Related papers: Measuring maximal eigenvalue distribution of Wisha…
The upper power limit of linear response of light trap detectors was recently measured [2,3]. We have completed this measurement with test of traps with bias voltage at several visible wavelengths using silicon photodiodes Hamamatsu S1337…
The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the $\beta$-Tracy-Widom distribution, which is the limiting distribution of the largest…
We report on the realization of an all-fiber laser source that delivers single-frequency pulses at 1645 nm, on a linearly polarized single-mode beam, based on stimulated Raman scattering in passive fibers. The pulse energy reaches 14…
Random fiber laser (RFL) based on random distributed feedback and Raman gain has earned much attention in recent years. In this presentation, we demonstrate a powerful linearly polarized RFL with spectral adjustment, in which the central…
Configurations for efficient free space coherent addition of four separate fiber lasers arranged in two dimensional array are presented. They include compact and robust interferometric combiners that can be inserted either inside or outside…
We discuss an application of the random matrix theory in the context of estimating the bipartite entanglement of a quantum system. We discuss how the Wishart ensemble (the earliest studied random matrix ensemble) appears in this quantum…
Broadband wavelength tuneability can ensure a new level of versatility for laser systems and extend areas of their applications. Principle limitations of achieving wide tuning wavelength ranges are generally defined by the spectral…
Coherent beam combination is one promising way to overcome the power limit of one single laser. In this paper, we use a Multi-Plane Light Converter to combine 12 fibers at 1.03 micron with a phase locking setup. The overall loss measurement…
We propose an energy transfer model with a cubic atomic population dependence to accurately model the behavior of various reported high-power erbium-doped fluoride fiber lasers operating near 2.8 microns. We first show that the previously…
The Tracy-Widom beta distribution is the large dimensional limit of the top eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator representation to show that as a tends to infinity the tail of the Tracy Widom…
Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each…
In this paper, we consider N-dimensional real Wishart matrices Y in the class $W_{\mathbb{R}}(\Sigma,M)$ in which all but one eigenvalues of $\Sigma$ is 1. Let the non-trivial eigenvalue of $\Sigma$ be $1+\tau$, then as N,…
Consider the random matrix obtained from the adjacency matrix of a random d-regular graph by multiplying every entry by a random sign. The largest eigenvalue converges, after proper scaling, to the Tracy--Widom distribution.
We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices $A = XX^*$, where $X$ is an $N \times n$ matrix with iid standard complex normal entries. Under the scaling $n = N + \lfloor \sqrt{ 4 c N}…
In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian…
Recently it has been shown that it is possible for a laser to produce a stationary beam with a coherence (quantified as the mean photon number at spectral peak) which scales as the fourth power of the mean number of excitations stored…
We propose a new approach based on random matrix theory to calculate the temporal second-order intensity correlation function $g^{(2)}(t)$ of the radiation emitted by random lasers and random fiber lasers. The multimode character of these…
Representing an ensemble of random lasers with an ensemble of random matrices, we compute average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to environment are considered.…
We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix $H$ converge to the Tracy-Widom laws at a rate nearly $O(N^{-1/3})$, as the matrix dimension $N$ tends to infinity. We allow the variances of the…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…