Delay-Induced Dynamics of Pinned Cavity Soliton in an Inhomogeneous Kerr Resonator

A cavity soliton (CS) consists of one or more regions in one state surrounded by a region of a qualitatively different state. Such patterns may be stationary or oscillatory, static or moving and they are important in a wide variety of fields [1, 2]. They are potentially interesting for all-optical control of light. To this end, a delayed feedback can be used to control these CSs [3, 4]. Indeed, slowly moving spots subject to delay appear in various other fields. For example, spreading depolarization waves responsible for both migraine and strokes have been described as reaction-diffusion waves subject to delay [5]. Of particular interest are time delayed feedback control (TDEC) schemes. TDFC is based on the use of the difference between systems variables at the current moment of time and their values at some time in the past. They are smooth controls because the steady states of the unperturbed problem are solutions of the delayed feedback problem. More recently, we have investigated the combined influence of an inhomogeneity of the pumping and delayed feedback and shown that it induces oscillations and drift of localized structures in the Swift-Hohenberg equation describing pattern formation in the transverse plane of an optical cavity [6].