Peculiar features of surface plasmon-polariton modulation instability in a metal film with varying thickness

Surface plasmon–polaritons (SPPs), propagating bound oscillations of electrons and light at a metal surface, exhibit the capacity for subwavelength field confinement and enhancement that make them a promising photonic platform at the nanometer scale. In this work we report the results of theoretical investigations of SPP propagation in metal film with varying thickness lying on a dielectric substrate. It is shown that the SPP propagation can be described by an equation of the type of the nonlinear Schrödinger equation. The main parameters of the nonlinear Schrödinger equation for the SPP − Kerr nonlinearity and dispersion coefficients− are derived from the basic SPP dispersion relation. The dependences of these coefficients on the film thickness are obtained. It is shown that the high-frequency SPP dispersive branch satisfies the conditions of the development of modulation instability. According to estimates, the magnitude of the modulation gain is sufficient to generate ultrashort pulse train from the initial modulated SPP wave on the propagation length of about 100 nm. The peculiar features of modulated SPP propagation in the metal film with varying thickness are studied. Analogies between the light wave propagation in a nonlinear dispersion decreasing fiber and SPP propagation in the metal film with increasing thickness are shown. Numerical simulations performed confirm the theoretically predicted generation of ultrashort pulse trains with THz an sub-THz repetition rates from an initially modulated SPP wave in a film with a longitudinally increasing thickness on propagation length of about 100-200 nm.