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.     

Emission and Absorption Properties of Atoms in a Trapping Potential

Abstract

We investigate the resonance fluorescence emission and absorption spectra for a one-dimensional harmonically trapped two-level ion. The master equation is used to generate the atomic polarizations from which the spectra are derived. Because of their size, the final density matrix equations are investigated numerically. The calculations are carried out in the Lamb-Dicke limit of tight localization of the ion. Sharp peaks are found to appear in the spectra at frequencies detuned from line centre by steps of the trap frequency. The frequency of the peaks and their superposition with Rabi sidebands above saturation are analysed for a variety of parameter ranges. Moreover, new features of the absorption spectra of a weak probe such as sharp gain regions around the trap sidebands are also discussed.     

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.     

Efficient coupling into and out of high-Q resonators

The temporal-coupled-mode theory is directly applied to the design of devices that feature a resonator with a high quality factor. For the temporal-coupled-mode theory we calculate the decay rate of the resonator to determine the transmission properties of the device. The analysis using the decay rates requires little computational effort, and therefore the optimum device properties can be determined quickly. Two examples, a wavelength filter and a resonator crossing, are presented to illustrate the use of the analysis.     

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.