Frequency pushing in lasers with injected signal

Cavity soliton inhibition of extreme events in lasers with injection

Vortex mediated turbulence can be the key element in the generation of extreme events in spatially extended lasers with optical injection. Here, we study the interplay of vortex mediated turbulence and cavity solitons on the onset of extreme events in semiconductor lasers with injection. We first analyze and characterize these two features separately, spatiotemporal chaotic optical vortices for low values of the injection intensity and cavity solitons above the locking regime. In regimes where vortex mediated turbulence and cavity solitons coexist, localized peaks of light inhibit instead of enhancing the generation of rogue waves by locally regularizing the otherwise chaotic phase of the optical field. Cavity solitons can then be used to manipulate and control extreme events in systems displaying vortex mediated turbulence.

Frequency pushing enhanced by an exceptional point in an atom-cavity coupled system

We observed the frequency pushing of the cavity resonance as a result of the coupling of the cavity field with the ground state 138Ba in a high-Q cavity. A weak probe laser propagated along the axis of a Fabry-Pérot cavity while ground-state barium atoms traversed the cavity mode perpendicularly. By operating the atom-cavity composite in the vicinity of an exceptional point, we could observe a greatly enhanced frequency shift of the cavity transmission peak, which was pushed away from the atomic resonance, resulting in up to 41 ± 7 kHz frequency shift per atom from the empty cavity resonance. We analyzed our results by using the Maxwell-Schrödinger equation and obtained good agreement with the measurements.

Integrability and dynamics of a simplified class B laser system

A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, 308-314 (1984)] and Politi et al. [Phys. Rev. A 33, 4055 (1986)], and still nowadays, it attracts the interest of the researchers. In this paper, we characterize its dynamics near infinity for all values of the parameters. When a=0, the partial integrability was already proved by Oppo and Politi [Z. Phys. B Con. Mat. 59, 111-115 (1985)]. Here, we prove that for a=0, it is completely integrable with two independent first integrals given by Liouvillian functions, and we present a complete study of its dynamics. When a≠0, we study its dynamics in the Poincaré ball B3, i.e., the interior of this ball is identified with R3 and its boundary the two-dimensional sphere S2 is identified with the infinity of R3.

Optical Rogue Waves in Vortex Turbulence

We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability density functions (PDFs) with long tails typical of extreme optical events.

Optically injected lasers: the transition from class B to class A lasers

We investigate changes in several features of the stability diagram of an optically injected single mode laser as the ratio of the photon lifetime to the carrier lifetime is progressively increased from very low values to very high values. In particular we consider the creation of a region of phase-locked bistability, changes in the nature of codimension-2 bifurcation points, and the presence or otherwise of chaos in the system. We show that many of the features associated with high values of the aforementioned ratio also emerge for very low pump currents regardless of the ratio of the lifetimes.

Optically injected laser system: characterization of chaos, bifurcation, and control

A single mode semiconductor laser subjected to optical injection, described by a set of three coupled nonlinear ordinary differential equations, exhibiting chaos is considered. By means of a recurrence analysis, quantification of the strange attractor is made. Analytical studies of the system using asymptotic averaging technique, derive certain conditions describing the prediction of 1-->2 bifurcation, which have subsequently been verified on numerical simulation. Furthermore, the locus of points on the parameter phase space representing Hopf bifurcation has been derived. The problem of control of chaos by a new procedure based on adaptive stabilization is also addressed. The results of such control are shown explicitly. Though this analysis deals with a very specific set of equations, the overall features that come out of the study remains valid for almost all laser systems.

Global bifurcations in a laser with injected signal: Beyond Adler's approximation

We discuss the dynamics in the laser with an injected signal from a perturbative point of view showing how different aspects of the dynamics get their definitive character at different orders in the perturbation scheme. At the lowest order Adler's equation [Proc. IRE 34, 351 (1946)] is recovered. More features emerge at first order including some bifurcations sets and the global reinjection conjectured in Physica D 109, 293 (1997). The type of codimension-2 bifurcations present can only be resolved at second order. We show that of the two averaging approximations proposed [Opt. Commun. 111, 173 (1994); Quantum Semiclassic. Opt. 9, 797 (1997); Quantum Semiclassic. Opt. 8, 805 (1996)] differing in the second order terms, only one is accurate to the order required, hence, solving the apparent contradiction among these results. We also show in numerical studies how a homoclinic orbit of the Sil'nikov type, bifurcates into a homoclinic tangency of a periodic orbit of vanishing amplitude. The local vector field at the transition point contains a Hopf-saddle-node singularity, which becomes degenerate and changes type. The overall global bifurcation is of codimension-3. The parameter governing this transition is theta, the cavity detuning (with respect to the atomic frequency) of the laser. (c) 2001 American Institute of Physics.