Delayed optical feedback-regulated artificial soliton molecule in a femtosecond optical parametric oscillator

Abstract Soliton molecules (SMs) play a crucial role in nonlinear optical systems, enriching our understanding of nonlinear science through the study of their interaction dynamics. While passively mode-locked fiber lasers offer an efficient platform for generating diverse types of SMs, the complex internal dynamics of the laser often pose challenges in achieving predetermined temporal separations between SMs. Here, we implement a delayed optical feedback technique within a femtosecond optical parametric oscillator, enabling the generation of SMs with precise and controllable temporal separations. A theoretical model, which models the intracavity iterations of the signal with a simplified Ikeda map, is proposed to study the impact of parametric gain, intracavity feedback delay, and cavity length on the internal separations of the SMs. Our experimental results confirm that adjusting the cavity length allows for producing desired temporal separations within SMs. To reveal the evolution dynamics of the SMs, we further develop a rigorous numerical model using the carrier-resolved Forward Maxwell Equation, which is capable of modeling ultra-broadband complex dynamics based on a single equation without relying on the slowly-varying envelope approximation. The numerical model unveils the rich formation dynamics of the SMs at various separations, which confirms the critical role of the gain window provided by the pump. This work opens up new opportunities for the on-demand generation of SMs and provides valuable insights into the complex dynamics in femtosecond optical parametric oscillator systems with optical delayed feedback.