We present a new general formalism for investigating the second-order optical response of solids, and 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 $\mathbf{P}$ 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 $\mathit{actual}$ 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.

• Received 29 June 1999

DOI:https://doi.org/10.1103/PhysRevB.61.5337