Statistical analysis of intensity fluctuations in the second harmonic of a multimode Nd:YAG laser through a modified Pearson correlation coefficient

Abstract

We apply a recently proposed modified Pearson correlation coefficient to investigate the statistical properties of intensity fluctuations in the second harmonic as well as fundamental mode of a multimode $Q$-switched Nd:yttrium aluminum garnet laser. Above threshold the system displays a photonic ferromagneticlike spontaneous mode-locking phase with replica symmetry breaking (RSB). Differently from the photonic glassy phase in random lasers in which modes do not oscillate synchronously, in the present case a relevant fraction of modes oscillate coherently, but the synchronous oscillation of some modes is frustrated with the RSB arising from the fact that a given subset of modes is randomly activated at each excitation pulse with dominating coherent oscillation, frustrating the emergence of other modes. From a single set of measurements, the modified Pearson coefficient allows to identify that the onset of the RSB phenomenon between distinct spectra as the lasing threshold is crossed coincides with the emergence of correlations between different wavelengths in the same spectrum. As different subsets of longitudinal modes are nondeterministically activated after each shot, the RSB property indicates that distinct spectra can be either correlated or anticorrelated around both the fundamental mode and the second harmonic.