Dissipative Phase Solitons in Semiconductor Lasers

Abstract

We experimentally demonstrate the existence of non dispersive solitary waves associated with a 2π phase rotation in a strongly multimode ring semiconductor laser with coherent forcing. Similarly to Bloch domain walls, such structures host a chiral charge. The numerical simulations based on a set of effective Maxwell-Bloch equations support the experimental evidence that only one sign of chiral charge is stable, which strongly affects the motion of the phase solitons. Furthermore, the reduction of the model to a modified Ginzburg Landau equation with forcing demonstrates the generality of these phenomena and exposes the impact of the lack of parity symmetry in propagative optical systems. PACS numbers: Valid PACS appear hereDissipative solitary waves have been observed as selflocalized optical wave packets along the direction of propagation in many out of equilibrium and nonlinear optical systems. In spite of their huge variety, many of the observations reported so far can be cast in two main categories depending on the presence or absence of coherent energy input, ie the (lack of) phase symmetry of the system [1]. In systems with phase symmetry, mode-locked laser pulses have been analyzed as dissipative solitons of the cubic-quintic Ginzburg Landau equation [2]. Their optical phase can wander in the course of time due to the neutral mode created upon the formation of a coherent wave. On the contrary, dissipative solitons in forced systems [3,4] have been analyzed in the framework of the Lugiato-Lefever equation [5], which includes a coherent forcing term acting as a phase reference to which solitons will lock. In both cases, the use of paradigmatic equations in addition to system-specific models has allowed to formally connect these optical solitary waves to localized states as they appear in fluid dynamics, plant ecology, granular media or reaction-diffusion systems [6][7][8][9]. In fact, optical dissipative solitons can often be explained as perturbed solitons of the nonlinear Schrödinger equation (in the weak dissipation limit [10-12]) or as locked fronts (in strongly dissipative systems [13,14]).In this Letter, we report on dissipative solitons which fundamentally consist of self-confined 2π phase rotations embedded in a homogeneously phase locked background. These "phase solitons" are generic features of spatially extended oscillatory media under nearly resonant forcing [15,16] and result from the mismatch between the natural periodicity and the forcing. Here, the mismatch between the free running laser and the external forcing frequencies leads to the formation of phase kinks * Electronic address: stephane.barland@inln.cnrs.fr as result of a commensurate-incommensurate transition [17,18]. This connects our observations with the kink solutions observed in many physical systems described by the Frenkel-Kontorova model [19], such as fluxons in Josephson arrays [20], local deformations in DNA chain [21], or excitable waves in chemical and biological systems [22,23]. In nonvariational systems, chirality acquire...

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