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.

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these localized structures (LSs) has been investigated so far in situations featuring parity symmetry. In this Letter we extend this analysis to systems lacking this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces.

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