Hydrodynamic model for sum and difference frequency generation at metal surfaces

Abstract

We develop a hydrodynamic model for the calculation of sum and difference frequency generation (SFG/DFG) at the surface of nonlocal conductors with arbitrary equilibrium electronic density profiles n(0). We apply our model to simple profiles and calculate the nonlinear surface susceptibility tensor chi(zzz)(s)(omega(1),omega(2)) and the radiated efficiency R(omega(3) = omega(1) +/- omega(2)) as a function of the pump frequencies omega(1) and omega(1). R is strongly enhanced due to the excitation of the dipolar surface plasmon characterized by a resonant frequency omega(d)

it displays ridges whenever omega(1), omega 2, Or omega(3) approximate to 5 omega(d) , an additional ridge at the bulk plasma frequency omega(3) approximate to omega(b) , and very large double resonance peaks whenever two ridges cross each other. These results suggest that SFG/DFG spectroscopy might be a useful probe of surface collective modes. [S0163-1829(98)03403-1].