We investigate the relationship between passive mode locking and the formation of time-localized structures in the output intensity of a laser. We show how the mode-locked pulses transform into lasing localized structures, allowing for individual addressing and arbitrary low repetition rates. Our analysis reveals that this occurs when (i) the cavity round-trip is much larger than the slowest medium time scale, namely the gain recovery time, and (ii) the mode-locked solution coexists with the zero intensity (off) solution. These conditions enable the coexistence of a large quantity of stable solutions, each of them being characterized by a different number of pulses per round-trip and with different arrangements. Then, each mode-locked pulse becomes localized, i.e., individually addressable. [11]. The possibility of using LS as information bits for processing information in optical devices [12][13][14] has attracted an increasing interest in the last twenty years. LS have been observed in the transverse section of broad-area semiconductor microcavities injected by a coherent electromagnetic field [15] (passive morphogenesis) and are also termed "cavity solitons." More recently, spatial LS have been observed in laser systems where they arise from spontaneous emission noise [16,17] (active morphogenesis), without requiring an injected field. Because these lasing LS appear in a phase invariant system, their dynamical ingredients and their properties are very different from the LS appearing in injected resonators [18].Recent works have addressed the question whether the concept of LS can be extended to the time domain [19][20][21][22] in the case of optically injected cavities. Here we propose to answer to this question considering a phase invariant system, namely a passively mode-locked laser. Passive mode locking (PML) is an elegant method leading to the emission of pulses much shorter than the cavity round-trip. It is achieved by combining two elements, a laser amplifier providing gain and a nonlinear loss element, usually a saturable absorber (SA). The different dynamical properties of the SA and of the gain create a window for regeneration only around the pulse. PML can be successfully described via the seminal Haus' master equation, which combines the nonlinear Schrödinger equation with dynamical nonlinear gain and losses [23]. In fiber or Ti:sapphire lasers [24], for which the gain and the absorption are respectively much slower and faster than all the other variables, the Haus equation can be approximated by the subcritical cubic-quintic complex Ginzburg-Landau equation where one replaces for simplicity the slowly evolving net gain-which has a typical time scale of Γ −1 ¼ 10 ms in doped fibers-by a constant. This constant must be determined self-consistently as it depends on the number of PML pulses per round-trip, which may be one (fundamental PML) or N h (N-th order harmonic PML). The stability of these different emission states is described by the so-called background stability criterion of PML [25], whic...

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed in an external cavity lead to the emission of temporal dissipative solitons. These are vectorial solitons because they appear as localized pulses in the polarized output, but leave the total intensity constant. When the cavity roundtrip time is much longer than the soliton duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solitons coexist together and with the background solution. The experimental results are well described by a theoretical model that can be reduced to a single delayed equation for the polarization orientation, which allows the vectorial solitons to be interpreted as polarization kinks. A Floquet analysis is used to confirm the mutual independence of the observed solitons.T he field of dissipative solitons (DS) in optical systems has been the subject of intensive research during the past 20 years (see, for example, Akhmediev and Ankiewicz 1,2 , Ackemann et al. 3 , Descalzi et al. 4 and Grelu and Akhmediev 5 , and references therein). Optical DS are localized light pulses in time or localized beams in space that appear in nonlinear systems kept out of equilibrium by a continuous flow of energy that counteracts the losses 5 . As a consequence, DS differ substantially from conservative solitons, which originate purely by a compensation between a spreading effect and the nonlinearity.A first important difference concerns the role of the nonlinearity. Although in the beginning DS were envisioned as weakly modified conservative solitons 6 , it was later shown that, for strong dissipation, the scenario that leads to DS formation may be more complex. For instance, bright cavity solitons, which appear in the transverse plane of driven resonators 7-10 , exist even in the presence of defocusing nonlinearities, which favour the spreading effect 11 . Cavity solitons are cellular patterns generated by fronts that connect different coexisting spatial solutions 12 and their existence cannot be reduced to a simple compensation mechanism between nonlinearity and diffraction.Another fundamental difference is that DS are attractors, that is stable solutions towards which the system evolves spontaneously from a wide set of initial conditions 13 . This entails that, at variance with their conservative analogues, DS do not rely on a proper seeding of the initial conditions. This renders them extremely interesting for applications and, in particular, for information processing in which DS are used as bit units. For example, recently all-optical buffers based on cavity solitons have been demonstrated both in spatial and in temporal domains 3,10,14-16 .Temporal DS have been studied largely in mode-locked lasers 5 and, more recently, in Kerr fibre cavities driven by an injected field 14 ; several interesting behaviours have been experimentally demonstrated, as, for example, soliton bound states 17 , molecules 18 , repulsive/attracting forces on an extremely lo...

We show that the pumping current is a convenient parameter for manipulating the temporal Localized Structures (LSs), also called localized pulses, found in passively mode-locked Vertical-Cavity Surface-Emitting Lasers. While short electrical pulses can be used for writing and erasing individual LSs, we demonstrate that a current modulation introduces a temporally evolving parameter landscape allowing to control the position and the dynamics of LSs. We show that the localized pulses drifting speed in this landscape depends almost exclusively on the local parameter value instead of depending on the landscape gradient, as shown in quasi-instantaneous media. This experimental observation is theoretically explained by the causal response time of the semiconductor carriers that occurs on an finite timescale and breaks the parity invariance along the cavity, thus leading to a new paradigm for temporal tweezing of localized pulses. Different modulation waveforms are applied for describing exhaustively this paradigm. Starting from a generic model of passive mode-locking based upon delay differential equations, we deduce the effective equations of motion for these LSs in a time-dependent current landscape.