Relationship between second-harmonic generation and electric-field-induced second-harmonic generation

We calculate the electric-field-induced second-harmonic-generation (EFISH) susceptibility of a homogeneously broadened two-level system with permanent dipole moments. This susceptibility has contributions from the second-harmonic-generation (SHG) susceptibility of the same system without the presence of a dc field and the four-wave-mixing (FWM) component of the susceptibility e(-2;0). The magnitude and phase of the various contributions to EFISH arising from SHG and from FWM depend on the frequency of the fundamental optical field, the transition dipole moment ab, the permanent dipole moment of the ground-state level aa, and the difference of the ground- and excited-state dipole moments . We present non-rotating-wave-approximation results for both the quasi-steady-state in systems where the dephasing time T2 is much shorter than the population decay time T1, so the polarization is in a steady state but the population is not, and for the complete steady state. Extraction of the SHG susceptibility from EFISH measurements is considered.