Transverse Magnetic Modes In Hybrid Slot Waveguide And Nonlinear Slot Waveguide

The traditional low index slot waveguide(LISW)can limit the light to the slot of the sub-wavelength level because of the continuity of the normal electrical displacement vector at the boundary of the slot layer,and the slot waveguide has a good prospect of optical application because it can break through the diffraction limit.Based on the LISW,in order to obtain the narrow mode width and all-optic controllable waveguides,we study the mode characteristics of transverse magnetic(TM)waves in the hybrid slot waveguide(HSW)and the nonlinear slot waveguide.We replaced the outermost low refractive index layer with a metal layer in LISW to get narrow mode,and the metal/high index/low index/high index/metal 5-layer symmetrical structure is termed as HSW.Transverse magnetic modes in HSW are analytically solved.We give six types of TM modes that can exist in a HSW according to the range of the effective refractive index of the waveguide,and their characteristic equations and cut-off conditions are derived and discussed.Based on these analytical expressions,we calculated the relationship between the effective refractive index and the waveguide structure parameters.The light-confined abilities between the HSW structure and the LISW structure have been compared.We found that the light-confined ability of HSW is much stronger than that of LISW when the width of the slot layer is 100 nm and the width of the high refractive layer is less than 90 nm.The light-confined ability of the HSW as a function of the width of the slot layer is also analyzed when the width of the high refractive index layer is constant,and the results show that the light-confined ability of the HSW is enhanced as the width of the slot layer increases.By replacing the outermost layer of the LISW with a metal layer,it is possible to simultaneously increase light-confined ability and reduce mode width of the waveguide.We consider the nonlinear effects of the slot layer on the basis of LISW and present two models to study mode characteristics of transverse magnetic waves in a nonlinear slot waveguide,where the self-focusing and self-defocusing Kerr effects are taken into account,respectively.In the first method termed as Jacobian elliptic function model(JEM),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.Under such assumptions,we completely solve the mode characteristics of the TM wave in the nonlinear slot waveguide,and give five different types of Jacobian elliptic functions to represent the modes of the TM wave in the nonlinear slot waveguide.It also provides a closed analytical formula for the nonlinear dispersion relation with each mode.In the second method termed as interface model(IM),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.This model allows us to get the numerical solutions of the field distribution and nonlinear dispersion relation.Next,we also compared the results of the two models and found that the results calculated by the two models agree well when the nonlinear index modification(35)n is small.Finally,for the JEM model,the magnetic-filed amplitude distributions in the linear slot waveguide and the nonlinear waveguides at low power have been compared,and the results show that the magnetic field distributions of the two structures are completely coincident for each Jacobian elliptic function.This also verifies the feasibility of the JEM model in the case of weak nonlinearities.