Surface modes in photonic crystal waveguides coated with a layer of dispersive left-handed material

In this work, we study the presence of surface modes in two different photonic crystal waveguides characterized by the presence of layers of a dispersive left-handed material. The periodicity required to have a photonic crystal waveguide is considered in two distinct ways. One of them is composed of two perfect electrical conducting rippled surfaces, and the other consists of two at infinite surfaces that surround a periodic one-dimensional array of circular cylindrical inclusions of a perfect electrical conductor, coated with a layer of left-handed material. To study these systems, integral numerical methods were applied to determine their band structures and the electromagnetic field distribution, under the TE and TM polarizations. Numerical results show the presence of surface modes for several frequencies with certain geometric configurations. One of these frequencies is known in the literature and corresponds to the frequency of a Surface Plasmon-Polariton.