Cavity soliton mobility in semiconductor microresonators

We show here different methods to demonstrate the intrinsic mobility of cavity solitons and realize a number of cavity soliton trajectories. These methods are based on one hand, on the drift of cavity solitons in phase or amplitude gradients and on the other hand, on the recently discovered spontaneous motion of cavity solitons induced by the thermal dynamics in semiconductor devices. When the holding beam corresponds to a doughnut mode (instead of a Gaussian as usually) cavity solitons undergo a rotational motion along the annulus of the doughnut. In a similar way, thermal motion can be controlled by introducing phase or amplitude modulations in the holding beam. Finally, we show that in presence of a weak 2D phase modulation, the cavity soliton, due to the thermally induced motion, performs a random walk from one maximum of the profile to another, always escaping from the temperature minimum generated by the soliton itself (fugitive soliton).