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Paul Mandel

Publications and source records attributed to Paul Mandel.

10 recordsLinked to original sources
PubMed2006

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.

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PubMed2006

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.

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PubMed2006

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.

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PubMed2006

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.

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PubMed2003

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.

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PubMed2003

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.

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PubMed2003

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.

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PubMed2002

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.

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PubMed2002

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.

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