Gian-Luca Oppo

Fundamentals and Applications of Spatial Dissipative Solitons in Photonic Devices

We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines.

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.

Statistical regimes of random laser fluctuations

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean-field description. Monte Carlo simulations of a simplified model which includes the population of the medium demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.

Laser with injected signal: perturbation of an invariant circle

We study the locked-unloked transition for a class of lasers with injected signal. The transition is produced by a parametric breaking of the invariant circle that represents the free running laser. A Hopf-saddle-node codimension two bifurcation coupled with a phase-drift re-injection mechanism organizes the flow. Fixed points (locked states), periodic orbits and tori, T2, of two inequivalent types as well as hetero-homoclinic loops are found by using methods of bifurcation theory and are illustrated with computer simulations. We discuss the dependence of the flow patterns with respect to the laser parameters and, in particular, we show that the detuning between atomic and cavity frequencies plays a fundamental role for the dynamics.

Phase-dependent interaction in a four-level atomic configuration

We study a four-level atomic scheme interacting with four lasers in a closed-loop configuration with a ⋄ (diamond) geometry. We investigate the influence of the laser phases on the steady state. We show that, depending on the phases and the decay characteristic, the system can exhibit a variety of behaviors, including population inversion and complete depletion of an atomic state. We explain the phenomena in terms of multiphoton interference, and compare our results with the phase-dependent phenomena in the double-Λ scheme. This investigation may be useful for developing nonlinear optical devices, and for the spectroscopy and laser cooling of alkali-earth atoms.

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.

Spatiotemporal Dynamics of Optical Parametric Oscillators

Abstract The coupling of diffraction and the x (2) nonlinearity is shown to lead to pattern formation in parametric oscillators in optical cavities. In particular the threshold for the generation of signal and idler waves is lowered by an off-axis emission for negative detunings. The output intensity is spatially modulated just above threshold while more complicated patterns appear for larger values of the pump amplitude. Competition between domains of rolls with different orientations leads to long transients until boundary effects prevail. In the case of finite-size input beams, the roll orientation is locally perpendicular to the boundary and the pattern tends to rotate. Finally, the effect of spatial structures on the spectrum of quantum fluctuations of the vacuum is considered and discussed.

Gauss-Laguerre modes: a “sensible” basis for laser dynamics

Abstract Modal decomposition of a system of partial differential equations is a useful analytical and numerical tool. In particular, it is often desirable to describe complex spatio-temporal behaviours by restricting the analysis to the interaction of few suitably chosen modes. We show how the Gauss-Laguerre modes have this property for many laser states, and are thus a “sensible” basis onto which to project the laser equations.

From quantum to classical images

We 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. An experiment on parametric down-conversion in lithium triborate shows strikingly similar results in both the near and the far field, displaying qualitatively the classical features of quantum images. c 1997 Optical Society of America.

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.