Surface and bulk modes for periodic structures of negative index materials

In this paper, we investigate surface and bulk modes for periodic structures made of negative index materials in one and two dimensions. The negative index material is a composite medium consisting of a network of thin wires and a periodic array of split ring resonators. In different ranges of frequencies, we identify five types of modes: surface plasmon (SP) modes for TE polarization, magnetic surface plasmon (MSP) modes for TM polarization, trapped modes or resonant cavity modes for both TM and TE polarizations, asymmetric surface (AS) modes for TE polarization, and some bulk modes for both polarizations in the range of negative material properties. In particular, we will discuss band flattening and broadening of SP and MSP modes, explain the trapped modes in terms of large positive dielectric constants, examine the properties of AS modes by an interface condition, and use the Rayleigh quotient to account for possibly infinite degeneracy of SP and MSP modes in two dimensions. All of the physical properties are computed by an interfacial operator approach in which we introduce an interfacial variable to measure the local strengths of various surface modes.