Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation

Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton that overlap with one another. When such soliton tails have spatial oscillations, locking or pinning between two solitons can occur at fixed distances related with the wavelength of these oscillations, thus forming a bound state. In this work, we study the formation and stability of various types of bound states in the Lugiato-Lefever equation by computing their interaction potential and by analyzing the properties of the oscillatory tails. Moreover, we study the effect of higher order dispersion and noise in the pump intensity on the dynamics of bound states. In doing so, we reveal that perturbations to the Lugiato-Lefever equation that maintain reversibility, such as fourth order dispersion, lead to bound states that tend to separate from one another in time when noise is added. This separation force is determined by the shape of the envelope of the interaction potential, as well as an additional Brownian ratchet effect. In systems with broken reversibility, such as third order dispersion, this ratchet effect continues to push solitons within a bound state apart. However, the force generated by the envelope of the potential is now such that it pushes the solitons towards each other, leading to a null net drift of the solitons.Comment: 13 pages, 13 figure

Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback

In this paper we study the formation and dynamics of self-propelled cavity solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs) subjected to external frequency selective feedback (FSF), and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wavenumber are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcation. We also show that a feedback phase variation of 2\pi can transform a CS (whether resting or moving) into a different one associated to an adjacent longitudinal external cavity mode. Finally, we investigate the influence of the carrier dynamics, relevant for VCSELs. We find and analyze qualitative changes in the stability properties of resting CSs when increasing the carrier relaxation time. In addition to a drifting instability of resting CSs, a new kind of instability appears for certain ranges of carrier lifetime, leading to a swinging motion of the CS center position. Furthermore, for carrier relaxation times typical of VCSELs the system can display multistability of CSs.Comment: 11 pages, 12 figure

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency selective feedback

We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.Comment: Submitted to PR

Frequency and phase locking of laser cavity solitons

Self-localized states or dissipative solitons have the freedom of translation in systems with a homogeneous background. When compared to cavity solitons in coherently driven nonlinear optical systems, laser cavity solitons have the additional freedom of the optical phase. We explore the consequences of this additional Goldstone mode and analyse experimentally and numerically frequency and phase locking of laser cavity solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback. Due to growth-related variations of the cavity resonance, the translational symmetry is usually broken in real devices. Pinning to different defects means that separate laser cavity solitons have different frequencies and are mutually incoherent. If two solitons are close to each other, however, their interaction leads to synchronization due to phase and frequency locking with strong similarities to the Adler-scenario of coupled oscillators

Squeezing resulting from a fourth-order interaction in a degenerate parametric amplifier with absorption losses

7 págs.; 8 figs.The squeezing properties of a model of a degenerate parametric amplifier with absorption losses and an added fourth-order nonlinearity have been analyzed. The approach used consists of obtaining the Langevin equation for the optical field from the Heisenberg equation provided that a linearization procedure is valid. The steady states of the deterministic equations have been obtained and their local stability has been analyzed. The stationary covariance matrix has been calculated below and above threshold. Below threshold, a squeezed vacuum state is obtained and the nonlinear effects in the fluctuations have been taken into account by a Gaussian decoupling. In the case above threshold, a phase-squeezed coherent state is obtained and numerical simulations allowed to compute the time interval, depending on the loss parameter, on which the system jumps from one stable state to the other. Finally, the variances numerically determined have been compared with those obtained from the linearized theory and the limits of validity of the linear theory have been analyzed. It has become clear that the nonlinear contribution may perhaps be profitably used for the construction of above-threshold squeezing devices. © 1991 The American Physical Society.Peer Reviewe

Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators

In Ref. [Parra-Rivas at al., 2013], using the Swift-Hohenberg equation, we introduced a mechanism that allows to generate oscillatory and excitable soliton dynamics. This mechanism was based on a competition between a pinning force at inhomogeneities and a pulling force due to drift. Here, we study the effect of such inhomogeneities and drift on temporal solitons and Kerr frequency combs in fiber cavities and microresonators, described by the Lugiato-Lefever equation with periodic boundary conditions. We demonstrate that for low values of the frequency detuning the competition between inhomogeneities and drift leads to similar dynamics at the defect location, confirming the generality of the mechanism. The intrinsic periodic nature of ring cavities and microresonators introduces, however, some interesting differences in the final global states. For higher values of the detuning we observe that the dynamics is no longer described by the same mechanism and it is considerably more complex.Comment: 11 pages, 9 figure

Iron deficiency in chronic heart failure: case-based practical guidance

In patients with chronic heart failure, iron deficiency, even in the absence of anaemia, can aggravate the underlying disease and have a negative impact on clinical outcomes and quality of life. The 2016 European Society of Cardiology guidelines for the diagnosis and treatment of acute and chronic heart failure recognize iron deficiency as a co-morbidity in chronic heart failure and recommend iron status screening in all newly diagnosed patients with chronic heart failure. Furthermore, the guidelines specifically recommend considerations of intravenous iron therapy, ferric carboxymaltose, for the treatment of iron deficiency. However, in spite of these recommendations, iron deficiency remains often overlooked and undertreated. This may be due, in part, to the lack of clinical context and practical guidance accompanying the guidelines for the treating physician. Here, we provide practical guidance complemented by a case study to assist and improve the timely diagnosis, treatment, and routine management of iron deficiency in patients with chronic heart failure

Transient behavior of a parametric amplifier with an added fourth-order interaction

8 págs.; 13 figs.; PACS number(s): 42.50.Dv, 42.65.Ky, 42.50.MdThe dynamical properties of an optical parametric amplifier with an added fourth-order (Kerr-effect term) nonlinearity are studied by means of a computer simulation of a semiclassical nonlinear Langevin formulation. The transient statistics above threshold are analyzed in detail, and the relevance of the present results for the production of squeezed light in traveling-wave devices is finally discussed. © 1992 The American Physical Society.Thiiss wwoork was supported in part by Grant No. TIC-90/80 (DGICYT, Spain).Peer Reviewe

O PAPEL DO VEREADOR NO ESTADO DE DIREITO NO BRASIL: A DEFESA DOS SUBSÍDIOS COMO EQUAÇÃO DEMOCRÁTICA

O presente estudo examina os subsídios dos vereadores à luz dos parâmetros constitucionais estabelecidos na Lei Fundamental brasileira. Após indicar a conexão entre os vereadores e o Parlamento moderno, o qual traz a marca institucional gestada na Revolução Francesa de 1789, busca-se definir a função da vereança e examinar o tratamento dispensado pelas diversas Constituições pátrias aos edis, em breve perspectiva histórica a auxiliar na compreensão do desenho dos parlamentares locais vertente na Constituição de 1988. Em relação a interrogação principal a que se propõe enfrentar o trabalho, parte-se dos argumentos dos defensores da vereança como serviço honorífico, passando pelos parâmetros normativos regentes da matéria, até chegar à defesa dos subsídios aos vereadores como equação democrática, decorrente dos mandados constitucionais e do modelo de Estado de Direito adotado pelo Brasil. Retribuir dignamente a quem trabalha para o público, longe de qualquer ilícito, além de ser medida de justiça é uma providência importante para combater a demagogia e afirmar as instituições democráticas