Wavelength conversions in quasi-phase matched LiNbO3 waveguide based on double-pass cascaded χ(2) SFG+DFG interactions

Based on the cascaded nonlinear interactions (χ⁽²⁾:χ⁽²⁾) of sum- and difference-frequency generation (SFG+DFG), a novel all-optical wavelength conversion scheme is proposed for the first time in periodically poled LiNbO₃ (PPLN) waveguide, in which a double-pass configuration is introduced. The performance of this scheme is thus different from the previous single-pass SFG+DFG scheme. The concept of the "balance condition" is presented to optimize the power and frequencies of the two pump sources. Under this condition, the energy is transferred irreversibly from the pump waves to the SF wave during the forward propagation. The equations describing the SFG can be solved analytically under this condition. Subsequently, the DFG equations are solved under the assumption that the SF wave would be constant during the backward propagation. Theoretical expressions are derived and are found to be consistent with numerical calculations. Compared with the conventional converter based on the cascaded χ⁽²⁾:χ⁽²⁾ interactions of second-harmonic generation and difference frequency generation SHG+DFG, the same conversion efficiency can be achieved in our scheme by employing two pump sources with lower power, or conversely higher conversion efficiency can be reached using two pump sources similar to that used in SFG+DFG scheme. The profile of the conversion efficiency can be further improved by adjusting the wavelengths of the two pump sources. In addition, compared with the single-pass SFG+DFG scheme, the main advantage of this new scheme rests on the fact that the conversion efficiency can be enhanced significantly. The advantages of the double-pass SHG+DFG scheme and the single-pass SFG+DFG scheme are combined in this new design to a great extent.