Disorder effects on second-harmonic generation from one-dimensional arrays of polarizable units

In order to study the effects of disorder in surface second-harmonic generation (SHG), we perform a numerical simulation on an infinite one-dimensional array of polarizable entities embedded in a homogeneous host. The position of each entity within the unit cell is generated by using two different types of disorder algorithms, and periodic boundary conditions are applied to generate an infinite chain. The contribution of the coherent and the incoherent radiation to the SHG radiated efficiency is calculated including the dipolar and quadrupolar interaction among the polarizable units in a self-consistent treatment, and within the long-wavelength approximation. The induced linear and nonlinear dipolar and quadrupolar moments on each entity are calculated by solving a set of linear algebraic equations. We consider that the entities are identical to each other and that each responds to the local field and to the gradient of the local field, like an isotropic harmonic oscillator.