Optimizing initial chirp for efficient femtosecond wavelength conversion in silicon waveguide by split-step Fourier method

Based on solving numerically the generalized nonlinear Schrödinger (GNLS) equation by a split-step Fourier method, efficient femtosecond wavelength conversion in the telecommunication bands via four-wave mixing in silicon rib waveguide is numerically investigated by optimizing the initial chirp of the pump and signal pulses. It is shown that the relative narrower four-wave mixing spectra with the most of the energy remains in the central peak can be obtained by the use of appropriate negative chirp, and the conversion bandwidth greater than 500 nm and peak conversion efficiency of −1.6 dB can be obtained by using 200 fs pulses with a repetition rate of 40 GHz in a 3.2-mm-long silicon rib waveguide.