Optical breathers and multiple rogue waves via the modulation instability for a complex Ginzburg–Landau equation in the mode-locked laser operation

Abstract

Investigation is made on a complex Ginzburg–Landau equation for the mode-locked laser operation. Optical breathers are numerically derived via the split-step Fourier method. Effects of the modulation instability on the dynamic behaviors of the optical breathers are investigated: when the growth rate of the modulation instability increases, the optical breather splits into two optical breathers earlier, and the two optical breathers separate faster. Via the energy distributions of the optical breathers, we obtain that when the fission phenomenon occurs, the energy decreases more than that of the fusion phenomenon. Multiple rogue waves in the chaotic wave field are obtained via the modulation instability. It is observed that multiple rogue waves occur earlier as the growth rate of the modulation instability becomes larger. Occurrence of the rogue wave can be predicted via the spectrum of the optical chaotic wave field.