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     

Beam-size effect in time-delayed laser-induced double gratings

We have studied theoretically the effect of the probe-beam size on time-delayed laser-induced double gratings by assuming that the probe beam is described as a Gaussian beam. LettingE _s1 andE _s2 be the Four-Wave Mixing (FWM) signals originating from the diffraction of the probe beam by the gratings, the condition for the occurrence of the FWM signal modulation is that the divergence angle ofE _s1 andE _s2 is larger than half of the intersection angle between the propagation directions ofE _s1 andE _s2. We have also proposed methods to increase the modulation contrast.     

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     

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     

Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003     

Multiphase patterns in self-phase-locked optical parametric oscillators

Multiphase patterns are found in a mean-field model of a singly-resonant optical parametric oscillator that converts a pump field at frequency 3ω into signal and idler fields at frequencies 2ω and ω. A complex Ginzburg-Landau equation without diffusion and with a quadratic phase-sensitive nonlinear term is derived under single-longitudinal and paraxial propagation approximations. Owing to the phase-matched multistep parametric process ω + ω = 2ω, phase locking of the resonated signal field is possible with three distinct phase states. Three-armed rotating spirals, target patterns and light filamentation are found by a numerical analysis of the mean-field equation. Received 19 April 2001 and Received in final form 21 June 2001     

High-order harmonic generation in nitrogen molecules with subpicosecond visible dye-laser pulses

An experimental study of high-order harmonic generation in nitrogen molecules (N₂) has been made using intense visible (616 nm) dye-laser pulses, where the harmonic radiation up to the 21st order is observed. The harmonic distribution represents a plateau that is preceded by an intensity minimum at the 7th order. The harmonic generation characteristics were atomic-like. It has been found that there are some similarities in the high-order harmonic generation characteristics for N₂ and Ar, including the highest-order harmonics, harmonic distributions, and the influence of the multiphoton ionization on the high-order harmonic generation. These similarities are reasonably attributed to the energetic correspondence of excited levels and ionization potentials. It is pointed out that the ac Stark shift of excited levels and ionization potentials plays an important role also in the high-order harmonic generation in N₂.     

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     

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     

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.     

Squeezing by second-harmonic generation in a monolithic resonator

We have measured the intensity fluctuations of the second-harmonic mode generated in a MgO:LiNbO₃ external monolithic cavity pumped by a Nd:YAG laser. The cavity has mirror coatings for both the fundamental and the second-harmonic mode. We scan the cavity using the electro-optic effect of the crystal and observe that the second-harmonic beam of 2 mW exhibits a quantum noise reduction of 40(±5)%. In addition, we report on the active frequency stabilization of the monolithic device used in our squeezing experiments. Several fast tuning parameters such as the electro-optic effect, the photo-elastic effect, and the laser frequency have been investigated. With these tuning parameters the monolithic resonator can be locked on double-resonance at the phase-matching temperature, which is a prerequisit for observing squeezing in a cw-regime.     

Rotational and vibrational temperature determination by DFWM spectroscopy

Using the DFWM technique we determined rotational and vibrational temperatures of NaH molecules in a dynamical system consisting of NaH, Na, H and H₂ for several heat-pipe oven temperatures. We applied a new way to determine the dependence of the DFWM signalI _c ^int on the power of the transition dipole momentµ without previous knowledge of the temperature. The revealed dependence isI _c ^int µ ⁴. In this case the laser intensities were found to be of the same order as the saturation intensity in accordance with simple DFWM theory. A usual Boltzmann plot was employed for the determination of the relevant rotational temperatures, which displayed higher values than the oven temperature.     

Power and beam-width dependence of a BaTiO3: Ce self-pumped phase conjugator

Power and beam-width dependences of the performance of self-pumped phase conjugators using a BaTiO₃: Ce crystal have been investigated. The incident beam was permitted to enter the crystal by thea-face or the +c-face. In both cases, the phase-conjugate reflectivity was observed to vary with the power and beam width of the incident beam. In the former case, two different optical beam patterns in the crystal can be observed under different conditions. Qualitative explanations are given to some of the results observed.     

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.     

Bistable behaviour in squeezed vacua: I. Stationary analysis

A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected simple closed curves depending on the cooperation parameter [0pt] : is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on [0pt] . We also present results which demonstrate more complicated switching behaviour in the dispersive case. Received 12 March 1999 and Received in final form 20 August 1999     

Percolation with constraints in the highly polarizable oxide KTaO<Subscript>3</Subscript>:Li

Experimental data on the temperature and electric field dependence of the Second Harmonic Generation Intensity in the solid solution KTaO₃:Li is analyzed in the framework of a new percolation-type approach which considers the history of cluster formation averaged over a large number of samples. In order to take into account that two cluster dipole moments turn when joining clusters together, a constraint is imposed on the cluster growth. This constraint leads to cluster-size saturation just after the percolation threshold. Owing to this circumstance, the connected cluster coexists with free clusters in some range of the impurity concentration and temperature. There is qualitative agreement between the computational results and experiments on Second Harmonic Generation intensities. The algorithm was written in C++ which allowed realistic computations to be performed on a standard PC. Received 26 August 1999 and Received in final form 27 December 1999     

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.     

Microfacetting of Au(110) electrodes: An optical second-harmonic generation study

The formation and lifting of microfacetting at an Au(110) electrode surface was studied by using in-situ optical Second-Harmonic Generation (SHG). In contrast to the unreconstructed (1×1) Au(110) surface which has aC _2v symmetry, the reconstructed surface exhibits aC _s symmetry due to essentially (111)-oriented microfacets. Hence, it shows SHG-anisotropy patterns fundamentally different to those of a non-reconstructed surface. Apparently, the nonlinear susceptibility tensor contains an additional threefold symmetry element. Its amplitude was determined using Fourier analysis of SHG-anisotropy curves and, thus, served as a measure of microfacetting of the Au(110) surface. We observed that adsorption of an organic molecule, such as pyridine, has little effect on the electrode-surface crystallography. In contrast, adsorption of bromide ions results in the lifting of microfacetting as indicated by the disappearence of the threefold symmetry term. Potential-step experiments gave time constants for the lifting of microfacetting in the range of < _1/2<150 ms.Paper presented at the 129th WE-Heraeus-Seminar on Surface studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994.     

Rotating surface soliton complexes in annular waveguides

We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a π-phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.