Round-Trip Model of Quadratic Cavity Soliton Trapping

In recent years a considerable interest has been focused on theoretical [1–10] and experimental [12, 13] studies of spatial dissipative structures in nonlinear optical resonators. Cavity soliton (CS) can be created and destroyed by localised pulses of light, and can thus be used to store images or information. The ability to control and manipulate CS has been proposed in the pioneering paper [2] for the case of two-level medium. The problem of stationary soliton solution has been numerically and analytically investigated mostly in the case of the semiconductor optical resonators [5] and cubic nonlinear cavity [6]. Note that the quadratic non-linearity provides a wide range of new opportunities. For instance, the threshold of pattern formation in a degenerate OPO was considered [7]. Some authors concentrate their attention on the CS interaction [8]. The problem of soliton stability in OPO is discussed in [9]. The most complicated case of SHG configuration with driving field corresponding to the fundamental frequency (FF) was studied in [10]. It was found that the quadratic CS can appear due to modulation instability of the steady-state solution. It should be emphasized that trapping dynamics of CS is not investigated sufficiently.