Analysis of TM-polarized nonlinear guided waves based on a conservation law

Abstract

In recent years, the properties of the transverse magnetic TM polarized guided waves in nonlinear layered structures have been investigated theoretically in a number of papers [1 - 4]. The presence of two electric field components, one parallel (Ez) and one orthogonal (Ex) to the boundaries of a thin film guiding structure makes the analysis of TM waves more complicated than for the transverse electric TE polarized waves. For simplify the analysis in some works was assumed that TM-wave nonlinearity arises only through one component electric field. The more elaborate is approximation referred to as longitudinal uniaxial approximation in which the nonlinearity is expressed as dependent only on the electric field component parallel to the boundary [1]. The more realistic is transverse uniaxial approximation in which the nonlinearity arises from the dominant transverse Ex component of the electric field [5]. In the few papers [6 - 7] has been investigated TM polarized waves / surface polaritons / propagating along the interface separating of two media, one / or both / of which is nonlinear with the general intensity dependent dielectric function. The effective method analysis of TM nonlinear guided waves is separation of the two electric field components EX and EZ achieved by means of a conservation law. In this approach the properties of TM nonlinear guided waves can be study without the need to solve for the field profile [8]. Since the two field components Ex and Ez of TM wave are everywhere interrelated through the conservation law, then it is possible formally express one in terms of the other.