A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied.In this analysis two different types of waveguide structures have been discussed,i.e.,(a) normal good/perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and (b) high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material.The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures. A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied. This analysis two different types of waveguide structures have been discussed, ie, (a) normal good / perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and (b) high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material. The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures.