arXiv subjects

Pedro Parra-Rivas

Publications and source records attributed to Pedro Parra-Rivas.

30 records · Page 2Linked to original sources

arXiv2022

Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology

Spatially extended patterns and multistability of possible different states is common in many ecosystems, and their combination has an important impact on their dynamical behaviours. One potential combination involves tristability between a patterned state and two different uniform states. Using a simplified version of the Gilad-Meron model for dryland ecosystems, we study the organization, in bifurcation terms, of the localized structures arising in tristable regimes. These states are generally related with the concept of wave front locking, and appear in the form of spots and gaps of vegetation. We find that the coexistence of localized spots and gaps, within tristable configurations, yield the appearance of hybrid states. We also study the emergence of spatiotemporal localized states consisting in a portion of a periodic pattern embedded in a uniform Hopf-like oscillatory background in a subcritical Turing-Hopf dynamical regime.

nlin.PS↗

arXiv2022

Quartic Kerr cavity combs: Bright and dark solitons

We theoretically investigate the dynamics, bifurcation structure and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are analysed, highlighting the main differences with the standard second order dispersion case. In the anomalous regime, single and multi-peak localised states exist and are stable over a much wider region of the parameter space. In the normal dispersion regime, stable narrow bright solitons exist. Some of our findings can be understood by a new scenario reported here for the spatial eigenvalues, which imposes oscillatory tails to all localised states. To be published in Optics Letters.

nlin.PS↗

arXiv2022

Neuron-like spiking dynamics in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer

We demonstrate neuron-like spiking dynamics in the asymmetrically driven dissipative photonic Bose-Hubbard dimmer model which describes two coupled nonlinear passive Kerr cavities. Spiking dynamics appear due to the excitable nature of the system. In this context, excitable excursions in the phase space correspond to spikes in the temporal evolution of the field variables. In our case, excitability is mediated by the destruction of an oscillatory state in a global homoclinic bifurcation. In this type of excitability (known as type-I) the period of the oscillatory state diverges when approaching the bifurcation. Beyond this point, the system exhibits excitable dynamics under the application of suitable perturbations. We have also characterized the effect that additive Gaussian noise has on the spiking dynamics, showing that the system undergoes a coherence resonance for a given value of the noise strength.

physics.optics↗

arXiv2022

Multimode soliton collisions in graded-index optical fibers

In this work, we unveil the unique complex dynamics of multimode soliton interactions in graded-index optical fibers through simulations and experiments. By generating two multimode solitons from the fission of an input femtosecond pulse, we examine the evolution of their Raman-induced red-shift when the input pulse energy grows larger. Remarkably, we find that the output red-shift of the trailing multimode soliton may be reduced, so that it accelerates until it collides with the leading multimode soliton. As a result of the inelastic collision, a significant energy transfer occurs between the two multimode solitons: the trailing soliton captures energy from the leading soliton, which ultimately enhances its red-shift, thus increasing temporal separation between the two multimode solitons.

physics.optics↗

arXiv2022

Self-pulsing and chaos in the asymmetrically-driven dissipative photonic Bose-Hubbard dimer: A bifurcation analysis

We perform a systematic study of the temporal dynamics emerging in the asymmetrically driven dissipative Bose-Hubbard dimer model. This model successfully describes the nonlinear dynamics of photonic diatomic molecules in linearly coupled Kerr resonators coherently excited by a single laser beam. Such temporal dynamics include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. The different states and dynamical regimes have been thoroughly characterized using bifurcation analysis. This analysis has allowed us to identify the main instabilities, i.e. bifurcations, responsible for the appearance of the previously stated dynamics.

nlin.PS↗

arXiv2022

Mode-locking induced by coherent driving in fiber lasers

The generation of stable short optical pulses in mode-locked lasers is of tremendous importance for many applications. Mode-locking is a broad concept that encompasses different processes enabling short pulse formation. It typically requires an intracavity mechanism that discriminates between single and collective mode lasing, which can be complex and sometimes adds noise. Moreover, known mode-locking schemes do not guarantee phase stability of the carrier wave. Here we theoretically propose that injecting a detuned signal seamlessly leads to mode-locking in fiber lasers. We show that phase-locked pulses, akin to cavity solitons, exist in a wide range of parameters. In that regime the laser behaves as a passive resonator due to the non-instantaneous gain saturation.

physics.optics↗

arXiv2021

Self-Pulsing in driven-dissipative photonic Bose-Hubbard dimers

We experimentally investigate the nonlinear dynamics of two coupled fiber ring resonators, coherently driven by a single laser beam. We comprehensively explore the optical switching arising when scanning the detuning of the undriven cavity, and show how the driven cavity detuning dramatically changes the resulting hysteresis cycle. By driving the photonic dimer out-of-equilibrium, we observe the occurrence of stable self-switching oscillations near avoided resonance crossings. All results agree well with the driven-dissipative Bose-Hubbard dimer model in the weakly coupled regime.

physics.optics↗

arXiv2021

Parametrically driven Kerr cavity solitons

Temporal cavity solitons are optical pulses that propagate indefinitely in nonlinear resonators. They are currently attracting a lot of attention, both for their many potential applications and for their connection to other fields of science. Cavity solitons are phase locked to a driving laser. This is what distinguishes them from laser dissipative solitons and the main reason why they are excellent candidates for precision applications such as optical atomic clocks. To date, the focus has been on driving Kerr solitons close to their carrier frequency, in which case a single stable localised solution exists for fixed parameters. Here we experimentally demonstrate, for the first time, Kerr cavity solitons excitation around twice their carrier frequency. In that configuration, called parametric driving, two solitons of opposite phase may coexist. We use a fibre resonator that incorporates a quadratically nonlinear section and excite stable solitons by scanning the driving frequency. Our experimental results are in excellent agreement with a seminal amplitude equation, highlighting connections to hydrodynamic and mechanical systems, amongst others. Furthermore, we experimentally confirm that two different phase-locked solitons may be simultaneously excited and harness this multiplicity to generate a string of random bits, thereby extending the pool of applications of Kerr resonators to random number generators and Ising machines.

physics.optics↗

arXiv2020

Observation of the Eckhaus Instability in Whispering-Gallery Mode Resonators

The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can take place in Kerr combs generated with ultra-high $Q$ whispering-gallery mode resonators. In our experiment, sub-critical Turing patterns (rolls) undergo Eckhaus instabilities upon changes in the laser detuning leading to cracking patterns with long-lived transients. In the spectral domain, this results in a metastable Kerr comb dynamics with a timescale that can be larger than one minute. This ultra-slow timescale is at least seven orders of magnitude larger than the intracavity photon lifetime, and is in sharp contrast with all the transient behaviors reported so far in cavity nonlinear optics, that are typically only few photon lifetimes long (i.e., in the ps range). We show that this phenomenology is well explained by the Lugiato-Lefever model, as the result of an Eckhaus instability. Our theoretical analysis is found to be in excellent agreement with the experimental measurements.

nlin.PS↗

arXiv2016

Dark solitons in the Lugiato-Lefever equation with normal dispersion

The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.

nlin.PS↗

arXiv2016

Origin and stability of dark pulse Kerr combs in normal dispersion resonators

We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato-Lefever model. We show that in the time domain these correspond to interlocked switching waves between the upper and lower homogeneous states, and explain how this fact accounts for many of their experimentally observed properties. Modulational instability does not play any role in their existence. Furthermore, we provide a detailed map indicating where stable dark pulse Kerr combs can be found in parameter space, and how they are destabilized for increasing values of frequency detuning.

nlin.PS↗

arXiv2014

Third-order chromatic dispersion stabilizes Kerr frequency combs

Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.

physics.optics↗