Light-induced instabilities driven by competing helical patterns in long-pitch cholesterics

We study theoretically the dynamical reorientation phenomena when a long-pitch cholesteric liquid-crystal film with homeotropic alignment is illuminated by a circularly polarized lightwave. In the present case, the natural cholesteric pitch is of the order of (or larger than) the film thickness. The helical cholesteric structure is thus frustrated by the boundary conditions without illumination. However, above a light intensity threshold reorientation occurs and the bifurcation scenario depends strongly on the natural cholesteric pitch. Recalling that a long-pitch cholesteric is achieved in practice by adding a small amount of chiral agents in a nematic liquid crystal, the observed dynamics can be viewed as the result of the competition between intrinsic and extrinsic unidimensional helical patterns. The intrinsic part consists of the helical deformations induced by the chirality of the dopant, whereas the extrinsic part is related to the chirality induced by the optical field through the non-uniform angular momentum transfer of light to a nematic. The all-optical analog in the case of a pure nematic (without chiral dopant), is also discussed.     

Frequency degenerate and non-degenerate nonlinear regimes for semi-linear photorefractive oscillator

We present a theoretical analysis, analytical and numerical, of the oscillation regimes for the semi-linear photorefractive oscillator beyond the instability threshold. This analysis includes the limiting cases of dominating transmission and reflection gratings as well as the cases of spontaneous violation of the frequency degeneracy between the oscillation and pump waves.     

Statistical properties for a class of nonlinear squeezed states

Theoretical investigations of dynamical behavior in optical parametric oscillators (OPO) have generally assumed that the cavity detunings of the interacting fields are controllable parameters. However, OPOs are known to experience mode hops, where the system jumps to the mode of lowest cavity detuning. We note that this phenomenon significantly limits the range of accessible detunings and thus may prevent instabilities predicted to occur above a minimum detuning from being evidenced experimentally. As a simple example among a number of instability mechanisms possibly affected by this limitation, we discuss the Hopf bifurcation leading to periodic behavior in the monomode mean-field model of a triply resonant OPO and show that it probably can be observed only in very specific setups.     

Radiation pressure induced instabilities in laser interferometric detectors of gravitational waves

The large scale interferometric gravitational wave detectors consist of Fabry-Perot cavities operating at very high powers ranging from tens of kW to MW for next generations. The high powers may result in several nonlinear effects which would affect the performance of the detector. In this paper, we investigate the effects of radiation pressure, which tend to displace the mirrors from their resonant position resulting in the detuning of the cavity. We observe a remarkable effect, namely, that the freely hanging mirrors gain energy continuously and swing with increasing amplitude. It is found that the “time delay”, that is, the time taken for the field to adjust to its instantaneous equilibrium value, when the mirrors are in motion, is responsible for this effect. This effect is likely to be important in the optimal operation of the full-scale interferometers such as VIRGO and LIGO. Received 12 July 1999     

Quantum correlations close to a square pattern forming instability

We analyze the quantum fluctuations of the degenerate optical parametric oscillator close to an instability for the formation of a square pattern. While strong correlations between the fluctuations of the signal modes emitted at the critical wave number and with opposite wave vector are present both below and above threshold, no features signaling the square character of the pattern forming above threshold have been identified below threshold in the spatio-temporal second-order coherence. We also explore in which regimes a reduced few mode model gives meaningful results. Received 17 September 2002 / Received in final form 11 November 2002 Published online 26 February 2003     

Pattern selection and stabilization in an annular CO laser

The formation and stabilization of spatio-temporal patterns in an annular CO₂ laser is studied. We give experimental and numerical evidence of the role of a small spatial perturbation (consisting of a thin metallic wire inserted in the optical cavity) in the selection and stabilization of patterns. Received 15 December 1999     

The pulse shape of a passively Q-switched microchip laser

The shape of the intensity pulse of a passively Q-switched microchip laser is investigated numerically and analytically. Our analysis is motivated by independent microchip laser experiments exhibiting nearly symmetric pulses in the case of a semiconductor saturable absorber and asymmetric pulses in the case of a solid state saturable absorber. Asymptotic methods are used to determine limiting behaviors of the pulse shape for both symmetric and asymmetric pulses. In the first case, we determine a sech² solution parametrized by one parameter which can be determined by solving two coupled nonlinear algebraic equations. In the second case, the pulse solution is decomposed into two distinct approximations exhibiting different amplitude and time scales properties. We review earlier approximations of the repetition rate and the pulse width. Received 2 August 1999     

Comparison of different switching techniques in a cavity soliton laser

We compare three different switching techniques for the control of cavity solitons in a VCSEL-based cavity soliton laser, one incoherent and the other two semicoherent with different injection frequencies. We show that the switching dynamics and energies can be very different depending on the type of injection.     

An analytical study of a periodically driven laser with a saturable absorber

We consider the rate equations for a laser with an intracavity saturable absorber and subject to a periodically modulated pump. By deriving simplified equations for a map valid for strongly pulsating regimes, analytical conditions are determined that specify the properties of both frequency-locked and unlocked behaviors. As the strength of the modulation is increased, quasiperiodic and period-doubling bifurcations are predicted. However, only the transition from locking to non-locking through a quasiperiodic bifurcation is possible for realistic values of the parameters. Our results are consistent with previous numerical and experimental studies of modulated lasers with a saturable absorber. Received 10 March 2001     

Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.     

Threshold behavior of semi-linear photorefractive oscillator

A general analysis of the threshold behavior for the photorefractive semi-linear oscillator is performed within the linear approximation on the basis of the classical wave-coupling model. This analysis shows that the well known particular results on the frequency degenerate oscillation are valid only within a restricted range of the external parameters. The theory specifies the conditions for onset and properties of the frequency non-degenerate oscillations, including the necessary values of the coupling strength, pump intensity ratio, the increments of the instability, and the frequency splits. Important generalizations of the basic model are considered.     

Nonlinear lensing mechanisms in a cloud of cold atoms

We present an experimental study of nonlinear lensing of near-resonant light by a cloud of laser-cooled rubidium atoms, specifically aimed at understanding the role of the interaction time between the light and the atomic vapor. We identify four different nonlinear mechanisms, each associated with a different time constant: electronic nonlinearity, Zeeman optical pumping, hyperfine optical pumping and radiation pressure. Our observations can be quite accurately reproduced using a simple rate equation model which allows for a straightforward discussion of the various effects. The results are important for planning more refined experiments on transverse nonlinear optics and self-organization in samples of cold atoms.     

Ultrafast spin dynamics of an individual CoPt3 ferromagnetic dot

We have studied the ultrafast magneto-optical response of CoPt₃ ferromagnetic nanodots with diameters ranging from 0.2 to 1 μm. Our experiments combine an accurate temporal resolution using femtosecond laser pulses and a high spatial resolution ( 300 nm) obtained with a reflective confocal Kerr microscope. Our experimental approach allows exploring the dynamics of the magnetization of magnetic nanostructures over a broad temporal scale ranging from 100 fs to 1 ns. We report the corresponding relaxation behavior of the electrons and the spins initially excited with a large excess energy above the Fermi level.     

Electron impact single and double ionization of argon

Stable two-mode, and three-mode oscillations due to the spatial hole burning effect were observed experimentally with the increase of the pump power ratio in a laser-diode pumped sub-nanosecond microchip Cr,Yb:YAG self-Q-switched multimode laser. The stability of the output pulse trains was attributed to the mode coupling through antiphase dynamics between different modes. Modified multimode rate equations including the spatial hole-burning effect in the active medium and the non-linear absorption of the saturable absorber were proposed. Numerical simulations of the antiphase dynamics of such a laser were in good agreement with the experimental data, and the antiphase dynamics were explained by the evolution of the inversion population and the bleaching and recovery of the inversion population of the saturable absorber.     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kr?nig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators. Received 25 January 1999 and Received in final form 26 April 1999     

Widely tunable amplified spontaneous emission of Pyrromethene-650-doped nematic liquid crystal

We study amplified spontaneous emission of Pyrromethene-650-doped nematic liquid crystal deposited onto quartz and glass substrates. We prepare samples with different dye-doped concentrations pumped with a Nd:YAG laser at 532 nm. With an applied electric field, a tuning range of the amplified spontaneous emission of more than 20 nm was realized in each sample due to changing the effective refractive index of the nematic-liquid-crystal layer caused by the reorientation of nematic-liquid-crystal molecules. We show that there exist a threshold voltage and a saturation voltage for all the samples. With the increase in the dye-doped concentration, the peak wavelength of the amplified spontaneous emission has a red shift of about several nanometers.     

Pattern dynamics in an annular laser

Competition among modes in an annular CO₂ laser has been experimentally and numerically analyzed. During the coexistence of different patterns, each of them resulting from the interaction of two transverse modes with opposite angular momentum, chaos has been experimentally detected. A numerical model, derived from the Maxwell-Bloch equations and including symmetry breaking terms, enables the interpretation of the main experimental features. Received 10 March 2000