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Mathematical Problems in Engineering
Volume 2016, Article ID 4152895, 11 pages
Research Article

Numerical Estimation of Spectral Properties of Laser Based on Rate Equations

1Faculty of Electrical Engineering, University of Zilina, Univerzitna 1, 010 26 Zilina, Slovakia
2Centre for Nanoscience and Nanotechnology, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N-Orsay, 91405 Orsay Cedex, France

Received 27 July 2016; Accepted 26 October 2016

Academic Editor: Luciano Mescia

Copyright © 2016 Jan Litvik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Laser spectral properties are essential to evaluate the performance of optical communication systems. In general, the power spectral density of the phase noise has a crucial impact on spectral properties of the unmodulated laser signal. Here the white Gaussian noise and -noise are taken into the consideration. By utilizing the time-dependent realizations of the instantaneous optical power and the phase simultaneously, it is possible to estimate the power spectral density or alternatively the power spectrum of an unmodulated laser signal shifted to the baseband and thus estimate the laser linewidth. In this work, we report on the theoretical approach to analyse unmodulated real-valued high-frequency stationary random passband signal of laser, followed by presenting the numerical model of the distributed feedback laser to emulate the time-dependent optical power and the instantaneous phase, as two important time domain laser attributes. The laser model is based on numerical solving the rate equations using fourth-order Runge-Kutta method. This way, we show the direct estimation of the power spectral density and the laser linewidth, when time-dependent laser characteristics are known.