Light and Complexity

Localization in a nonlocal medium sounds like a contradiction. However, it is interesting trying to figure out the interplay between processes of localization and nonlocal effects. This is even more complicated if one takes into account localizations induced by structural disorder. The interplay between the characteristic length scales of localization and nonlocality was not considered before.

In the manuscript Opt. Lett. 37, 332 (2012), [arXiv:1201.3923], Viola Folli and Claudio Conti report on a theoretical analysis of Anderson localization in a nonlocal nonlinear medium; it is shown that nonlocality stabilizes localizations with respect to the action of nonlinearity, and analytical expressions for the power needed to destabilize the Anderson states are obtained. The nonlocal model allows indeed a simple treatment of the nonlinear Anderson localizations.

The picture below shows the evolutions of the states in the presence of nonlocal nonlinearity.

Within the fundamentals of nonlinear optics there are the processes of instability of a beam, either temporal or spatial. In the presence of nonlinearity,  a beam can break up because of a variety of physical effects, in primis, the so-called modulational instability (MI). MI appears in focusing media, and destroy (in the spatial case) a wide beam into fragments, which are characterized by a dominant spatial period. In other words, through MI a periodical pattern arises from a plane wave, the period being determined by the wave intensity; this intensity dependent period is the dominant spatial scale.

In scale-free optics, beam evolution is not affected by the spatial scales: non-diffracting beams can be generated at any beam size and power independently. Thus one could expect that MI is not present for scale-free nonlinearities, because MI has a dominant spatial case. And this is indeed the case: if one makes the standard analysis, no MI is retrieved in the scale-free model.

However, as shown by Viola Folli, Eugenio Del Re, and Claudio Conti in Physical Review Letters 108, 0339012 (2012), [http://arxiv.org/abs/1201.3865], other kinds of instabilities arise in the peculiar nonlocal nonlinearity of the out-of-equilibrium crystals, which are used to activate the scale-free response. At variance with MI, no spatial scale arises in these instabilities and the beam breaks into many spots with a distributions of sizes and powers. Preliminary evidence of the process was reported in the first observartion of the scale-free solitons, the figure below shows the numerical evidence of the scale-free instabilities and the corresponding spectrum.

The reported analysis is just a first step in of several theoretical open roads of the scale-free model.

The occurrence of the spontaneous synchronization of coupled oscillators is a well known phenomenon.

For example, in standard lasers, by employing specific devices like acousto-optics modulators, it is possible to couple orthogonal electromagnetic modes, make them synchronously oscillating and emitting short pulses.

On the other hand, in ultra-fast femtosecond oscillators, the mode-locking occurs because of the presence of a saturable absorber; as in the former case no disorder is present.

As reported in Nature Photonics, Marco Leonetti, Claudio Conti, and Cefe Lopez show that Random Lasers, i.e. lasers with disorder, may be driven through a mode-locking regime when changing the spatial distribution of the excited modes. Indeed, in random lasers, modes are naturally coupled because of the fact that the cavity is open and exhibit a sort of condensation above threshold. When tailoring the pump profile, and exciting modes with a different degree of coupling (from the weakly coupled regime for distant modes, to the strongly coupled one for overlapping modes), random lasers can be made oscillating either in an asynchronous or in a mode-locked regime.

Such an effect has strong influence on the spectral shape of the emitted radiation, showing that random lasers can be made strongly tunable and are engineerable.

This is the first evidence of such a mode-locking transition in the presence of disorder, may have a role in the development of novel kind of laser sources, and it is another step for the assessment of complexity in photonic systems.

The picture below shows an example of a laser cluster pumped by a shaped beam (courtesy of Marco Leonetti)

There is a very limited number of ways for artificially changing the refractive index of a medium. But if one could be able to arbitrarily increase it, unprecedented possibilities would open the road to a novel generation of optical devices.

In a paper in Nature Photonics (January 2011),  E.DelRe, E.Spinozzi, A.J.Agranat and C.Conti demonstrate through theory and experiments that supercooled ferroelectrics (a class of "complex" optical media) display a largely tunable refractive index when acting on their thermal history and resorting to their out-of-equilibrium state.

The so called "polar nano-regions" furnish such a possibility, and lead to the demonstration of a nonliner optical behavior which is intensity independent and may provide the complete suppression of evanescent waves, with a potential impact in whole field of microscopy.

This may constitute the first example of a novel class of non-ergodic metamaterials, where the wavelength of light is effectively cancelled and the propagation is "Scale-Free", that is, beams propagate without distortion at any beam size and intensity.