Self-generation of dark and bright envelope pulses in bidirectionally coupled Vyshkind–Rabinovich parametric oscillators

The generation modes of dark and bright envelope pulses are obtained in the system of two bidirectionally coupled Vyshkind–Rabinovich parametric oscillators. Each oscillator describes the temporal dynamics of a quadratic medium with inertialess amplification at a given point in space. Oscillations of an unstable wave amplify linearly, while oscillations of parametrically excited waves attenuate in a linear approximation. It is shown that a sequence of dark envelope pulses is formed on an unstable wave and is parametrically coupled with a sequence of bright envelope pulses generated on parametrically excited waves only at certain values of the bidirectional coupling.