Gian Luca Lippi - Institut de Physique de Nice (INPHYNI) - Keywords: Self-organization, phase transition, noise

Gian Luca Lippi - Institut de Physique de Nice (INPHYNI) - Keywords: Self-organization, phase transition, noise

Contribution title: Self-organization and noise in small scale lasers and beyond

Lasers are nowadays ubiquitous devices which find their place not only in science and technology, but also in medicine, entertainment, etc. Their special properties, such as "single emission frequency", directionality and (relatively) large power derive from self-organization, which can be loosely described as collecting the energy normally dissipated in all directions into a collective state. As an illustration consider the following: a large group of people panicking in the presence of a large fire run in all directions. Their collective energy is wasted in disorder. If through some external inducement the same people organize into a human chain, buckets of water can be passed to extinguish the fire. The external inducement is equivalent to the mirrors’ action in lasers. The transition from disorder to order is technically called the laser threshold, and can be seen as a "phase transition" which self-organizes the system.

Much work has been invested in miniaturizing lasers to render their use more flexible, thanks to reduced space occupation, lower energy consumption and thermal waste (some energy is always lost, even in the "human chain" example). While technology has been very successful in this task and size reduction has steadily progressed, the fundamental understanding of the self-organization transition in ever smaller devices has not kept up the pace. In order to understand the challenges, let us continue with the previous illustration. Think, as an extreme case, of a single person having to confront a fire: s/he may oscillate between using the nearest extinguisher and running away, and actually alternate between the two kinds of behaviour in a more or less regular way in the panick of not succeeding in either task (extinguishing the fire or escaping from it). There is no longer an obvious external inducement and there is no collective effect coming from the strength of the group! The inducement is gradually lessened as the group size shrinks while the relative effect of strong panic by a single individual may have a large impact on the (smaller) ensemble!

In the past couple of years, we have been looking at the threshold properties of small lasers as a function of their size and operating conditions, and have found a number of interesting features which characterize their self-organization, in the form of intermediate steps where more or less regular oscillations take place (groups of people starting to organize and being overcome by panic, in our illustration) of different type, until the ordered (i.e., self-organized) state is attained.

While the illustration used here belongs to mass/individual psychology, connections in many different fields may be expected. For instance, in the social sciences, the self-organization of small groups (villages?, associations?); in economics, the fabric of the local activity tissue (distribution of stores or professions in a town section? or the growth of new activities through cooperation?). In the natural sciences there may interesting parallels in the self-organization of DNA, in the operation of the so-called "biological circuits" and in evolution at the sub-cellular level.