104 research outputs found
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
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
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.Comment: 4 pages and 4 figure
(Invited) Spatiotemporal soliton stability in multimode fibers. A Hamiltonian approach
We introduce a Hamiltonian approach to study the stability of three-dimensional spatiotemporal solitons in graded-index multimode optical fibers. Nonlinear light bullet propagation in these fibers can be described by means of a Gross–Pitaevskii equation with a two-dimensional parabolic potential. We apply a variational approach, based on the Ritz optimization method, and compare its predictions with extensive numerical simulations. We analytically find that, in fibers with a pure Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low energies, in perfect agreement with numerical simulations. However, above a certain energy threshold, simulations reveal that the spatiotemporal solitons undergo wave collapse, which is not captured by the variational approach
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
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
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
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 may include self-pulsing oscillations, period doubled oscillatory states, chaotic dynamics, and spikes. We have thoroughly characterized such dynamical states, their origin, and their regions of stability by applying bifurcation analysis and dynamical system theory. This approach has allowed us to identify and classify the instabilities, which are responsible for the appearance of different types of temporal dynamics
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
Mode-locking induced by coherent driving in fiber lasers
Mode-locking is a broad concept that encompasses different processes enabling short optical pulse formation in lasers. 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
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