Dynamics of dissipative temporal solitons

Abstract

The properties and the dynamics of localized structures, frequently termed solitary waves or solitons, define, to a large extent, the behavior of the relevant nonlinear system [1]. Thus, it is a crucial and fundamental issue of nonlinear dynamics to fully characterize these objects in various conservative and dissipative nonlinear environments. Apart from this fundamental point of view, solitons (henceforth we adopt this term, even for localized solutions of non-integrable systems) exhibit a remarkable potential for applications, particularly if optical systems are considered. Regarding the type of localization, one can distinguish between temporal and spatial solitons. Spatial solitons are self-confined beams, which are shape-invariant upon propagation. (For an overview, see [2, 3]). It can be anticipated that they could play a vital role in all-optical processing and logic, since we can use their complex collision behavior [4]. Temporal solitons, on the other hand, represent shapeinvariant (or breathing) pulses. It is now common belief that robust temporal solitons will play a major role as elementary units (bits) of information in future all-optical networks [5, 6]. Until now, the main emphasis has been on temporal and spatial soliton families in conservative systems, where energy is conserved. Recently, another class of solitons, which are characterized by a permanent energy exchange with their environment, has attracted much attention. These solitons are termed dissipative solitons or auto-solitons. They emerge as a result of a balance between linear (delocalization and losses) and nonlinear (self-phase modulation and gain/loss saturation) effects. Except for very few cases [7], they form zero-parameter families and their features are entirely fixed by the underlying optical system. Cavity solitons form a prominent type. They appear as spatially-localized transverse peaks in transmission or reflection, e.g. from a Fabry-Perot cavity. They rely strongly on the nonlinear interaction of forward and backward propagating fields, where cavity (radiation) losses are compensated for by gain or an external holding beam. Cavity solitons have been observed in Fabry-Perot cavities and single mirror feedback setups (for an overview see [8]). In contrast, propagating dissipative solitons consist of forward-propagating fields only. Recently, the existence of both stable temporal [9] and spatial propagating dissipative solitons [10] was experimentally demonstrated. It is evident that the study of dissipative solitons is of great practical relevance, because most real optical systems are dissipative by nature.