Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites

Abstract

A scaling theory of local field fluctuations and optical nonlinearities is developed for random metal-dielectric 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 (s.p.). The localization maps the Anderson localization problem described by the random Hamiltonian with both on- and off-diagonal disorder. The local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of various optical phenomena. A new numerical method based on the developed theory is suggested. This method is employed to calculate the giant field fluctuations and enhancement of various optical processes in 2D metal-dielectric composites – semicontinuous metal films. The local field fluctuations appear to be highly correlated in space. These fluctuations result in dramatically enhanced Rayleigh and Raman light scattering. The scaling analysis is performed to describe the giant light scattering in a vicinity of the percolation threshold. The developed theory describes quantitatively enhancement of various nonlinear optical processes in percolation composites. It is shown that enhancement depends strongly on whether nonlinear multiphoton scattering includes an 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 processes without photon subtraction, such as sum-frequency and high-harmonic generation. Electromagnetic properties of metal-dielectric crystals and composites beyond the quasistatic approximation are also studied. Equations of macroscopic electromagnetism are presented for these systems. Both linear and nonlinear optical responses are considered in the case of a strong skin effect in metal grains. It is shown that the magnetic field undergoes giant spatial fluctuations. Scaling properties of the local magnetic field and its high-order moments are analyzed.