Exploding Solitons and Rogue Waves in Optical Cavities

Exploding solitons and rogue waves both belong to the class of chaotic pulses. However, they have different characteristics and so far have been studied independently. The amplitude of exploding solitons does not exceed certain limit comparable with the amplitude at its stationary state. Thus, generally, they share no common features with dissipative rogue waves, which are defined as the pulses with exceptionally high amplitudes. However, a special choice of laser parameters allows one to obtain exploding solitons that reach significantly higher amplitudes when they explode. In this chapter, we present evidence for the existence of exploding solitons with extreme peak intensities. This is done in numerical modeling of dissipative solitons in a mode-locked laser with normal cavity dispersion. Using common definitions, we demonstrate that the pulses generated this way are rogue waves.