Long-cavity quantum dot laser.

We propose a delay-differential equation to model dynamical instabilities in a quantum dot laser. We focus on a laser with a small gain section and a long empty section. A long cavity reduces the strong damping of the relaxation oscillation frequency. It leads to the appearance of dropouts at the delay period, which evolve to chaos.

Low-frequency fluctuations in two-state quantum dot lasers.

We study the feedback-induced instabilities in a quantum dot semiconductor laser emitting in both ground and excited states. Without optical feedback the device exhibits dynamics corresponding to antiphase fluctuations between ground and excited states, while the total output power remains constant. The introduction of feedback leads to power dropouts in the ground state and intensity bursts in the excited state, resulting in a practically constant total output power.

Left-handed properties of erbium-doped crystals.

We show that lanthanide-doped crystals can be made left handed for a finite spectral range. The electronic transitions in the dopant ions are both dipolar electric and dipolar magnetic allowed. This enables tuning the permittivity and the permeability at the same frequency. The analysis focuses on erbium-doped crystals where left-handed properties are predicted inside an experimentally reachable domain of parameters.

Electromagnetically induced left handedness in optically excited four-level atomic media.

We show that left-handed properties can be electromagnetically induced in a general four-level atomic medium for a finite spectral range. We use an electric (magnetic) atomic transition as an electric (magnetic) resonator to modify the permittivity (permeability), both at the same frequency. The implementation of the four-level model is carried out in atomic hydrogen and neon. In each case the existence of left-handed properties is predicted inside an experimentally reachable domain of parameters.

Synchronization and clustering in a multimode quantum dot laser.

We analyze experimentally the intensity oscillations of the longitudinal modes of quantum dot semiconductor lasers. We show that the modal intensities can oscillate chaotically with different average frequencies, but obey a highly organized antiphase dynamics leading to a constant total output power. The fluctuations are in the MHz range. We report the first experimental observation of frequency clustering associated with synchronization. We also observe the propagation of perturbations across the optical spectrum from blue to red.

Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump.

We consider a passive optical cavity containing a photonic crystal and a purely absorptive two-level medium. The cavity is driven by a superposition of two coherent beams forming a periodically modulated pump. Using a coupled mode reduction and direct numerical modeling of the full system we demonstrate the existence of bistability between uniformly periodic states, modulational instabilities and localized structures of light. All are found to exist within the conduction band of the photonic material. Moreover, contrary to similar previously found intra-band structures, we show that these localized structures can be truly stationary states.

Feedback induced instabilities in a quantum dot semiconductor laser.

We analyse the properties of GaAs based quantum dot semiconductor lasers emitting near 1310 nm. The line-width enhancement factor is shown to depend strongly on device temperature, ranging from 1.5 at 20 degrees C to 5 at 50 degrees C. With optical feedback from a distant reflector, devices remained stable at 20 degrees C but displayed a range of instabilities at 50 degrees C, including irregular power drop--outs and periodic pulsations, before entering a chaotic regime. Such dynamical features are unique to quantum dot lasers -- quantum well lasers are significantly more unstable under optical feedback making such a clear route to chaos difficult to observe.

Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals.

We study numerically the counterpropagating vector solitons in SBN:60 photorefractive crystals. A simple theory is provided for explaining the symmetry-breaking transverse instability of these solitons. Phase diagram is produced that depicts the transition from stable counterpropagating solitons to bidirectional waveguides to unstable optical structures. Numerical simulations are performed that predict novel dynamical beam structures, such as the standing-wave and rotating multipole vector solitonic clusters. For larger coupling strengths and/or thicker crystals the beams form unstable self-trapped optical structures that have no counterparts in the copropagating geometry.

Low-frequency fluctuations in the Lang-Kobayashi equations.

The Lang-Kobayashi equations are simplified by a local analysis that focuses, in the long-delay-time limit, on one pair of mode-antimode only. In the domain of hysteresis between the two steady states, low frequency fluctuations (LFF) can be observed if there is a domain of bistability where both steady states are unstable. The high-frequency oscillations and the drop-offs in the LFF regime are associated with a dynamics close to the unstable upper and lower branch steady states, respectively.

Body-centered cubic dissipative crystal formation in a dispersive and diffractive optical parametric oscillator.

We show that coupling diffraction and chromatic dispersion lead to body-centered cubic and hexagonally packed cylinders of dissipative optical crystals in a degenerate optical parametric oscillator. The stabilization of these crystals is a direct consequence of the interaction between the modulational and the quasi-neutral modes.

Bifurcation diagram of a complex delay-differential equation with cubic nonlinearity.

We reduce the Lang-Kobayashi equations for a semiconductor laser with external optical feedback to a single complex delay-differential equation in the long delay-time limit. The reduced equation has a time-delayed linear term and a cubic instantaneous nonlinearity. There are only two parameters, the real linewidth enhancement factor and the complex feedback strength. The equation displays a very rich dynamics and can sustain steady, periodic, quasiperiodic, and chaotic regimes. We study the steady solutions analytically and analyze the periodic solutions by using a numerical continuation method. This leads to a bifurcation diagram of the steady and periodic solutions, stable and unstable. We illustrate the chaotic regimes by a direct numerical integration and show that low frequency fluctuations still occur.

Dynamical properties of lasers coupled face to face.

We derive a reduced model to describe two identical lasers coupled face to face. Two limits are introduced in the Maxwell-Bloch equations: adiabatic elimination of the material polarization and large distance between the two lasers. The resulting model describes coupled homogeneously broadened lasers, including semiconductor lasers. It consists of two coupled delay differential equations with delayed linear cross-coupling and an instantaneous self-coupling nonlinearity. The study is analytical and numerical. We focus on the properties of steady and periodic amplitudes of the electric fields. In steady state, there are symmetric, antisymmetric, and asymmetric solutions with respect to a permutation of the two fields. A similar classification holds for the periodic states. The stability of these solutions is determined partly analytically and partly numerically. A homoclinic point is associated with the asymmetric periodic solutions.

Curvature instability in passive diffractive resonators.

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.

Two regimes of synchronization in unidirectionally coupled semiconductor lasers.

We analyze unidirectionally coupled semiconductor lasers in the feedback/injection scheme to determine their synchronization performance. As the mismatch between the two lasers increases, there is a transition from complete synchronization for identical lasers to time lag synchronization which is only partial. This corresponds to a continuous change of the global minimum that becomes a relative minimum of the synchronization error function and vice versa.

Low-frequency pulsations in class-B solid-state lasers with delayed feedback.

We report on the numerical observation of short-duration low-frequency pulsations in class-B solid-state lasers subject to delayed feedback. The period of these pulsations is much larger than either the delay induced by the feedback or the relaxation oscillation period of the laser without feedback. A link is established between the low-frequency pulsations and the low-frequency fluctuations observed in semiconductor lasers subject to coherent optical feedback.