Bruno Garbin

Topological solitons as addressable phase bits in a driven laser

Optical localized states are usually defined as self-localized bistable packets of light, which exist as independently controllable optical intensity pulses either in the longitudinal or transverse dimension of nonlinear optical systems. Here we demonstrate experimentally and analytically the existence of longitudinal localized states that exist fundamentally in the phase of laser light. These robust and versatile phase bits can be individually nucleated and canceled in an injection-locked semiconductor laser operated in a neuron-like excitable regime and submitted to delayed feedback. The demonstration of their control opens the way to their use as phase information units in next-generation coherent communication systems. We analyse our observations in terms of a generic model, which confirms the topological nature of the phase bits and discloses their formal but profound analogy with Sine-Gordon solitons.

Refractory period of an excitable semiconductor laser with optical injection

Injection-locked semiconductor lasers can be brought to a neuronlike excitable regime when parameters are set close to the unlocking transition. Here we study experimentally the response of this system to repeated optical perturbations and observe the existence of a refractory period during which perturbations are not able to elicit an excitable response. The results are analyzed via simulations of a set of dynamical equations which reproduced adequately the experimental results.

Interactions and collisions of topological solitons in a semiconductor laser with optical injection and feedback

We present experimental and numerical results about dynamical interactions of topological solitons in a semiconductor laser with coherent injection and feedback. We show different kind of interactions such as repulsion, annihilation, or formation of soliton bound states, depending on laser parameters. Collisions between single structures and bound states conserve momentum and charge.

Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields

We report on a systematic study of temporal Kerr cavity soliton dynamics in the presence of pulsed or amplitude-modulated driving fields. In stark contrast to the more extensively studied case of phase modulations, we find that Kerr cavity solitons are not always attracted to maxima or minima of driving field amplitude inhomogeneities. Instead, we find that the solitons are attracted to temporal positions associated with specific driving field values that depend only on the cavity detuning. We describe our findings in light of a spontaneous symmetry breaking instability that physically ensues from a competition between coherent driving and nonlinear propagation effects. In addition to identifying a previously unfamiliar type of Kerr cavity soliton behavior, our results provide valuable insights into practical cavity configurations employing pulsed or amplitude-modulated driving fields.

Dynamics and locking of switching waves in a normally dispersive fiber ring resonator (Conference Presentation)

Switching waves (SWs) are walls that connect two homogeneous stable states of a multistable system. They are typically transient: a single SW will travel until the more stable state invades completely the less stable one. A single SW is only ever stationary at the so-called Maxwell point, a set of parameters where the two states have the same marginal stability. For parameters close to the Maxwell point, two approaching SWs can form a stable stationary structure provided that they have oscillatory tails through which they interlock. Such structures have recently been observed in the normal dispersion regime of microresonators and are known to correspond to dark pulse Kerr frequency combs. However, the small physical size of microresonators means that quantitative study of the transient dynamics that leads to their formation is difficult. In this contribution, we overcome this challenge by performing systematic experiments and simulations in a synchronously-driven macroscopic fiber ring resonator, and report on observations of transient SW dynamics. Our resonator is made of normal dispersion fiber, which allows for the coexistence of two homogeneous steady states and their connection through a SW. We have measured the SW velocities across a wide range of parameters, and close to the identified Maxwell point, observed interlocked SWs persisting for 100’s of resonator photon lifetimes. Our results provide significant experimental insights on the transient dynamics of SWs that have been theoretically predicted to underpin the formation of Kerr frequency combs in normally dispersive microresonators.

Coherent effects in mode-locked lasers: new theory and experiments

We present the predictions of a new theory for mode-locking in lasers valid also for fast gain media (e.g. semiconductor lasers). Substantial deviations from Haus theory are found, which are validated by experimental results.

Intensity trapping of temporal cavity solitons

Temporal cavity solitons (TCSs) are optical pulses that persist inside coherently driven passive Kerr resonators [1]. Since their discovery, TCSs have been suggested as bits for all-optical buffers due to their flexibility [2]: they can be individually addressed, erased and moved around at will. To that end, a reliable method is required to move, position, and trap TCSs to precise locations. So far a successful method to achieve this has been to use a phase modulation of the driving field in space [3] or time [4]. Here, we demonstrate that TCS trapping and manipulation can also be achieved by inducing intensity gradients on the background field.

Experimental investigations of switching wave dynamics and locking in a normally dispersive Kerr ring resonator

Switching waves (SWs) are fronts that connect two homogeneous stable states of a multistable system [1]. An isolated SW typically propagates until the most stable state completely invades the other and can only be stationary at the so-called Maxwell point, where the two states have the same marginal stability. Close to the Maxwell point, it may still be possible however for two SWs to form a stable stationary structure provided the SWs have oscillatory tails through which they interlock [2]. In the normal dispersion regime of coherently driven passive resonators, such structures are known to correspond to dark pulse Kerr frequency combs [3] as observed recently in microresonators [4]. Note that the observations reported in [4] only correspond to the stationary structures: the small physical size of microresonators prevents quantitative study of the transient dynamics. As a result, no experimental evidence of the dynamical propagation and locking of SWs has been reported yet.

Bifurcation analysis of nonlinear coupled photonic nanocavities

Recently, various research groups have studied spontaneous symmetry breaking and bistable behaviour in both active and passively driven coupled photonic nanocavities[1]. This work is of interest both in itself and because it naturally extends to coupled nonlinear quantum systems described by the Bose-Hubbard model [2]. Here we present a theoretical study of the dynamics in such a system by considering the bifurcation behaviour as the different parameters are varied. In normalised units the model can be written as: dA/dt = i(δ τ + |A|²)A-A+(iκ + γ)τB+f (1) dB/dt = i(δ τ + |B|²)B-B+(iκ + γ)τA+f (2) where A and B are the slowly varying normalised amplitudes of the fields in each nano-cavity. Further, δ is the detuning from the cavity resonance, τ is the photon lifetime, κ and γ describe the linear coupling between the cavities (if γ = 0 and κ < 0 the model is identical to the Bose-Hubbard model [2] in the semiclassical regime), while f represents a coherent driving term. In deriving the above equations it is assumed that the cavities are identical, and so a focus is the switching between the symmetrical state [A(t) = B(t)] and asymmetrical states, which must come in pairs. Fig. 1(a) shows a typical boundary curve dividing the (δ, f) plane into the regions where the symmetric and asymmetric solutions exist. Further analysis shows that more complicated dynamics arise from the asymmetric state. Fig. 1(b) shows the field intensity for the symmetric and asymmetric steady-states as a function of f, where stable solutions are represented by solid and unstable ones by dashed curves. Hopf bifurcations, marked by H, cause the asymmetric solution to change stability. A typical bifurcating periodic solution is shown in Fig. 1(c) for f = 6.

Resonance and multipulse excitability

Already several years ago [3], it was suggested that a laser with optical injection can respond to external perturbations by emitting spikes if the perturbation overcomes a certain threshold, all the spikes being identical to each other, in complete analogy with the behaviour of the simple theta-model neuron [1]. The underlying explanation of this phenomenon lies in the isomorphism between a model of neuron [1] and that of an over-damped oscillator with periodic forcing (often called the Adler equation [2]). The control of these spikes was only achieved recently [5], while their observation goes back to [4]. Although there is an excellent agreement between these observations and the predictions of the reduction to pure phase dynamics of a laser model [3], it was soon noticed that whenever the pure phase dynamics reduction ceases to be valid, more complex dynamical phenomena can take place, leading to multipulse excitability [6]. This has led to the investigation of the behaviour of a semiconductor laser locked to an external forcing in response to external perturbations beyond the simple case of the Adler-like mode. We observe resonator features of the neuron-like system and multi-spike responses. Beyond improving the understanding of the neuron-like excitable dynamics of the laser with injected signal, our aim is to leverage the multipulse excitability and the resonator features of the optical neuron analogue for optical data processing and to provide possible insight about complex solitons interactions in forced oscillatory media [7, 8].