Bound states of temporal Kerr solitons mediated by pump depletion in a doubly resonant optical parametric oscillator

We theoretically study the interaction between two parametrically driven Kerr cavity solitons in a doubly resonant optical parametric oscillator. In the presence of weak walk-off, the depletion dynamics induce oscillating tails in the temporal profile of the pump, leading to the formation of bound states. Our study reveals the critical role of walk-off and depletion effects in governing the long-range interaction and binding mechanisms between solitons, offering new insights into the control and stabilization of soliton pairs in parametric systems. • Dissipative solitons in a degenerate OPO form bound states through pump depletion. • Analytical analysis reveals stable equilibrium positions of these bound states. • Analytical results agree well with numerical solutions of the degenerate OPO model.