Statistical dependence analysis of Erbium doped fiber ring lasers (EDFRL) chaos

Abstract

Utilizing ergodic nature of chaotic lasers, the probability density function (PDF) estimation is carried out for peak amplitudes of pulsed chaos in Erbium Doped Fiber Ring Laser (EDFRL) in relation to varying the four key cavity parameters i.e. cavity gain, pump power, modulation index and modulation frequency. Kernel based non-parametric probability distributions are found more suitable to fit the chaos peaks data instead of parametric Gaussian, Rayleigh or Poisson Probability Density Functions. The resulting non-parametric PDFs’ shape, modes, skew and variance is found controllable by changing cavity parameters which is beneficial for random number generation with desired properties. The non-parametric distribution changed its shape between uni-modal and bimodal Gaussian like PDFs alternately and the variance also changes. The PDF shape corresponds to density of points in chaotic data bifurcation plots. This statistical in depth analysis is important while employing the EDFRL for random number generation and in chaotic secure communication applications. EDFRL chaos is found here to be a non-Poisson doubly stochastic point process implying it does depend on history of the chaos generation process, which is hidden in the slowly varying population inversion density of the laser. The bimodality skew keeps altering between left and right while becoming uni-modal every time between switching with modulation index and pump power changes. At high gain the variance of PDF decreases and it approaches uni-modal Gaussian. At high modulation frequency the PDF is left skewed with higher number of shorter pulses bursting.