consider the waveguiding by thin patterned slabs embedded in a homogeneous medium. In the longwave limit, the wave spectra of slabs are found to be well described by a single frequency-independent parameter, which we call the "guiding power". The guiding power can be evaluated in an effective medium approximation, similar to the Maxwell Garnett theory, but modified for the local field corrections specific to the two-dimensional geometry. The guiding power is different for the transverse magnetic (TM) and transverse electric (TE) polarizations. We show that the confinement factor of TM waves in a porous layer with high index ratio can exceed that for a homogeneous layer. Similarly enhanced confinement of TM waves is demonstrated for a layer of elongated cylinders or elliptic inclusion with a high axis length ratio. The effect originates from the suppression of local field effects and the increasing internal field in the inclusion. It may be useful in the design of far-infrared or THz quantum cascade lasers.