Second-order optical response in semiconductors

We present a new general formalism for investigating the second-order optical response of solids, and I illustrate it by deriving expressions for the second-order susceptibility tensor chi(2) (-omega(Sigma);omega(beta),omega(gamma)), where omega(Sigma) = omega(beta) + omega(gamma), for clean, cold semiconductors in the independent particle approximation. Based on the identification of a polarization operator P that would be valid even in a more complicated many-body treatment, the approach avoids apparent, unphysical divergences of the nonlinear Optical response at zero frequency that sometimes plague such calculations. As a result, it allows for, a:careful examination of actual divergences associated with physical phenomena that have been studied before, but-not in the context of nonlinear optics. These are (i) a coherent current control effect called "injection current," or "circular photocurrent," and (ii) photocurrent due to the shift of the center of electron charge in noncentrosymmetric materials in; the process of Optical excitation, called ''shift current.'' The expressions:We present:are amenable for numerical calculations, and;we demonstrate this by performing a full band-structure Calculation of the shift current coefficient for GaAs.