Third-harmonic generation at a silver/vacuum interface using surface plasmon polaritons

We present an analytical study of a third-harmonic generation process by surface plasmon polaritons at a Kerr-nonlinear-metal/dielectric interface. Using a planar silver/vacuum interface, we obtain a solution to the frequency-tripling process, showing a semibound third-harmonic surface wave. Unlike the fundamental surface-bound mode, the nonlinear signal radiates into the metal, while remaining bound at the dielectric side of the interface. The propagation of the tripled frequency wave into the metal is generally lossy, except within a narrow range of ultraviolet frequencies, where it is minimally attenuated. The latter is enabled by a transparency window that is unique to the permittivity of silver.