Theoretical and experimental study of the lévy statistics and photonic spin glass phase in random lasers

Abstract

Since Albert Einstein established the foundations for stimulated emission of radiation in 1916, he paved a long road that culminated in the beginning of the 1960s with the invention of the laser. In a conventional laser avoiding losses by light scattering is very important. However, this paradigm is broken by the theoretical proposal of Letokhov in 1968, which says that in a disordered with gain, the scattering of light plays a positive role increasing the dwell time of light in an active medium, thereby increasing the laser amplification. Due to the disordered nature of the materials used was adopted the name Random Lasers (RLs). Random lasers have taken a new boom because they have recently been exploited as a photonic platform for studies of complex systems. This thesis covers this interdisciplinary approach that opens important new avenues for understanding the behavior of random lasers. We recently studied the intensity fluctuations in the emission of Random lasers, finding the existence of non-Gaussian statistics in these emissions behaving with Lévy-type statistics. On the other hand, in another set of theoretical and experimental work, the glassy behavior of random lasers was studied by other authors, which led to the recent experimental demonstration of symmetry replica breaking phase transition. The investigations mentioned above were taken separately, and in this work shows that these two phenomena are connected. In the first chapter we study the most important concepts of a conventional laser that are necessary to understand the random lasers. In the second chapter, we present the random lasers. We begin with the presentation of the main features of random lasers. Then, we present a connection between the phenomenon of speckle and random lasers where Speckle Contrast is used to demonstrate the multimodal nature of random lasers. This feature is applied to determine the number of modes in a random fiber laser. At the end of this chapter a work is presented where it is demonstrated for the first time Bichromatic random laser in a NdAl₃ (BO₃)₄ crystalline powder. This observation opens an avenue for random lasers applications, and, as a proof of concept, we demonstrate an optical thermometer owing to the thermal dependence of the RL emissions. The third chapter is dedicated to studying the fundamental concepts of complex systems, to understand the glassy behavior of light in random lasers. In chapter 4 essential rudiments are also given to understand Lévy statistics. In chapter 5 we show a work where we use employ the NdY BO random laser system to show that from a single set of measurement the physical origin of the complex correspondence between the Lévy fluctuation regime and the replica symmetry breaking transition to spin glass phase occurs. In chapter 6 shows the observation of replica symmetry breaking phase transition in a solution of Rhodamine and particles of TᵢO₂, where specially designed amorphous TᵢO₂ particles were synthesized to obtain identical copies of the system.