Characteristic frequencies of transverse electric modes in a double negative slab waveguide with Kerr-type nonlinearity

The evolution equation for guided transverse electrical modes in a slab waveguide having a double negative core is derived for the electrical field. Special solutions of the dispersion equation for the case with double positive symmetric cladding are searched for. Relevant eigenmodes are formulated in terms of characteristic frequencies as a new method, and these frequencies corresponding to the oscillating guided modes are found for different wave numbers and core widths assuming the lossless Drude model can be used for the core medium with a Kerr-type nonlinearity. Results show that normalized characteristic frequencies increase with increasing wave numbers and mode numbers.