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ABSTRACT: Defects play an important role in a number of fields dealing with ordered structures. We demonstrate theoretically and experimentally the possibility of an active manipulation of defects in terms of an externally induced motion. We focus on the spontaneous formation of two-dimensional spatial structures in a nonlinear-optical system, a liquid crystal light valve under single optical feedback. For a particular parameter setting, a spontaneously formed hexagonal intensity pattern contains several dislocation-type defects. A scheme based on Fourier filtering allows us to restore spatial order in a selectable part of the pattern. Starting without control, the controlled area is progressively expanded, such that defects are swept out of the pattern.
Physical Review Letters 10/2003; 91(11):113903. · 7.37 Impact Factor
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ABSTRACT: This work characterizes the process of cracking of optical patterns by studying the evolution of the homogeneous islands for different values of the parameters, the initial wave-vector and the amplitude of an additive noise. In particular, an initial hexagonal structure is considered with wave-vector smaller than the critical wave-vector of the incoming modulational instability.
Quantum Electronics Conference, 2003. EQEC '03. European; 07/2003
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ABSTRACT: This study investigates the phase-dependent behaviour of the four-level closed-loop atomic diamond configuration. A ground state is quasi-resonantly coupled to two intermediate states which are themselves coupled to an excited state. Transitions between any two states occur via two alternative paths. The interference between these transition amplitudes can be constructive or destructive, depending on the relative phase between the excitation amplitudes. As a consequence also the population as well as the one- and two-photon coherences are periodic functions of the relative phase. This phase in general comprises the wavevector mismatch, the two-photon detuning, the initial laser phases and the individual atomic-dipole phases. In this paper, the authors concentrate on the steady state solutions for the case of two-photon resonance. The behaviour of the system is determined by the concurrence of the phase-dependent Hamiltonian dynamics and the relaxation processes.
Quantum Electronics Conference, 2003. EQEC '03. European; 07/2003
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ABSTRACT: Spatial structures in extended nonlinear optical devices can display important quantum features. For example, quantum images in degenerate optical parametric oscillators (DOPO) show quadrature squeezing in the near field and Einstein-Podolsky-Rosen correlations in the far field. We present here a new kind of spatial structure induced by quantum fluctuations in the DOPO: arrays of cavity solitons.
Quantum Electronics Conference, 2003. EQEC '03. European; 07/2003
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ABSTRACT: Two kinds of cavity solitons, stable circular domain walls (droplets) and dark-ring cavity solitons, are presented in models of vectorial Kerr resonators and degenerate optical parametric oscillators. These structures are universal in systems with two equivalent homogeneous states and are found for parameter values close to those of a modulational instability of a flat front. Stable droplets owe their existence to curvature effects and, therefore, they are not present in one-dimensional systems. We show that stable droplets nucleate out of dark-ring cavity solitons and that in some systems there are regimes in which they coexist.
IEEE Journal of Quantum Electronics 03/2003; · 1.88 Impact Factor
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ABSTRACT: Quantum fluctuations of the signal field are shown to induce packed arrays of cavity solitons in a degenerate optical parametric
oscillator above threshold in the limit of large pump finesse relative to the signal finesse. The cavity solitons in the array
are formed by locked domain walls, and lead to a highly correlated quantum structure. The effect of the quantum fluctuations
is non-trivial since the arrays of cavity solitons have a far less stable than other stable solutions and disappear with decreasing
pump finesse. The transition from disorder to order due to quantum noise is also discussed.
The European Physical Journal D 01/2003; 22(3):453-459. · 1.48 Impact Factor
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ABSTRACT: 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.
The European Physical Journal D 01/2003; 22(3):441-451. · 1.48 Impact Factor
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ABSTRACT: Domain walls with oscillatory tails are commonplace in models of spatially extended nonlinear optical devices. Their interaction and locking at discrete distances lead to asymptotically stable spatial disorder. We show that noise in the presence of domain walls with oscillatory tails can suppress spatial disorder by privileging highly correlated dynamical states consisting of arrays of spatial solitons.
Physical Review Letters 01/2003; 89(25):254102. · 7.37 Impact Factor
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ABSTRACT: We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.
Physical Review E 11/2002; 66(4 Pt 2):046605. · 2.26 Impact Factor
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ABSTRACT: We apply quasi-exact numerical techniques to the calculation of stationary one- and two-dimensional, bound multipeaked cavity soliton solutions of a model describing a saturable absorber in a driven optical cavity. We calculate the existence and stability domains of a wide range of such states and determine the perturbative eigenmodes that cause loss of stability. We relate the existence of N-peaked states to the locking range between patterned and homogeneous solutions, as a function of two parameters.
Physical Review E 11/2002; 66(4 Pt 2):046606. · 2.26 Impact Factor
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ABSTRACT: Previous studies of lasers and nonlinear resonators have revealed that the polarization degree of freedom allows for the formation of polarization patterns and novel localized structures, such as vectorial defects. Type- II optical parametric oscillators are characterized by the fact that the down-converted beams are emitted in orthogonal polarizations. In this paper we show the results of the study of pattern and defect formation and dynamics in a type-II degenerate optical parametric oscillator, for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations that appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.
Physical Review E 04/2002; 65(3 Pt 2B):036610. · 2.26 Impact Factor
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ABSTRACT: We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Ising walls, deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion. We then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities.
Physical Review E 12/2001; 64(5 Pt 2):056618. · 2.26 Impact Factor
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ABSTRACT: We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. An amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to shrinking circular droplets is derived. We predict the existence of stable droplets with a radius R that diverges at the bifurcation point, where a curvature driven growth law R(t) approximately t(1/4) is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.
Physical Review Letters 12/2001; 87(19):194101. · 7.37 Impact Factor
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ABSTRACT: Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered. Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO/
11/2001;
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ABSTRACT: Mean field models of spatially extended degenerate optical parametric oscillators possess one-dimensional stable domain wall solutions in the presence of diffraction. We characterize these structures as spiral heteroclinic connections and study the spatial frequency of the local oscillations of the signal intensity which distinguish them from diffusion kinks. Close to threshold, at resonance or with positive detunings, the dynamics of two-dimensional diffractive domain walls is ruled by curvature effects with a t(1/2) growth law, and coalescence of domains is observed. In this regime, we show how to stabilize regular and irregular distributions of two-dimensional domain walls by injection of a helical wave at the pump frequency. Further above threshold the shrinking of domains of one phase embedded in the other is stopped by the interaction of the oscillatory tails of the domain walls, leading to cavity solitons surrounded by a characteristic dark ring. We investigate the nature and stability of these localized states, provide evidence of their solitonic character, show that they correspond to spiral homoclinic orbits and find that their threshold of appearance lowers with increasing pump cavity finesse.
Physical Review E 07/2001; 63(6 Pt 2):066209. · 2.26 Impact Factor
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ABSTRACT: Summary form only given. In recent years, studies into transverse effects in nonlinear optical systems have revealed a wealth of spatial complexity, ranging from periodic patterns to localised structures. We present here a computer-assisted technique, valid for arbitrary values of the system parameters, which can find the stationary solutions of a model. It uses a Newton-type method and a Fourier transform to evaluate the spatial derivatives. The Newton method automatically gives the linearisation around the solutions found and therefore can be extended to find their eigenspectrum and hence stability. We will demonstrate the method by finding exact hexagonal, roll and square solutions for a model of a saturable absorber in a cavity. We will show these pattern solutions as a function of their wavenumber and of the intensity of the input pump.
Quantum Electronics Conference, 2000. Conference Digest. 2000 International; 10/2000
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ABSTRACT: The mean-field model of a degenerate optical parametric oscillator (DOPO) is known to exhibit pattern formation at threshold for negative signal detunings. On the other hand, for positive detunings there are two stable, equivalent, spatially-homogeneous solutions which may be connected by domain walls. In one transverse dimension these walls are stable and stationary. In two dimensions, however, a domain of one solution embedded in the other will shrink due to curvature effects. We show here that by using input pump beams formed by Gauss-Laguerre modes with zero radial index and azimuthal index m≠0, single and multiple domain walls can be asymptotically trapped in the signal output beam. Several configurations of regularly and irregularly spaced domain walls can be generated with either m=1 or m=2. A collection of "optical sprinklers" is obtained by numerically integrating the partial differential equations of a DOPO in the presence of diffraction.
Quantum Electronics Conference, 2000. Conference Digest. 2000 International; 10/2000
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ABSTRACT: Summary form only given. Spatially extended degenerate cw optical parametric oscillators (DOPOs) are predicted to display a rich variety of spatio-temporal behaviour in two transverse dimensions. Typical examples are the dynamical scaling of phase domains, randomly distributed cavity solitons, formation of spatial patterns and optical turbulence. Many of these features can be difficult to observe in real devices since they require input energies which are too large. Here we show that in the case of a higher finesse for the pump field than for the signal field, complex spatio-temporal phenomena can move extremely close to the signal generation threshold thus making their experimental observation more feasible.
Quantum Electronics Conference, 2000. Conference Digest. 2000 International; 10/2000
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ABSTRACT: A numerical model for a singly resonant, nondegenerate optical
parametric oscillator, which includes diffraction and idler absorption,
has been developed. This model requires just one equation for the
resonated signal field to be numerically integrated, while the pump and
idler fields are reconstructed from their analytic solutions and the
dynamics of the signal field. Typical results from our simulations are,
for example, output intensities and threshold fluencies, which can be
compared with those obtained from experiments. The spatial beam quality
of output beams produced by our model is evaluated via the M<sup>2</sup>
factor. We present results from the simulation which are consistent with
experimental evidence, particularly in reference to the impact of idler
absorption
IEEE Journal of Quantum Electronics 06/2000; · 1.88 Impact Factor
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Quantum Electronics Conference, 1998. 1998 EQEC. European; 10/1998
