Ab initio nonlinear optics in solids: linear electro-optic effect and electric-field induced second-harmonic generation

Second-harmonic generation (SHG), linear electro-optic effect (LEO) and electric-field induced second-harmonic generation (EFISH) are nonlinear optical processes with important applications in optoelectronics and photovoltaics. SHG and LEO are second-order nonlinear optical processes described by second-order susceptibility. Instead, EFISH is a third-order nonlinear optical process described by third-order susceptibility. LEO and EFISH are only observed in the presence of a static electric field. These nonlinear processes are very sensitive to the symmetry of the systems. In particular, LEO is usually observed through a change in the dielectric properties of the material while EFISH can be used to generate a "second harmonic" response in centrosymmetric material. In this work, we present a first-principle formalism to calculate second- and third-order susceptibility for LEO and EFISH. LEO is studied for GaAs semiconductor and compared with the dielectric properties of this material. We also present how it is possible for LEO to include the ionic contribution to the second-order macroscopic susceptibility. Concerning EFISH we present for the first time the theory we developed in the framework of TDDFT to calculate this nonlinear optical process. Our approach permits to obtain an expression for EFISH which does not contain the mathematical divergences in the frequency-dependent second-order susceptibility that caused until now many difficulties for numerical calculations.