Guided optical modes in asymmetric left-handed waveguides

We study the guided optical modes in the asymmetric slab waveguide structures with a core of the left-handed material surrounded by two normal dielectrics. A graphical method is proposed to determine the transverse wave numbers for the guided optical modes. The existence and the type of the solutions to the surface guided modes with respect to different physical parameters are discussed in detail, which are different from that in symmetric left-handed waveguides. The total energy flux for the oscillating guided modes is negative. It can be positive or negative for different surface guided modes. For higher-order guided optical modes the propagation constant for TM-polarized ones is greater than that for the TE-polarized ones for a fixed width of the left-handed material slab. Mode degeneracy appears for the first-order TE-polarized guided modes in the asymmetric left-handed waveguide. Both TE-polarized and TM-polarized surface guided modes can be sustained in a left-handed waveguide.