Pump Depletion Limits the Existence of Kerr Solitons in Singly-Resonant Optical Parametric Oscillators

Optical temporal dissipative solitons are pulses that form thanks to the double balance between dispersion and nonlinearity, and driving (or gain) and losses. Cavity Solitons (CS) are one of the most paradigmatic kinds of DS since they underpin the formation of coherent Kerr frequency combs [1]. CSs form in Kerr cavities coherently driven at the soliton carrier frequency $\omega_{0}$ through a linear coupler [2]. However, forcing the cavity through a linear coupler provides a poor frequency conversion from the driving to the pulse [3]. An alternative manner to sustain dissipative solitons is through parametric driving. In this case they are called parametrically driven CS (PDCS) [4], and have been recently experimentally observed [5].