We consider four-photon resonant six-wave mixing and show that the efficiency of harmonic generation is limited due to destructive interference between different optical harmonics. Following the idea of ``induced transparency'' of Harris et al. [Phys. Rev. Lett. 64, 1107 (1990)], it is shown that in the presence of an auxiliary electromagnetic coupling between the four-photon excited level and a third level, the interference between various excitation channels can be made constructive. Depending upon the strength of the auxiliary wave, absorption and dispersion-free propagation of the generated wave lead to high conversion efficiency.
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 ${\ensuremath{\gamma}}_{\mathit{e}}$(-2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},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 ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{b}}$, the permanent dipole moment of the ground-state level ${\mathrm{\ensuremath{\mu}}}_{\mathit{a}\mathit{a}}$, and the difference of the ground- and excited-state dipole moments \ensuremath{\Delta}\ensuremath{\mu}. 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.
Using Schrodinger-Maxwell formalism, we propose and analyze a continuous-wave four-wave mixing (FWM) scheme for the generation of coherent light in a six-level atomic system based on electromagnetically dual induced transparency. We derive the corresponding explicit analytical expressions for the generated mixing field. We find that the scheme greatly enhances FWM production efficiency and is also capable of inhibiting and delaying the onset of the detrimental three-photon destructive interference by choosing the proper decay rate in the second electromagnetically induced transparency (EIT) process. In addition, such an optical process also provides possibilities for producing short-wave-length coherent radiation at low pump intensities.