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SIAM Workshop on Nonlinear Waves in ROME !

We are organizing the next workshop on multidimensional nonlinear waves

NLW08: Multidimensional localized structures

the 18 and 19 July 2008.

The partecipation to the workshop is free and coffee and a nice reception will be at disposal.

The workshop will be followed by the

SIAM Nonlinear Waves conference

Many outstanding scientists from all over the world will enjoy a nice summer science-week in Rome!


Laser beam filamentation in fractal aggregates

Light propagation in soft materials, like colloids, gives rise to many nonlinear phenomena. With reference to a continuous wave excitation and slow nonlinear responses, the most important are thermal defocusing, thermophoresis and electrostriction.

As far as light absorption is negligible, electrostriction is dominant. This is the leading process for optical tweezing, and has been investigated since the early 80s. A nonlinear optical response due to electrostriction is associated to the fact that colloidal particles with refractive index higher than the host liquid (e.g. latex spheres in water) tend to be attracted in the high laser intensity region; conversely particles with lower refractive index (e.g. bubbles) are repelled from the beam focus. In both cases the resulting nonlinear response is focusing.

In recent papers, we developed a theory of the electrostrictive nonlinearity that accounts for the specific structure of a soft-colloidal materials. By this approach, we investigated the role of the fractal dimension of aggregates in the process of laser beam filamentation. We found that this parameter has a leading role in determing the number and the spatial distribution of laser filaments that spontaneously generate from a wide beam; this is a universal effect in nonlinear wave physics and it is typically denoted as spatial modulational instability.




Aging of the Nonlinear Susceptibility

Our z-scan experiments provide evidences of the aging of the nonlinear optical susceptibility in an out-of-equilibrium soft-colloidal material (details in http://babbage.sissa.it/abs/cond-mat/0609659v1); conversely the linear optical response, as the refractive index or the material absorption, does not change with time.
Generally speaking, the nonlinear susceptibilities are more sensible to the presence of a landscape in complex systems (as soft-materials): they involve large solicitations, while linear responses are limited to small perturbations around local minima.

The following picture shows a comparison between dynamic light scattering experiments (left panel) and z-scan data (right panel) on long time scales. The nonlinear optical response is roughly proportional to the peak to peak distance in panel B.

Optical shocks (intro)

shockAn optical spatial shock is a steep wavefront that is generated in the presence of strong nonlinear effects. The image shows a radial spatial optica shock in a nonlocal optically nonlinear medium (details in http://arxiv.org/abs/0704.0610).




Dynamic Z-scan Experimental Setup

A dynamic Z-scan experimental setup has been realized to measure the strength and the dynamics of the nonlinear susceptibility in various soft materials. The computer assisted positioning system enables to monitor the nonlinear response in various regions on time scales ranging from millisecond to days; this enables to follow out-of-equilibrium dynamics and aging processes.



Optical Solitons in Soft-Matter

Soft-matter displays various kinds of optically nonlinear responses; for negligible absorption the mostly relevant effect is electrostriction. The latter is always focusing, as a result one may expect that soft-matter can sustain bright spatial solitons, which could find a variety of applications from laser surgery to optical tweezing.

However the existence of a nonlinear response does not necessarily imply that optical spatial solitons can be observed. The key point is that optical spatial solitons must be stable, and this depends on the nature of the optically nonlinear response.

From a strictly theoretical perspective, the first analysis of the electrostricitve response (after Ashkin and coworkers in 80s, see our papers and references therein) was based on a purely local nonlinear response, i.e. the so-called Kerr effect, which states that the refractive index is proportional to the optical intensity.

A purely Kerr like nonlinearity does not support solitons; indeed in this kind of media laser beams undergoes the so-called catastrophic self-focusing and stable light filaments, which propagate without distortion, cannot be observed.

Conversely, other kinds of nonlinear responses are not affected by this instability, and can sustain solitons. An important example is given by the so-called nonlocal nonlinear response (see Conti and Assanto in Encyclopaedia of Modern Optics), where the nonlinear refractive index perturbation at a given position is determined by the intensity in various points in the material.

For example, liquid crystals display a nonlocal nonlinear response as demonstrated by Conti, Peccianti and Assanto in  in 2004. The existence of solitons in electrostrictive media, and specifically in soft-colloidal solutions, can be ruled out as far one accepts the validity of a simple Kerr model.

However we have extended the theoretical model of electrostriction and predicted that, in soft-colloidal matter, optical solitons can be observed because the structure of the soft-material (due to the particle-particle interaction) induces nonlocality (details here) . In the previous theoretical approaches to optical electrostriction, the role of particle-particle interaction was overlooked.

A group at the University of Glasgow has reported the first experimental evidences ; we are currently working on experiments on solitons in soft-matter.