In this paper we extend our previous results concerning the enhancement of nonlinear optical responses near rough self-affine metal surfaces to different objects in a wider spectral range and also beyond the quasistatic limit. In our previous work [E. Poliakov et al., Phys. Rev. B 57, 14 901 (1998)] we studied local and averaged enhancement factors for the second- and third-harmonic generation and degenerate four-wave mixing for nonlinear molecules adsorbed on nanostructured self-affine metal surfaces in the quasistatic approximation in the spectral range from 0.4 to $1.8\mu \mathrm{m}.$ In the present work, we study the same nonlinear effects for surfaces formed by deposition on a plane substrate of fractal clusters rather than individual nanoparticles. The spectral range is extended to $10\mu \mathrm{m}.$ We have calculated the enhancement factors for the above nonlinear process with the account of retardation and performed numerical calculations for significantly larger samples. Our numerical results indicate that the enhancement factors increase with the wavelength up to $\lambda =10\mathrm{}\mu \mathrm{m}.$ The enhancement of the degenerate four-wave mixing can reach, for example, the value of ${10}^{22}$ in the far-infrared spectral region (the maximum enhancement reported by us earlier for this process was $\sim {10}^{16}$ near $\lambda =1.8\mathrm{}\mu \mathrm{m}).\mathrm{}$

• Received 28 April 1999

DOI:https://doi.org/10.1103/PhysRevB.60.10739