Complexity in Photonics

This research endeavour will directly address complexity and self-organization of the light in laser sources based on micro-cavities. The comprehension of the emergent behaviours in complex systems is in general seen as one of the next frontier of Science. Emergence is the property of a system composed by the interaction of simple entities of showing functionalities beyond the capabilities of each single element. This behaviour is common to many systems spanning from zoology, biology, social sciences, and its fascination maybe arises from the prospected possibility to tackle the mystery of intelligence. Complexity and collective behaviour are fundamental concepts in physics: for example, they are at the core of phase transitions in condensed matter. In this framework, ordering phenomena and the progressive onset of long-range correlations have been deeply investigated with properly developed sophisticated theoretical approaches, experimental protocols and numerical techniques. Those methodologies represent powerful tools of investigation to address complexity in other fields.
The physics of complex condensates, is characterized by some of the best established tools for the description of collective behaviours. Indeed, phase transitions are a classical example of macroscopic effects resulting from the interaction of a large number of microscopic particles. Phase transitions can be consistently addressed with a reduced number of global parameters, such as temperature, pressure, etc. From the early seventies mathematical approaches borrowed from statistical mechanics have been applied to the quantitative analysis of chaotic dynamical systems. Such approaches allow defining equivalent phase transitions regulated by equivalent overall parameters. More recently, these approaches have been extended to mode-locked lasers, also discriminating thermodynamic from complex transitions.
Two 'phases' of the dynamical system are identified: a "continuous wave" and a "mode-locked" phase, governed by the pumping rate in the laser cavity that is the state variable controlling the phase transition. If the degrees of freedom are increased, the system can show a larger number of phases. An increased number of phases have also been found in random lasers, where also a random mode-locked state can be reached. The transition between continuous wave oscillation, passive mode-locking and random mode-locking in such systems is governed by the degree of randomness of the system, additional state variable to the pumping rate.
The above concept has a profound and interdisciplinary meaning, and in this PhD programme will be applied to the study of optical radiation generated in state-of-the-art optical microcavities, namely optical microcombs. Microcombs, based on micrometre size optical resonators, are presently seen as promising candidates for shrinking the size of optical frequency combs. Optical Frequency Combs (OFCs) are often referred to as optical rulers: their spectrum consists of a precise sequence of discrete, equally spaced lines, which represent precise "marks" in frequency. Their importance was recognized in the 2005 Nobel Award to T. W. Hänsch and J. Hall, because they have enabled the measurement of physical constants with unparalleled precision and became powerful tools in many disciplines, from astronomy to geology, biology and GPS navigation.