Biomedical subjects

G Kozyreff

Publications and source records attributed to G Kozyreff.

8 recordsLinked to original sources

PubMed2006

Asymptotics of large bound states of localized structures.

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.

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PubMed2004

Bistability between different localized structures in nonlinear optics.

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.

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PubMed2004

Optical patterns with different wavelengths.

The semiconductor resonator is an example of an optical system where two modulational instabilities with different wave numbers coexist. In the limit of nascent bistability, the dynamics is generically described by a nonvariational real order parameter equation, of which we give a detailed derivation. This considerably simplifies the linear and weakly nonlinear stability analyses. When the two instabilities are close together, we derive normal form equations and put special emphasis on "envelope" branches of solutions. These particular solutions may connect the two instability points or form an isola. On the basis of these rigorous results, we finally discuss the case of distant modulational instabilities, in both one and two transverse dimensions.

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PubMed2003

Interaction of two modulational instabilities in a semiconductor resonator.

The interaction of two neighboring modulational instabilities in a coherently driven semiconductor cavity is investigated. First, an asymptotic reduction of the general equations is performed in the limit of a nearly vertical input-output characteristic. Next, a normal form is derived in the limit where the two instabilities are close to one other. An infinity of branches of periodic solutions are found to emerge from the unstable portion of the homogeneous branch. These branches have a nontrivial envelope in the bifurcation diagram that can either smoothly join the two instability points or form an isolated branch of solutions.

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PubMed2002

Controlling absorption of gamma radiation via nuclear level anticrossing.

A significant reduction of absorption for single gamma photons has been experimentally observed by studying Mössbauer spectra of 57Fe in a FeCO3 crystal. The experimental results have been explained in terms of a quantum interference effect involving nuclear level anticrossing due to the presence of a combined magnetic dipole and electric quadrupole interaction.

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PubMed2001

Electromagnetically induced transparency via adiabatic following of the nonabsorbing state.

It is shown that the adiabatic following of the dark, nonabsorbing state improves significantly the electromagnetically induced transparency performance and slows down the group velocity of the probe pulse. This concept can be used for fast selective gating of one pulse out of a pulse train.

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PubMed2001

Dynamics of a semiconductor laser array with delayed global coupling.

We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far field intensity. We show that the delay may be a useful control parameter to achieve in-phase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic regime and a delay-independent Hopf bifurcation leading to an antiphased periodic regime. Both regimes are described analytically and secondary Hopf bifurcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are generalized by the addition of second and third order time derivatives of the phases.

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PubMed2000

Global coupling with time delay in an array of semiconductor lasers

Synchronization due to a weak global coupling with time delay in a semiconductor laser array is investigated both in the cw and self-pulsing regimes. A generalized form of the Kuramoto phase equations is derived and discussed analytically. The time delay is shown to induce in-phase synchronization in all dynamical regimes. Another form of synchronization is found which leads to local extinction of self-pulsing in the array.

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