Excitation of third harmonic terahertz surface plasmon over a rippled graphene-free space interface

Abstract

We examined the third harmonic (TH) terahertz (THz) surface plasmon waves (SPWs) generation over a graphene surface deposited on a rippled dielectric substrate (SiO2) by obliquely incidenting a p-polarized laser beam on a graphene surface with frequency ω0 and wave numbers k0x and k0z at an incident angle θ. Laser beam exerts ponderomotive force on free electrons of the graphene surface and produce nonlinear second harmonic (SH) oscillatory velocity v→2ω0 at frequency 2ω0. SH oscillatory velocity couples with perturbed ripple electron density to produce TH nonlinear current density J→3ω0nl at frequency 3ω0. Ripple wave number (q) provides an extra wave number to develop resonant TH THz SPWs at frequency 3ω0 and wave number kz=3k0z+q. The required ripple wave number for the excitation of THz TH SPWs is lower for the higher Fermi energy of the graphene sheet as compared to lower Fermi energy. Graphene sheet’s Fermi energy and angle of incidence laser beam significantly modify the amplitude of TH THz SPWs.