Variable Forbidden Regions in Metamaterial Planar Waveguide with Nonlinear Cladding

In this paper, we used the modal theory to analyze TE waves in the three-layer planar waveguide with the metamaterial guiding film and the nonlinear cladding layer, and derive a formula for the guiding power density. The power density is very helpful to analyze the forbidden regions of the proposed waveguide structure. In recent years, the metamaterial in the planar waveguide has been widely studied in many researches. The feature of the metamaterial includes the permittivity E and the permeability mu less than zero. The forbidden regions always exist in the three-layer planar waveguide with the metamaterial guiding film and the nonlinear cladding layer. In this study, the guiding power density can help to provide a clear picture of forbidden regions in the metamaterial film with different permeability values. The numerical results show that the forbidden regions are different in metamaterial film with the same width but the permeability values are different. The greater permeability value is, the narrower the forbidden region is. The study shows that the value of guiding power density is less than zero at metamaterial and is greater than zero at right-handed medium. Therefore, the guiding power density is at the opposite direction because the values of permeability are positive and negative. It agrees with the phenomenon of negative refraction in metamaterial. The simulation result is helpful to find out the propagation situation of the TE polarized waves