Editorial on Dissipative Optical Solitons

Abstract

The fundamental mechanism that defines the concept of an optical soliton is the exact balance between two opposite mechanisms, one allowing for the spreading, the other for the concentration of a localized distribution of light. Historically, this was found in conservative systems and can be described by the nonlinear Shrodinger equation and other related equations. This situation applies both to the case of temporal solitons where group velocity dispersion and self-phase modulation counteract one another in the longitudinal dimension of light propagation and to the case of spatial solitons where diffraction spreading and Kerr lensing compensate, leading to a stable distribution of light with a constant beam waist. Solitons have been known as an experimental evidence since the early observation by John Scott Russel of a water solitary wave in 1844. The study of temporal optical solitons more than a century later has benefited from the very rapid development during the 70’s of optical fiber performance whose residual Kerr effect could be used to propagate short intense pulses across distances that can reach now thousands of kilometers. From the 1990’s a new branch of soliton studies has developed in dissipative optical systems defined as lossy systems fed with an external input of energy. Therein, it has been progressively shown through the pioneering theoretical work of Lugiato and Lefever [1], Rosanov [2], Mandel [3], and Firth [4] that nonlinear optical cavities or feedback systems can reach various levels of self-organization among which patterned and localized bistable states are expected. These predictions were rapidly confirmed by their observation in various systems including liquid crystal light valves [5], sodium vapors [6], photorefractive materials [7], and most recently semiconductors [8,9]. These localized states, when exhibiting bistability, were called cavity solitons and appeared to display new properties. The term “soliton”, though not strictly matching the requirement of being an exact solution of a conservative non linear propagation equation, conveys however the concept that an equilibrium is reached between counteracting mechanisms, one of them at least being nonlinear. Indeed, in addition to obtaining