Second harmonic generation due to action of light on a metal surface with a periodic profile

The complete problem of second harmonic generation (SHG) for light incident on a metal surface is reduced to an external electromagnetic problem by generalization of the Leontovich boundary condition. Calculations are made of the SHG intensity on a metal surface having a sinusoidal profile. It is shown that resonance excitation of surface plasma waves on a periodic surface may result in enhancement of SHG by a factor of the order of 10⁶.