Dominique Derozier

Dynamical behavior of a doped fiber laser under pump modulation

Abstract The dynamics of a doped fiber laser have been examined under various conditions of pump modulation. A global description of its evolution towards chaos is provided by the comparison of bifurcation diagrams obtained at various amplitudes and frequencies of the pump modulation. In spite of the large number of longitudinal modes which oscillate, the fiber laser exhibits a behaviour which is very similar to that of the monomode CO 2 laser with modulated parameters.

Fast oscillations in an optical parametric oscillator

We report on the observation of fast oscillations at frequencies of a few MHz in a triply resonant optical parametric oscillator. These oscillations can appear alone, or superimposed on slow oscillations due to thermo-optical instabilities, and display a great variety of waveforms. The analysis of the regimes observed experimentally leads us to conjecture that the mechanism responsible for this instability is not the Hopf bifurcation of the single-mode mean-field model, but that it is based on the interaction of two signal fields oscillating in cavity modes with neighboring frequencies. This interpretation is supported by numerical simulations of the mean-field model with two coupled modes, which reproduce well the behaviors observed experimentally. We also find chaotic solutions of this model, which unveils another possible scenario leading to deterministic chaos in this system.

Stabilizing or destabilizing lasers by continuous delayed feedback

The equations for a class B laser with loss modulation and delayed feedback have been analysed. By using asymptotic methods, an amplitude equation is determined which describes the first period doubling bifurcation. From this equation, it is shown that the feedback may stabilize an initially unstable periodic solution by shifting the period doubling bifurcation point. However, we also show that the feedback may destabilize an initially stable periodic solution for different values of the parameters. Our results are substantiated by a numerical study of the laser equations and by new experiments on a CO2 laser.

Periodic mode hopping induced by thermo-optic effects in continuous-wave optical parametric oscillators

We show that thermal effects can lead to periodic mode hopping in cw optical parametric oscillators (OPOs). This mode hopping may occur as soon as two modes have different intensities at the point where they exchange their stability; this condition is easily fulfilled in OPOs that are triply resonant, or doubly resonant with a weakly resonant pump. We have observed such oscillations experimentally in a type II OPO in both configurations. A simple thermo-optic multimode model reproduces well the experimental regimes. We expect that multimode instabilities based on this mechanism can be observed with various aspects in many experimental setups at high pumping rate.

Optical time division multiplexing: a powerful technique for experimental investigations of spatiotemporal dynamics

We show that fast and complex spatio-temporal dynamics of pulsed lasers or OPOs can be recorded using a simple and low-cost technique. The system is based on the well-known principle of time-division multiplexing currently used in telecommunications, and is composed of a set of fibers, conventional photodiodes, and an oscilloscope. The resolution is typically limited by the ratio between the oscilloscope sampling rate and the pulse repetition rate. We have tested this technique on a femtosecond titanium:sapphire laser. This allowed us to observe in real time the irregular displacement of one-dimensional cuts of the output beam (every 12 ns), a process that has been studied up to now only by indirect means. This device can be potentially extended to non-mode-locked sources.

Incompatibility between cavity resonances and wavevector matching: influence on threshold and beam structures of OPOs

We investigate theoretically and experimentally the interplay between cavity and double-refraction in continuous-wave optical parametric oscillators. We show that very basic geometrical effects can prevent transverse wavevector matching for the TEM/sub 00/ modes, and thus increase the threshold and change dramatically the beam structures when using a resonant (or double-pass) pump. We extend the work of Boyd and Kleinman to take these cavity-induced mismatches into account, and test experimentally the theoretical results using a cw type II KTP OPO. The transverse wavevector mismatch leads to the appearance of transverse modes with increasing order (up to TEM/sub 40-0/) and surprisingly induces structures that are different on signal and idler. The theory is able to predict quantitatively all selected transverse modes, and allows a simple interpretation in transverse Fourier space.

Incompatibility of cavity resonances with wave-vector matching: influence on threshold and beam structures of optical parametric oscillators

We investigate theoretically and experimentally the interplay between cavity and double refraction in continuous-wave optical parametric oscillators. We show that basic geometrical effects can prevent transverse wave-vector matching for TEM00 modes and thus increase the threshold and dramatically change the beam structures when a resonant (or double-pass) pump is used. We extend the results of Boyd Kleinman [J. Appl. Phys.39, 3597 (1968)] to take these cavity-induced mismatches into account and test the theoretical results experimentally, using a continuous-wave type II KTP optical parametric oscillator. The transverse wave-vector mismatch leads to the appearance of transverse modes with increasing order (up to TEM40 0). The theory is able to predict quantitatively all selected transverse modes and admits of a simple interpretation in transverse Fourier space.

Control of laser chaos

Further modifications of the method proposed by Ott, Grebogi and Yorke to control chaos [Phys. Rev. Lett. 64, 1196 (1990)] have been achieved allowing us to stabilize and characterize unstable states (stationary or periodic) in their whole domain of existence. We demonstrate the possibility of stabilizing unstable periodic orbits in an experiment by applying a continuous feedback method. It has been checked experimentally on a CO2 laser with a modulated parameter. This kind of method is very attractive opening the way to the control of chaos in very fast systems.

Cooperative oscillation of nondegenerate transverse modes in an optical system: multimode operation in parametric oscillators.

We show experimentally that parametric interaction can induce a cooperative oscillation of non-simultaneously resonant transverse modes in an optical parametric oscillator. More generally, this effect is expected to occur in any spatially extended system subjected to boundary conditions where nonlinear wave mixing of two nonresonant spatial modes can generate a resonant oscillation.

Spatiotemporal chaos in a laser

This paper concentrates on spatiotemporally chaotic regimes. The investigation shows different types of spatiotemporal chaos (extensive and non-extensive) stemming from at least three different origins. The first mechanism is linked to spatial nonuniformities (here the Gaussian lineshape of the laser) that can induce low dimensional spatiotemporal chaos. A second scenario is the interaction between two patterns of different wavenumbers, the pattern with the smallest wavenumber playing the role of spatial nonuniformities for the other pattern. Numerical simulations show that it leads to extensive chaos (linear growth of the number of positive Lyapunov exponents with the size of the system). The third mechanism is a cascade of parametric instabilities: each of the two waves appearing at the primary instability act as a pump for the parametric excitation of two new traveling waves, leading eventually to spatiotemporal chaos.