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Discrete breathers and negative-temperature states
Full text linkWe explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter region where the system evolves towards a state characterized by a finite density of discrete breathers and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. We also discuss two possible mechanisms for the generation of negative-temperature states in experimental setups, namely, the introduction of boundary dissipations and the free expansion of wavepackets initially in equilibrium at a positive temperature
Combined effects of polarization and non-paraxial propagation on pattern formation
No full textWe show analytically that the presence inside an optical cavity of a polarizer and a hard diffracting object, for example, a circular aperture or waveguide, reduces the symmetry of the system from cylindrical to rectangular. As a consequence, patterns with concentric rings of bright or dark spots made up by modes whose azimuthal indexes are not multiples of one another, appear when the zero-field solution becomes unstable. These types of bifurcations are anomalous if the symmetry is cylindrical and therefore indicate the presence of polarization effects induced by diffraction. As an example of this type of system, we investigate numerically the bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity
Pulse compression by slow saturable absorber action in an optical parametric oscillator
No full textWe present numerical simulations of a singly-resonant, synchronously pumped optical parametric oscillator with intra-cavity slow saturable absorber. These indicate that compression ratios of about five or more may be achieved for realistic absorber parameters. The behaviour of the parametric oscillator with absorber presents a novel nonlinear resonance which is due specifically to the nature of the parametric three-wave interaction and which would not appear in a laser system
Diffraction-induced polarization effects in optical pattern formation
No full textWe show theoretically that patterns with concentric rings of bright or dark spots made up by modes with coprime azimuthal indexes may arise in codimension one bifurcations in optical systems with a metallic diffractor, a polarizer, and a nonlinear medium. These patterns are a consequence of diffraction-induced polarization in systems without polarization dynamics. As an example of this type of system, we investigate numerically the symmetry-breaking bifurcations of a ring laser with a metallic duct and a polarizer inside the optical cavity
Centre manifold reduction of laser equations with transverse effects: an approach based on modal expansion
No full textCentre Manifold theory is a valuable method for analysing and simplifying partial differential equations that appear in the study of transverse effects in nonlinear optics. In this paper we analyse its application to the Maxwell-Bloch equations for lasers with spherical mirrors and finite size pumps. By taking advantage of the expansion in cavity modes, we successfully compare reduced models with the original one for broad ranges of the parameters
Self-localization of Bose-Einstein condensates in optical lattices via boundary dissipation
Full text linkWe introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries
Feasibility of controlling complex dynamics in multi transverse mode lasers
No full textWe show that a Periodic Proportional Feedback (PPF) method can be successfully applied to the multi-transverse mode laser. We have simulated the laser by integrating the Maxwell-Bloch equations with the electric field projected onto the empty cavity Gauss-Laguerre modes. By applying the PPF technique to chaotic dynamics of low dimension density, we can control periodic orbits which differ only slightly from the unstable periodic orbits of the system, via modulation of the cavity losses and pump parameters, both for the cylindrically symmetric laser and for the case where the symmetry is removed. Our results show that although various periodic orbits can be controlled temporally, pattern selection (i.e. spatio-temporal control) needs more elaborate techniques
Macroscopic Quantum Effects in Nonlinear Optical Patterns
No full textWe display the results of the numerical simulations of a set of Langevin equations, which describe the dynamics of a degenerate optical parametric oscillator in the Wigner representation. The scan of the threshold region shows the gradual transformation of a quantum image into a classical roll pattern. Thus the quantum image behaves as a precursor of the roll pattern which appears above threshold. In the far field, suitable spatial correlation functions of intensity and field quadratures show unambiguously the quantum nature of fluctuations that generate the image, leading to effects of quantum noise reduction below the shot noise level and to the formulation of an EPR paradox
Langevin treatment of quantum fluctuations and optical patterns in optical parametric oscillators below threshold
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