Surface-induced nonlinearity enhancement of TM modes in planar subwavelength waveguides

Using an asymptotic expansion of Maxwell equations and boundary conditions, we derive an amplitude equation for nonlinear TM modes in planar metal and dielectric waveguides. Our approach reveals that the physics of the significant enhancement of the nonlinear response in subwavelength waveguides with respect to their weakly guiding counterparts is hidden in surface effects. The corresponding enhancement factor is determined by the products of the surface discontinuities of the transverse field components and of the surface values of the longitudinal components of the electric field summed over all the interfaces. We present an insightful expression for the enhancement factor induced by the surface plasmon polaritons and discuss numerical and analytical results for the subwavelength dielectric and metal slot waveguides. Our theory also includes diffraction effects along the unbound direction in these waveguides.