Out-of-plane dispersion and homogenization in photonic crystal slabs

We report a measurement of out-of-plane dispersion in two-dimensional photonic crystal slabs. Using terahertz time-domain spectroscopy, we obtain the complex transmission coefficient over a broad spectrum, ranging from the long wavelength (homogeneous) limit up to beyond the first few guided resonances. Despite the absence of a band gap, the out-of-plane dispersion is significant and in addition exhibits a complicated spectral dependence. Calculations of the effective refractive index which assume translational invariance in the direction perpendicular to the slab are in only approximate agreement with the measured homogeneous effective index and dispersion. In contrast, numerical simulations which accurately account for the finite slab thickness give much more accurate predictions.