Dissipative solitons characterization in singly resonant optical parametric oscillators: a variational formalism

Abstract

In this work, the emergence of single-peak temporal dissipative solitons in singly-resonant degenerate optical parametric oscillators is investigated analytically. Applying the Kantarovich optimization method, through a Lagrangian variational formalism, an approximate analytical soliton solution is computed using a parameter-dependent ansatz. This permits to obtain analytical estimations for the dissipative soliton energy, peak power, and existence boundaries, which are of great value for experimentalist. To confirm the validity of this procedure, these analytical results are compared with a numerical study performed in the context of pure quadratic systems, showing a good agreement.