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Pedro Parra-Rivas

Publications and source records attributed to Pedro Parra-Rivas.

At least 19 recordsLinked to original sources

Topological Soliton Frequency Comb in Nanophotonic Lithium Niobate

Frequency combs have revolutionized metrology, ranging, and optical clocks, which have motivated substantial efforts on the development of chip-scale comb sources. The on-chip comb sources are currently based on electro-optic modulation, mode-locked lasers, quantum cascade lasers, or soliton formation via Kerr nonlinearity. However, the widespread deployment of on-chip comb sources has remained elusive as they still require RF sources, high-Q resonators, or complex stabilization schemes while facing efficiency challenges. Here, we demonstrate an on-chip source of frequency comb based on the integration of a lithium niobate nanophotonic circuit with a semiconductor laser that can alleviate these challenges. For the first time, we show the formation of temporal topological solitons in a on-chip nanophotonic parametric oscillator with quadratic nonlinearity and low finesse. These solitons, independent of the dispersion regime, consist of phase defects separating two $\pi$-out-of-phase continuous wave solutions at the signal frequency, which is at half the input pump frequency. We use on-chip cross-correlation for temporal measurements and confirm formation of topological solitons as short as 60 fs around 2 $\mu$m, in agreement with a generalized parametrically forced Ginzburg-Landau theory. Moreover, we demonstrate a proof-of-concept turn-key operation of a hybrid-integrated source of topological frequency comb. Topological solitons offer a new paradigm for integrated comb sources, which are dispersion-sign agnostic and do not require high-Q resonators or high-speed modulators and can provide access to hard-to-access spectral regions, including mid-infrared.

physics.optics

Bistable soliton optical frequency combs in a second harmonic generation Kerr cavity

We study the dynamics and stability of soliton optical frequency comb generation in a dissipative, coherently pumped cavity with both second and third-order nonlinearity. Cavity sweep simulations and linear stability analysis based on path continuation reveal the existence of bistable solitons. These families of solutions represent a continuous transition between a purely quadratic and a Kerr cavity soliton frequency comb. Perspective demonstrations of these novel optical sources is an ongoing relevant subject within the frequency comb community.

nlin.CD

Spatial localization in the FitzHugh-Nagumo model

The FitzHugh-Nagumo model, originally introduced to study neural dynamics, has since found applications across diverse fields, including cardiology and biology. However, the formation and bifurcation structure of spatially localized states in this model remain underexplored. In this work, we present a detailed bifurcation analysis of such localized structures in one spatial dimension in the FitzHugh-Nagumo model. We demonstrate that these localized states undergo a smooth transition between standard and collapsed homoclinic snaking as the system shifts from pattern-uniform to uniform-uniform bistability. Additionally, we explore the oscillatory dynamics exhibited by these states when varying the time-scale separation and diffusion coefficient. Our study leverages a combination of analytical and numerical techniques to uncover the stability and dynamic regimes of spatially localized structures, offering new insights into the mechanisms governing spatial localization in this widely used model system.

nlin.PS

Light tailored by multimode fiber for multiphoton fluorescence microscopy

We study the diffraction of a particular class of beams, composed only by a combination of azimuthally invariant guided modes of an optical fiber. We demonstrate that such beams can be obtained by injecting a Gaussian beam in a small piece of silica graded-index multimode fiber. This minimalistic low-cost method is applied for improving the axial resolution of a two-photon microscope.

physics.optics

Six decades of the FitzHugh-Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines

The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like cardiac physiology, cell division, population dynamics, electronics, and other natural phenomena. In this review spanning six decades of research, we discuss the diverse spatio-temporal dynamical behaviors described by the FitzHugh-Nagumo equation. These include dynamics like bistability, oscillations, and excitability, but it also addresses more complex phenomena such as traveling waves and extended patterns in coupled systems. The review serves as a guide for modelers aiming to utilize the strengths of the FitzHugh-Nagumo model to capture generic dynamical behavior. It not only catalogs known dynamical states and bifurcations, but also extends previous studies by providing stability and bifurcation analyses for coupled spatial systems.

nlin.PS

Implications of tristability on localization phenomena: a necking bifurcation's tale

We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended states. In the tristable regime investigated here two extended uniform states coexist with one periodic Turing pattern. This scenario leads to the transition from the standard-homoclinic-snaking-related localized states associated with uniform-pattern bistability to the collapsed-homoclinic-snaking-related states which arise in a uniform-bistable configuration. We find that this transition is mediated by the emergence of hybrid states through codimension-two necking bifurcations. To perform this study we use bifurcation analysis on a non-variational mean-field model describing the spatiotemporal dynamics of light pulses in passive Kerr cavities.

nlin.PS

Multidimensional localized states in externally driven Kerr cavities with a parabolic spatiotemporal potential: a dimensional connection

In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations, we transform higher-dimensional models into a single 1D model with a dimension parameter. This transformation not only yields a substantial reduction in computational complexity, but also enables an efficient examination of how dimensionality impacts the system dynamics. In the absence of nonlinearity, we analyze the eigenstates of the linear systems. This allows us to uncover a heightened concentration of the eigenmodes at the center of the potential well, while witnessing a consistent equal spacing among their eigenvalues, as the dimension parameter increases. In the presence of nonlinearity, our findings distinctly reveal that the stability of the localized states diminishes with increasing dimensionality. This study offers an approach to tackling high-dimensional problems, shedding light on the fundamental dimensional connections among radially symmetric states across different dimensions, and providing valuable tools for analysis.

physics.optics

Multimode resonance transition to collapsed snaking in normal dispersion Kerr resonators: Bright versus dark solitons

We study the dynamics of Kerr cavity solitons in the normal dispersion regime, in the presence of an intracavity phase modulation. The associated parabolic potential introduces multimode resonances, which promote the formation of high-order bright solitons. By gradually reducing the potential strength, bright solitons undergo a transition into dark solitons. We describe this process as a shift from a multimode resonance to a collapsed snaking bifurcation structure. This work offers a comprehensive overview of cavity dynamics and may provide a potential pathway to access multi-stable states by effectively varying the phase modulation.

physics.optics

Pure quartic three-dimensional spatiotemporal Kerr solitons

We analyze the formation of three-dimensional spatiotemporal solitons in waveguides with a parabolic refractive index profile and pure quartic chromatic dispersion. We show, by applying both variational approaches and full three-dimensional numerical simulations, that fourth-order dispersion has a positive impact on soliton stabilization against spatiotemporal wave collapse. Specifically, pure quartic spatiotemporal solitons remain stable within a significantly larger energy range with respect to their second-order dispersion counterparts.

nlin.PS

Dissipative solitons characterization in singly resonant optical parametric oscillators: a variational formalism

In this work, the emergence of single-peak temporal dissipative solitons in singly-resonant degenerate optical parametric oscillators is investigated analytically. Applying the Kantarovich optimization method, through a Lagrangian variational formalism, an approximate analytical soliton solution is computed using a parameter-dependent ansatz. This permits to obtain analytical estimations for the dissipative soliton energy, peak power, and existence boundaries, which are of great value for experimentalist. To confirm the validity of this procedure, these analytical results are compared with a numerical study performed in the context of pure quadratic systems, showing a good agreement.

nlin.PS

Nonlinear dynamics of dissipative structures in coherently-driven Kerr cavities with a parabolic potential

By means of a modified Lugiato-Lefever equation model, we investigate the nonlinear dynamics of dissipative wave structures in coherently-driven Kerr cavities with a parabolic potential. The potential stabilizes system dynamics, leading to the generation of robust dissipative solitons in the positive detuning regime, and of higher-order solitons in the negative detuning regime. In order to understand the underlying mechanisms which are responsible for these high-order states, we decompose the field on the basis of linear eigenmodes of the system. This permits to investigate the resulting nonlinear mode coupling processes. By increasing the external pumping, one observes the emergence of high-order breathers and chaoticons. Our modal content analysis reveals that breathers are dominated by modes of corresponding orders, while chaoticons exhibit proper chaotic dynamics. We characterize the evolution of dissipative structures by using bifurcation diagrams, and confirm their stability by combining linear stability analysis results with numerical simulations. Finally, we draw phase diagrams that summarize the complex dynamics landscape, obtained when varying the pump, the detuning, and the strength of the potential.

physics.optics

Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross-Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations are based on comparing variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, solitons with progressively increasing energies eventually undergo wave collapse, which is not predicted within the variational framework. In a self-defocusing scenario, again for low energies there is good agreement between the variational predictions and simulations. Whereas, for large soliton energies complex spatiotemporal dynamics emerge.

nlin.PS

Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion

We theoretically investigate the dynamics, bifurcation structure and stability of dark localized states emerging in Kerr cavities in the presence of second- and fourth-order dispersion. These states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states. They undergo a generic bifurcation structure known as collapsed homoclinic snaking. We characterize the robustness of these states by computing their stability and bifurcation structure as a function of the main control parameter of the system. Furthermore, we show that by increasing the dispersion of fourth order, bright localized states can be also stabilized.

nlin.PS

Robust three-dimensional high-order solitons and breathers in driven dissipative systems: a Kerr cavity realization

We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr cavity with diffraction and anomalous dispersion, with the addition of an attractive three-dimensional parabolic potential. The potential breaks the translational symmetry along all directions, and impacts the system in a qualitatively unexpected manner: three-dimensional solitons, or light-bullets, are the only existing and stable states for a given set of parameters. This property is extremely rare, if not unknown, in passive nonlinear physical systems. As a result, the excitation of the cavity with any input field leads to the deterministic formation of a target soliton or breather, with a spatiotemporal profile that unambiguously corresponds to the given cavity and pumping conditions. In addition, the tuning of the potential width along the temporal direction results in the existence of a plethora of stable asymmetric solitons. Our results may provide a solid route towards the observation of dissipative light bullets and three-dimensional breathers.

physics.optics

Spatiotemporal mode decomposition of ultrashort pulses propagating in graded-index multimode fibers

We develop a spatiotemporal mode decomposition technique to study the mode power distribution of ultrashort pulses emerging from long spans of graded-index multimode fiber, for different input laser conditions. We find that beam mode power content in the dispersive pulse propagation regime can be described by the Bose-Einstein law, as a result of the process of power diffusion from linear and nonlinear mode coupling among nondegenerate mode groups. In the soliton regime, the output mode power distribution approaches the Rayleigh-Jeans law

physics.optics

Depletion-limited Kerr solitons in singly-resonant optical parametric oscillators

We analyze the impact of pump depletion in the generation of cavity solitons in a singly-resonant parametrical oscillator that includes a $\chi^{(3)}$ nonlinear section. We find an analytical expression that provides the soliton existence region using variational methods, study the efficiency of energy conversion, and compare it to a driven Kerr resonator modeled by the Lugiato-Lefever equation. At high walk-off, solitons in singly-resonant optical parametric oscillators are more efficient than those formed in a Kerr resonator driven through a linear coupler.

physics.optics

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

Dissipative Kerr solitons, breathers and chimera states in coherently driven passive cavities with parabolic potential

We analyze the stability and dynamics of dissipative Kerr solitons in the presence of a parabolic potential. This potential stabilizes oscillatory and chaotic regimes, favoring the generation of static DKSs. Furthermore, the potential induces the emergence of new dissipative structures, such as asymmetric breathers and chimera-like states. Based on a mode decomposition of these states, we unveil the underlying modal interactions.

physics.optics