Marco Santagiustina

Walk-off and pattern selection in optical parametric oscillators.

The effect of walk-off in pattern selection in optical parametric oscillators is theoretically examined. We show that a dynamic mechanism also allows us to observe the formation of structures for positive signal detunings. In this regime the pattern that is generated is a periodic array of kinks that separate regions in which one of two stable steady states is alternately selected. This structure can be regarded as a train of dark soliton stripes because the two solutions have opposite signs. The wavelength of the selected pattern is theoretically predicted, and the prediction agrees with the results of the numerical solutions of the equations governing the device.

Bloch domain walls in type II optical parametric oscillators

Evidence of Bloch domain walls in nonlinear optical systems is given. These walls are found in the transverse fields of optical parametric oscillators when the polarization degree of freedom, the cavity birefringence, and (or) dichroism are taken into account. These domain walls arise spontaneously and exhibit defects where Bloch walls of different chirality join together. Two dynamic regimes are found:In the first one the vector field approaches a final homogeneous state, and in the other the walls are continually generated and annihilated. This dynamic behavior is caused by the fact that walls of opposite chirality move spontaneously with opposite velocity.

Pattern formation in the presence of walk-off for a type II optical parametric oscillator

We show the relevance of walk-off effects in pattern formation in a type II optical parametric oscillator at frequency degeneracy. With walk-off neglected only phase patterns are formed, and the intensity distribution is homogeneous. Walk-off changes the instability from absolute to convective for some parameter range. In the absolutely unstable regime it induces for each polarization component of light a competition between two phase stripe patterns (traveling waves) of different wavelength. Phase stripe patterns at each of the wavelengths are equally likely to be selected, and, after a transient regime of coexistence, one of them takes over. In the convectively unstable regime the existence of intensity patterns sustained by noise is shown. The patterns arise from the interference between traveling waves that are generated by the dynamical amplification of noise.

Growth dynamics of noise-sustained structures in nonlinear optical resonators

The existence of macroscopic noise-sustained structures in nonlinear optics is theoretically predicted and numerically observed, in the regime of convective instability. The advection-like term, necessary to turn the instability to convective for the parameter region where advection overwhelms the growth, can stem from pump beam tilting or birefringence induced walk-off. The growth dynamics of both noise-sustained and deterministic patterns is exemplified by means of movies. This allows to observe the process of formation of these structures and to confirm the analytical predictions. The amplification of quantum noise by several orders of magnitude is predicted. The qualitative analysis of the near- and far-field is given. It suffices to distinguish noise-sustained from deterministic structures; quantitative informations can be obtained in terms of the statistical properties of the spectra.

SPACE INVERSION SYMMETRY BREAKING AND PATTERN SELECTION IN NONLINEAR OPTICS

Pattern formation in nonlinear optical cavities, when an advection-like term is present, is analysed. This term breaks the space inversion symmetry causing the existence of a regime of convective instabilities, where noise-sustained structures can be found, and changing the pattern orientation and the selected wavevector. The concepts of convective and absolute instability, noise-sustained structures and the selection mechanisms in two dimensions are discussed in the case of optical parametric oscillators and a Kerr resonator. In the latter case, in which hexagons are the selected structure, we predict and observe that stripes are the most unstable structures in the initial linear transient. In the nonlinear regime of the absolute instability these stripes destabilize and hexagons form. Their orientation is dictated by that of the transient stripes and therefore by the advection term. In the convective regime we predict and observe disordered noise-sustained hexagons, preceded in space by noise-sustained stripes.

Vectorial vortices in type-II optical parametric oscillators

Summary form only given. We study the characteristics, stability and robustness of vectorial optical vortices in a type-II optical parametric oscillator (OPO) model describing the interaction of pump, signal and idler when the pump field is not resonated. Mean field equations have been obtained for the two orthogonal and linearly polarised amplitudes A/sub x/ and A/sub y/ of the signal and idler fields.

Bloch domain walls in transverse patterns in type-II optical parametric oscillators

Summary form only given. We show that the presence of a birefringent and/or dichroic mirror into a type-II optical parametric oscillator (OPO) yields to a new kind of domain walls. In these walls the field amplitude remains constant while the phase rotates when going from one domain to the neighboring one. These domain walls are similar to Bloch walls in magnetic systems. They appear here for positive or null detunings, where the zero wavenumber is selected. Idler and signal fields show a similar pattern.

From hexagons to optical turbulence

Summary form only given. The transition from regular static patterns observed in optical systems to spatio-temporal chaotic regimes is not yet well understood. We address this problem in a ring cavity filled with a nonlinear self-focusing Kerr medium pumped by an external field. In the mean-field approximation the transverse dynamics of the slowly varying electric field amplitude E is governed by a driven-damped nonlinear Schroedinger equation.

Noise-Sustained Transverse Structures in Nonlinear Optical Cavities

We theoretically demonstrate the existence of noise-sustained patterns in passive nonlinear quadratic or cubic (Kerr) optical cavitia [I], in the regime of convective instability. This regime refers to the c m of system in which advection overwhelms the growth dynamics due to the instability. Thus the formed pattern leaves the system and a structure can be permanently obaerved only if noise continuously regenerates it. Henceforth. in this condition patterns arise BS macroscopic manifestations of amplified noise; in particular, in optical cavities this noise can be of quantum origin [Z]. For optical parametric oscillators (OPOs) an advection-like term is given by the transversal walk-off between the pump and the signal. This effect is due to the crystal birefringence, vhich is exploited to phasematch the nonlinear interaction. More generally. any misalignement between the pump and the cavity field can produce the same effect. In our presentation we show hou, to determine the range in the parameter space where the instability is of convective nature. Two specific examples of calculation are given. The first refers to a Kerr resouator with a pump misalignemenl: a simple on?-dimensional transversal modcl allows us to introduce the main concepts of convective instabilities. In the semnd example. u~e will analyae a two-dimensional transversal model of an OPO. In this ease the walk-off term breaks the spatial rotational symmetry of the equations. The analysis indicates that this causes a preferential stripe pattern orientation both in the convectively and ahsalutely unstable regimes. In the latter rqime, it also predicts the co-existence of absolutely and convectively unstable spatial modes BS B result of the symmetry breaking. In both c e s . the numerical solutions of the equations governing the pattern evolution confirm all the predictions and noisesustained structures are found and characterized. The differences between noisesustained and deterministic patterns are shown. qualitatively in terms of the nearand far field observation and quantitatiwly through the statistical properties of the field spectral intensity. The numericai solutions also provide valuable informations about the growth dynamics of these structureb. Although txo particular kind of devices were investigated the concipts explained are relevant to other similar optical systems where walk-off or misalignment are present. Noisesustained patterns have been probably found but not recognized and charaeterized in previous experiments. This hypothesis is mainly based on the fact that for system with an advection-like term the instabilities just abwe threshold are always convective.

Walk-Off Effect on Pattern Selections in Optical Parametric Oscillators

In optical parametric oscillators (OPOs) the phasematching condition among the pump and the signallidler is reached by exploiting the crystal birefringence. Quite often. this implies that beams transversally walk off each other because of the misalignement of the Poynting vectors. The walk-off can affect the transverse patteni formation causing the pattern to drift and turning the instability to be convective. In the convectively unstable regime noise can be amplified and gives rise to macroscopic patterns [I]. Here. we demonstrate that the preseocc of the walk-of also affects the process of pattern selection. The term breaks the rotational symmetry and stripes orthogonal to the direction of the walk-offare preferentially selected. The wave vector of the selected stripes dfpends an thc walk-oK too. This effect is enhanced at small signal detunings. both negative and positive; there. the valw of the selected wave-vector can be sensibly different from the predictions obtained neglecting the walk-OK. Io particular, the analysis indicates that a structure can be also observed for posidive detunings, where the zero wavenumber (no pattern) is selected when neglecting walk-off effects. This is confirmed by the numerical solutions of the governing equacions which model a realistic device where pumping is restricted to a portion of spce of large enough size. The observed patterns consist of a sequence of dark stripes (i.e. stripes of phase defects) aq shown in figures 1 and 2. Recently stable topological spatial dark solitons have been predicted in OPOs (21; here. we observe the continuous generation o f a train of dark stripes, which appear at the botron and drift upwards in the direction of the walk-off. For negative detunings the usual bright stripe pattern is observed. For both positive and negative signal detuninp the agreement between the navevector predicted by the anaiysis and that resulting from the numerical resolution of the governing equations is very good.