A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity

The propagation of pulses through waveguides with subwavelength features, inhomogeneous transverse structure, and high index contrast cannot be described accurately using existing models in the presence of nonlinear effects. Here we report the development of a generalised full vectorial model of nonlinear pulse propagation and demonstrate that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient $\gamma,$ $A_{eff}$, and mode orthognality. While new definitions reduce to standard definitions in some limits, significant differences are predicted, including a factor of $\sim2$ higher value for $\gamma$, for emerging waveguides and microstructured fibers.