Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites

A scaling theory of local-field fluctuations and optical nonlinearities is developed for random metaldielectric composites near a percolation threshold. The theory predicts that in the optical and infrared spectral ranges the local fields are very inhomogeneous and consist of sharp peaks representing localized surface plasmons. The localization maps the Anderson localization problem described by the random Hamiltonian with both onand off-diagonal disorder. The local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of various optical phenomena. The developed theory quantitatively describes enhancement in percolation composites for arbitrary nonlinear optical process. It is shown that enhancement strongly depends on whether a nonlinear multiphoton scattering includes the act of photon subtraction ~annihilation!. The magnitudes and spectral dependencies of enhancements in optical processes with photon subtraction, such as Raman and hyper-Raman scattering, Kerr refraction, and four-wave mixing, are dramatically different from those in processes without photon subtraction, such as in sum-frequency and high-harmonic generation. At percolation, a dip in dependence of optical processes on the metal concentration is predicted. @S0163-1829~99!15547-4#