Bruno Zambon

Elliptic gaussian beam self-focusing in nonlinear media

Abstract A semi-analytical treatment of elliptic gaussian beam propagation in a nonlinear medium, in the WKB, paraxial approximation is presented. It is shown that the self-trapping threshold increases with ellipticity. This suggests the possibility of controlling diffraction and self-focusing collapse by varying the beam geometry. It is also shown that, at fixed wavelength and intensity, four intervals of ellipticity, in which the propagation properties show marked differences in the longitudinal intensity profile of the beam, can be identified.

Instabilities and chaos in an infrared laser with saturable absorber: experiments and vibrorotational model

The instabilities and chaos in a CO2 laser containing SF6 and 15NH3 absorbers have been studied as a function of the parameters. By making use of a phase-portrait analysis, the instabilities have been classified through laser-control orbits in the phase space around the laser-with-saturable-absorber (LSA) fixed points. A chaotic regime, their a sequence of period-doubling bifurcations, has been observed for an instability of limit cycles reached through one fixed point. The transition between different instability operations presents an intermediate regime, around defined as the hesitation regime and have characterized through the fluctuations in the return times. which we have phenomena have been reproduced within a model, including the rotational–vibrational structure of The observed and absorber media. The numerical analysis has shown that the LSA time evolution, as described the amplifier orbits in the LSA phase space, depends on the relative attractions of the saddle point and the through homoclinic saddle focus fixed points.

Reflection and transmission of light by thin vapor layers

Abstract Optical properties of thin vapor layers are strongly affected by the influence of the boundaries. We study the transmission and reflection properties of a short vapor cell. The system is modeled as a thin layer between two parallel surfaces, filled with two-state atoms. The symmetry properties of the optical coherence with respect to the detuning of the light frequency from resonance show up in specific symmetries of the spectra. In the case of reflection, this symmetry depends on whether a quarter wavelength fits an even or an odd number of times in the layer thickness. Also the magnetically induced optical rotation and circular dichroism is discussed, both in transmission and in reflection.

Quantum-jump approach to dissipative processes: application to amplification without inversion

Several recent studies have shown that the time evolution of an atom submitted to coherent laser fields and to dissipative processes, such as spontaneous emission of photons or excitation by a broadband incoherent field, can be considered to consist of a sequence of coherent evolution periods separated by quantum jumps occurring at random times. A general statistical analysis of this random sequence is presented for the case in which the number of relevant atomic states is finite and the delay functions giving the distribution of the time intervals between two successive jumps can easily be calculated. These general considerations are then applied to a simple model recently proposed for demonstrating the possibility of amplification without inversion of populations. We show how the quantum-jump approach allows one to calculate the respective contributions of the various physical processes responsible for the amplification or the attenuation of the probe field and to get new insights into the relevant physical mechanisms.

The Duffing oscillator in the low-friction limit: Theory and analog simulation

By a joint use of theory and analog simulation the low-friction regime of the Duffing oscillator is explored. In the weak-temperature case it is shown that the low-friction regime, in turn, must be divided in two well-distinct subregimes. In the former one, characterized by the frictionγ ranging from 2Ω0 (Ω0 is the harmonic frequency) up to a lower bound γT, the method of statistical linearization applies and a continued fraction procedure (CFP) generated by the Zwanzig-Mori projection techniques is shown to provide correct information for both the renormalized frequency of the oscillator and the corresponding line shape. The latter subregime, characterized by the frictionγ ranging fromγ = 0 toγ = γT, is fraught with the complete breakdown of the statistical linearization method. The CFP is shown to provide an incorrect picture of the line shape while suggesting a novel mean field approximation which is then proven analytically via an alternative method of calculation. This method consists of expressing the system in a form reminiscent of the model of Kubos stochastic oscillator. By using this alternative approach we are in a position to account for the residual linewidth which is shown by the analog experiment to survive forγ → 0.

Lyapunov exponents and return maps for a model of a laser with saturable absorber

Maximum Lyapunov exponents and return maps are derived from a numerical integration of equations describing a laser with intracavity saturable absorber. Different sets of parameters are used in the models. It is shown that deterministic chaos with a small positive Lyapunov exponent is associated to multibranched return time return maps while noisy evolution leads to maps with a lattice structure.

Stochastic resonance as a tool for signal processing: discrete Markov schemes versus continuous dynamics in a toy model of ion channel conduction

Abstract We speculate that the stochastic resonance (SR) phenomenon could provide a useful and alternative tool in the understanding of the microscopic dynamics of complex systems in the presence of noise. Our ideas are tested in the case of a very simple toy model of a biophysical process, portraying ionic channel conduction.

Influence of noise on the quasi-homoclinic behavior of a laser with saturable absorber

Abstract The influence of noise on a laser with saturable absorber is investigated. In particular, the effect of an external added noise on the return time fluctuations and on the hesitation regime is studied. Numerical simulations based on a model with three-levels in the amplifier and four-levels in the absorber lead to an interpretation of of these behaviors.

ON THE BREAKDOWN OF THE LINEAR RESPONSE THEORY IN THE LOW-FRICTION LIMIT

Abstract It is shown, via joint use of computer calculation, analog experiment and theoretical arguments, that the linear response theory is completely invalidated in the regime of extremely low friction.

Increased trapping efficiency with force-assisted velocity-selective coherent population trapping

We study a class of laser cooling schemes that combine velocity-selective coherent population trapping (VSCPT) with Doppler cooling mechanisms. The Doppler mechanism prevents the atoms from diffusing into the region of high momentum, thereby removing the characteristic long-time asymptotic behaviour of VSCPT where, in the end, all the atoms escape from the trap. It is shown that the transition Jg = 2 to Je = 1 while maintaining the simple field configuration present in the original VSCPT case provides the additional Doppler mechanism and leads to virtually zero temperature without the loss of atoms that characterize the original VSCPT dynamics.