Transverse pattern dynamics in the output of a laser are studied by detailed numerical solutions of the full set of Maxwell Bloch equations. The effects of different parameters on the behavior of the solutions are investigated. Our numerical results reveal a rich variety of behaviors in the pattern evolution, phase vortex formation and spatiotemporal dynamics in the output of a laser beam.

We consider a degenerate optical parametric oscillator consisting of a crystal in a ring resonator. The occurrence of spatial instabilities in such system due to diffraction are studied and it is shown that they may lead to the formation of stationary or dynamical spatial patterns. The thresholds for such instabilities are derived when either the pumped and the generated modes are detuned with respect to the cavity reference frequency; the patterns that emerge from the instability are calculated analytically by bifurcation analysis. Numerical simulations substantially confirm the onset of such phenomena giving evidence of the formation of rolls, zig-zag patterns, dislocations, filamentation and optical chaos.

The transverse dynamics of a highly multimode CO₂ laser is studied. The spatial distribution of the intensity is shown to remain ordered even at high Fresnel numbers. Parameters as the effective cavity symmetry or the gain bandwidth are shown to be very important and alter significantly the oscillating pattern. The interpretation of this behavior is helped by adding a saturable absorber inside the cavity of the laser. The effect of the absorber is to stabilize the modes of the empty cavity, which are so demonstrated to be relevant for the description of the transverse dynamics. Following this approach, the dynamics of the laser without absorber is shown to result from the competition of a small number of the empty cavity eigenmodes.

The light propagation through a system of coupled bistable thin films is considered. In the limit of short relaxation times the problem is reduced to a infinite-dimension map. It is shown that self-pulsation regimes occur when the incident light intensity is not high enough to switch all bistable elements in the upper state. In the case of the gaussian incident beam, spatio-temporal structures of the beam profile are studied.

We consider a passive optical system consisting of a ring cavity and a homogeneously broadened two-level medium. After a first modulational instability we find several secondary instabilities which lead to a temporally chaotic, spatially homogeneous state and to temporally chaotic states where the spatial symmetry is broken. These spatio-temporal chaotic states are characterized by the decrease of the auto-correlation and the spatial cross- correlation function. In order to analyze the bifurcations in the spatio- temporal chaotic regime we investigate the dynamical behavior of spatially significant quantities. Three states are found which arise from different intermittent transitions. We quantify the observed bifurcations by means of Lyapunov exponents.

Under a continuum approximation we derive a complex Ginzburg-Landau equation describing either a set of weakly coupled class A lasers, or the fast-time dynamics of a set of weakly coupled class B lasers. We show that phase locked behavior is described by the so-called Stokes wave solution and by performing a linear stability analysis we confirm analytically some numerical observations--namely that the Stokes wave can often be made unstable for perturbations of sufficiently short wavelength and that the coupling phase plays at least as significant a role in determining the spatio-temporal behavior of the system as does the coupling strength. As with our previous work on the simulation of discrete systems a stable phase-locked solution is found to be particularly difficult to achieve as the relative coupling phase approaches (pi) /2. The continuum approach also highlights other scalings, not immediately apparent from the discrete model. The coupling strength, for example, is shown to set the scale of spatial fluctuations.

We study numerically a single-mode homogeneously broadened three-level model for a coherently pumped laser in a ring cavity with pump and generated fields having gaussian transverse profiles. For a range of parameters suitable for a NH₃ laser, we find dynamics in the phase space provided that the radius of the pump field is small compared with the beam waist of the generated field. Otherwise, we find that the laser emits a constant intensity output.

A theory is presented taking into account both the superradiance and local field effect of a thin-layer laser. Two laser configurations are considered: a one-mirror laser and traveling-wave laser. Numerical calculations are provided to illustrate the regimes of laser instability.

The dynamics of an actively mode-locked lasers is investigated experimentally and the results of numerical simulations are presented. Different regimes corresponding to the relaxation oscillations and spiking are observed depending on the level of loss modulation are observed when the mode-locking is destroyed. The experiments show that spiking never occurs when the modulation signal is below the critical value. The numerical results demonstrate in detail the processes of pulse profile and pulse-train instabilities.

The numerical model of the dynamical regimes of the active and additive-pulse mode-locking in solid state lasers is performed. The model is based on plane wave approximation and includes the coherent pulse propagation and group- velocity dispersion. The examples of different dynamics in the YAG:Nd and Ti:Sph laser are presented.

A theoretical analysis of the optically injected single-mode diode laser outside the locking regime is presented. After a short overview of our model and its description of the locking regime, we concentrate on the nonlinear interaction between diode and injection signal that occurs outside this locking regime. When the injection is sufficiently weak this process can be approximated by four-wave mixing (FWM). We will present an extensive analytical treatment of the FWM behavior and find good agreement with the results of a recent experiment.

On the basis of Jones' vectors and matrices formalism the theoretical study is made of the energy and polarization characteristics of a two-frequency (single-mode) standing-wave Helium-Neon laser with weakly anisotropic cavity possessing linear phase anisotropy. The possibility is shown of the existence of polarization instability of lasers operating at j yields j + 1 transitions. Polarization multistability has been found. The results of the theory are in agreement with the known experimental data.

A theoretical study of a He-Ne laser operation at (lambda) equals 1.15 micrometers with a rotating and simultaneously oscillating amplitude-phase element has been carried out. The laser is shown to generate the radiation with periodic and quasiperiodic oscillations of intensity and polarization parameters. A region of control parameters at which there exists the regime of parametric resonance characterized by a jump-like change of the rotation rate of polarization ellipse has been found.

The dynamics of an optically pumped single mode laser with pump and laser fields with either parallel or crossed linear polarizations and a homogeneously broadened four-level medium is theoretically investigated in detail. Numerical simulations reveal dramatically different dynamic behaviors for these two polarization configurations. The analysis of the model equations allows us to find the physical origin of both behaviors. In particular, the Lorenz-type dynamics exhibited by the orthogonal configuration arises from the lack of coherent effects in spite of the optical pumping.

Two coupled complex Ginzburg-Landau equations are derived to described multimode operations of a ring unidirectional laser with a saturable absorber near the lasing threshold. We show that unlike a laser without absorber this laser can exhibit in low-intensity domain the Benjamin-Feir instability which is known to lead to very complicated behaviors including chaotic ones.

Results of theoretical consideration of the multistable states and instabilities in the two-channel laser with a saturable absorber in the presence of additional optical feedback between channels are proposed. Various steady states with regular pulsations or cw radiation in one or in both channels, or oscillations of the type two-, three- or some other multiple periods are demonstrated, both pulsations with breaking of regularity. Action of additional feedback on the multistability, instabilities, and laser dynamics is analyzed.

We analyze the behavior of a thin-layer absorbing element taking into account superradiance, the local field effect and detuning. The dynamical range of optical bistability and its contrast ratio are calculated.

The review of results of theoretical investigations of dynamics in lasers with parameters controlled by external feedback (FB) is presented. The case of an arbitrary length of the FB loop has been considered, so the delay connected with the time of the signal passage along the loop can be significant. The lasing behaviors evolution accompanying changes in the delay have been defined.

In this paper we study the laser system in which the output mirror is an optical bistable device formed by a nonlinear Fabry-Perot etalon. Based on the semiclassical dynamical model for this laser system, we analyze the stability and the dynamic response of this system by using the linear stability analysis and the numerical solving the differential equations of this system. From the linear stability analysis, we obtain that in this system (1) there are not only the saddle-node bifurcation but also the hopf bifurcation; (2) there may be at most three operating points where the hopf bifurcation will occur; (3) the relative initial phase shift and the detuning parameter will effect the number and distribution of the hopf bifurcation points. From the second method, we give how the variables of this system change with time when a perturbation occurs in the system (or an external optical pulse is inputed into the laser) and the results show that this system may be switched from one stable state to another by optical method. The results given by two methods are coincident.

Low Frequency Fluctuations (LFF) in diode lasers with optical feedback from an external reflector have been experimentally investigated by determining the control parameter region for their occurrence and by measuring statistical distributions of the return times between fluctuations. Two LFF regimes with different return time statistics have been identified. As asymmetry in the temporal dependence of the output intensity from the front and rear facets of the diode has been detected and explained in terms of coherent properties of the optical field.

A description of the principal bifurcations which lead to the appearance of the Lorenz attractor is given for the 3D normal form for codimension-3 bifurcations of equilibria and periodic orbits in systems with symmetry. We pay special attention to two bifurcation points corresponding to the formation of a homoclinic butterfly of a saddle with unit saddle index and to a homoclinic butterfly with zero separatrix value.