Amacroscopic formalism to describe the second-order nonlinear optical response of nanostructures

We present a macroscopic formalism to describe the second-order nonlinear optical response of nanostructures. Rapid variations in local nonlinearity and electric field distributions on scales smaller than a wavelength preclude a simple, direct relationship between the macroscopic and nanoscopic nonlinear response functions in arrays of metal nanoparticles. We develop an approach that bypasses these difficulties by focusing on the macroscopic nonlinear optical response of the sample in terms of the input and output fields. The main advantage of this macroscopic formalism is that it naturally includes contributions from higher multipoles, although symmetry properties can be addressed using electric-dipole-type selection rules. It is limited by being specific to the experimental geometry, although experimental variations are expected to provide additional insight into the underlying physical processes. The formalism is applied to the second-harmonic response of an array of L-shaped gold nanoparticles.