Modulation instability of silicon optical waveguide considering linear loss and biphotonic absorption

Taking into account the linear loss and biphotonic absorption effect of silicon-on-insulator (SOI) waveguide simultaneously, condition and gain spectra of modulation instability (MI) induced by combined effects of self-phase modulation and waveguide dispersions were investigated. Formulation for calculating the gain of MI was deduced theoretically, and expressions of peak gain, peak gain frequency and bandwidth of modulation instability were obtained as well. Impacts of various parameters on gain spectra of MI were analyzed theoretically and simulated in detail. Both theoretical analysis and simulation show that strong MI takes place even in the existence of low light power. The peak gain of MI is 2 to 3 orders of magnitude larger than that achieved in optical fibers with the same light power. Both peak gain frequency and bandwidth of gain spectra of MI are decreased exponentially with linear loss of waveguide, and peak gain is decreased exponentially with bi-photonic absorption of waveguide as well. The work provides an important reference for experimentally investigating modulation instability and supercontinuum generation in silicon waveguide.