Abstract
A theoretical treatment of the nonlinear mixing of two contra-directional surface plasmons of frequency ω1 and ω2 propagating on a semi-infinite metal surface is presented. The nonlinear interaction is analysed in terms of (a) nonlinear surface currents due to the breaking of inversion symmetry and the rapid variation of the normal electric field component at the surface, and (b) the nonlinear response of the electron gas in the bulk of the metal. These currents are treated as source terms for Maxwell's equations and electromagnetic fields are found which satisfy the driven wave equation and boundary conditions at the frequencies ω1 ± ω2. At the difference frequency ω1 − ω2 the solution fields decay exponentially into both the air and the metal. However, at the sum frequency ω1 + ω2, coupling to transverse electromagnetic waves in both the air and the metal is predicted under appropriate wavevector and frequency conditions. The free-space radiation field is treated in detail and the feasibility of its experimental detection is discussed. No coupling to longitudinal bulk plasmons is predicted in this model of the nonlinear interaction.
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