Plasmon-soliton waves in planar slot waveguides. I. Modeling

Abstract

We present two complementary models to study stationary nonlinear solutions in one-dimensional plasmonic slot waveguides made of a finite-thickness nonlinear dielectric core surrounded by metal regions. The considered nonlinearity is of focusing Kerr type. In the first model, it is assumed that the nonlinear term depends only on the transverse component of the electric field and that the nonlinear refractive index change is small compared to the linear part of the refractive index. This first model allows us to describe analytically the field profiles in the whole waveguide using Jacobi elliptic special functions. It also provides a closed analytical formula for the nonlinear dispersion relation. In the second model, the full dependency of the Kerr nonlinearity on the electric field components is taken into account and no assumption is required on the amplitude of the nonlinear term. The disadvantage of this approach is that the field profiles must be computed numerically. Nevertheless analytical constraints are obtained to reduce the parameter space where the solutions of the nonlinear dispersion relations are sought.

Improved nonlinear slot waveguides using dielectric buffer layers: properties of TM waves

“…The nonlinear Kerr-type dielectric is isotropic with ϵ core ϵ l;core αjE x j 2 (ϵ l;core being the linear part of the core permittivity and E x being the x component of the electric field), and with α > 0 (focusing nonlinearity). This approximation of the Kerr nonlinearity, taking into account only the transverse component of the electric field, has already been used in models of the NPSWs [6,12]. It allows us to use the fixed power algorithm in the finite element method (FEM) to compute the nonlinear stationary solutions and their nonlinear dispersion curves [13][14][15][16].…”

“…Compared to the already studied simple NPSW made of a nonlinear dielectric core surrounded by two semi-infinite metal regions [1,2,6], the improved structure contains additional linear dielectric layers between the core and the metal regions. In this study, we will only consider the symmetric structures even if the asymmetric simple NPSWs have already been considered [12]. d core is the core thickness and d buf is the dielectric buffer thickness of each of the supplementary layers with their permittivity denoted by ϵ buf .…”

“…In this study, ϵ l;core 3.46 2 i10 −4 and n 2 1:10 −17 m 2 ∕W corresponding to amorphous hydrogenated silicon [6], and ϵ met −90 i10 corresponding to gold at 1.55 μm, the wavelength for which all the simulations are done. Losses will be estimated using the method based on the field profiles and permittivity of the imaginary parts described in [3,10,12,18]. We stress that used parameter values can affect the given critical values, but would not affect its main conclusions.…”

“…It is important to note that the first type of mode is not found in the simple NPSW as a linear mode whatever the used optogeometric parameters are [12,20], but a corresponding mode can be observed in structures with a semi-infinite nonlinear region and a metal one, separated by a dielectric buffer layer [5].…”

“…In the two previous figures, the results for a simple NPSW made from the improved NPSW by removing the buffer dielectric layers are, also, shown in gray for comparison (symmetric S0-plas, asymmetric AS1plas, and antisymmetric AN0-plas). The mode notation used in our study has been chosen to coherently extend the one already introduced for the simple NPSW [12,20]. As it can be seen, in the improved NPSW, the bifurcation of the asymmetric mode from the symmetric mode and the relative positions of the three main modes are preserved.…”