V.V. Belousov1, O.V. Druzhinina2

1,2 FRС «Computer Science and Control» of RAS (Moscow, Russia)

1vbelousov@frccsc.ru, 2odruzhinina@frccsc.ru

The study of stochastic models of laser systems is an urgent area of research. The relevance is due to the need to develop and improve mathematical models of laser systems in various fields of science and technology. Of particular importance is the development of methods for analyzing the probabilistic structure of interference and elucidating stochastic effects in multilevel lasers. Among the significant problems, the problems of analyzing stochastic models using the normal approximation method should be highlighted. The objectives of the paper include the construction and analysis of a stochastic dynamic model of a three-level laser, stochastification and transition to a system of ordinary differential equations with respect to probabilistic moments, as well as the analysis of the influence of nonparametric white noise and Poisson-type interference on the trajectory dynamics of the laser system model. A stochastic dynamic model of a three-level laser is constructed based on the transition from a deterministic model defined by the generalized Lotka – Volterra system. Based on the extended Ito equation taking into account both Wiener (white noise) and Poisson (discontinuous) perturbations a stochastic model is developed that takes into account the features of laser processes of spontaneous emission, pumping fluctuations and losses in the resonator. The application of the normal approximation method to the study of the constructed stochastic model of the laser system is considered.  Using the developed algorithm for studying multidimensional stochastic systems a system of differential equations with respect to mathematical expectations, variances, and covariance of the phase variables under consideration is obtained as a result of symbolic calculations. Computer modeling has been performed and a comparative analysis of the dynamics of deterministic and stochastic models has been performed for two sets of Poisson noise parameters. Stochastic effects are described and research prospects are considered. The results can be used in the development of algorithmic and software for solving problems of modeling the dynamics of processes in multilevel laser systems, as well as in solving problems of estimating the noise characteristics of laser systems and optimal filtration problems.

Belousov V.V., Druzhinina O.V. Construction and analysis of a stochastic dynamic model of a three-level laser using the method of normal approximation and the algorithm of symbolic calculations. Electromagnetic waves and electronic systems. 2026. V. 31. № 3. P. 75−87. DOI: https://doi.org/10.18127/j15604128-202603-09 (in Russian)

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