Photonic band structure of 2D lattices with left-handed materials

We study the out-of-plane photonic band structure of a two-dimensional (2D) lattice with left-handed and right-handed elements. The band structures of 2D photonic crystals made of impedance-matched or impedance-unmatched elements look differently and show resemblance to dielectric-dielectric and metal-dielectric structures respectively. In particular, lossless LHM-RHM impedance-unmatched lattice supports lossless "slow" surface modes analogous to lossy modes at a metal-dielectric boundary.