A.J. Scroggie

Pattern formation in a passive Kerr cavity

Analytic and numerical investigations of a cavity containing a Kerr medium are reported. The mean field equation with plane-wave excitation and diffraction is assumed. Stable hexagons are dominant close to threshold for a self-focusing medium. Bistable switching frustrates pattern formation for a self-defocusing medium. Under appropriate parametric conditions that we identify, there is coexistence of a homogeneous stationary solution, of a hexagonal pattern solution and of a large (in principle infinite) number of localized structure solutions which connect the homogeneous and hexagonal state. Further above threshold, the hexagons show defects, and then break up with apparent turbulence. For Gaussian beam excitation, the different symmetry leads to polygon formation for narrow beams, but quasihexagonal structures appear for broader beams.

All-optical delay line using semiconductor cavity solitons

An all-optical delay line based on the lateral drift of cavity solitons in semiconductor microresonators is proposed and experimentally demonstrated. The functionalities of the device proposed as well as its performance is analyzed and compared with recent alternative methods based on the decrease of group velocity in the vicinity of resonances. We show that the current limitations can be overcome using broader devices with tailored material responses.

From domain walls to localized structures in degenerate optical parametric oscillators

Degenerate optical parametric oscillators (DOPO) possess one-dimensional stable domain wall solutions in the presence of diffraction. Such domain walls connect two homogeneous stable states and display damped spatial oscillations. In two dimensions, domains of one homogeneous phase inside the other tend to shrink for zero and positive detunings. For pump values above an appropriate threshold, the shrinking of the domains is stopped by the short-range interaction of the oscillatory tails of pump and signal domain walls leading to local back conversion and radially symmetric localized states. This mechanism corresponds to the stabilization of a homoclinic orbit and is generic in that it requires neither peculiar bistability conditions nor the existence of a patterned state. Neither domain walls nor domain-wall-induced localized states survive in the non-degenerate case with a large frequency difference between signal and idler fields.

Polarization patterns and vectorial defects in type-II optical parametric oscillators

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.

Stable droplets and dark-ring cavity solitons in nonlinear optical devices

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.

Controlling pattern formation and spatio-temporal disorder in nonlinear optics.

We present a feedback control method for the stabiliza- tion of unstable patterns and for the control of spatio-temporal disor- der. The control takes the form of a spatial modulation to the input pump, which is obtained via filtering in Fourier space of the output electric field. The control is powerful, exible and non-invasive: the feedback vanishes once control is achieved. We demonstrate by means of computer simulation, the effect of the control in two different optical systems.

Complex spatio-temporal dynamics of optical parametric oscillators close to threshold

Abstract Spatially extended degenerate cw optical parametric oscillators are predicted to display a rich variety of spatio-temporal dynamic 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. In spite of recent encouraging experimental results, 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 move closer to the signal generation threshold thus making their experimental observation more feasible.

Pulse compression by slow saturable absorber action in an optical parametric oscillator

We 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.

Slow light and all-optical delay lines using cavity solitons in semiconductor lasers

An all-optical delay line that is based on injecting an optical bit stream into an optical resonator, creating cavity solitons (CS) that drift transversely with a controllable velocity, is proposed and demonstrated. An optical injection experiment is performed in a broad area vertical cavity surface emitting laser emitting at 980 nm.

Transient and sustained mode-locking of cavity solitons in a VCSEL with frequency-selective feedback

Self-confinement of light and the control of light by light are both major thrusts of modern photonics. Recently, optically controllable microlasers were realized within the aperture of a broad-area vertical-cavity surface-emitting laser (VCSEL) with frequency selective feedback and interpreted as cavity solitons (CS), i.e. as spatially self-localized nonlinear states [1]. Like any free-running laser, a lasing CS has the freedom to choose polarization, phase and frequency, which gives exciting new opportunities for fundamental studies and applications. In particular this implies that the microlasers might operate on multiple longitudinal cavity modes leading to self-pulsing, if the modes are locked in phase. This is interesting in its own right but the intriguing long-term vision is that modelocked spatial laser solitons might lead to full three-dimensional confinement or spatio-temporal light bullets where the pulse length and duration are smaller that the cavity length and round-trip time, respectively.