On some algorithms for comparing models of femtosecond laser radiation propagation in a medium with gold nanorods

Abstract

The study of the features of the nonlinear optical interaction of laser radiation with various media is currently widely studied, including by mathematical modeling methods. In particular, the interaction of the laser pulse with the medium doped with nanorods leads to the melting of these nanorods and distortion of the laser pulse. In addition, the passage of a laser pulse through a medium with nanoparticles can lead to a change in the shape of the pulse and a significant distortion of its spectrum, as a result of which a number of undesirable effects may occur. The corresponding process can be described by the nonlinear Schrödinger equation. Analytical studies of the corresponding variants of the equation and numerical calculations have shown that the propagation of the resulting soliton subimpulses is characterized by the formation of a so-called nonlinear frequency chirp in the region of subimpulses. When considering the graphs of such a process, the following assumption arose: it is possible to measure the degree of nonlinearity by calculating the correlation coefficient between the frequency distribution in a linear and nonlinear medium. In the course of calculations using correlation analysis, we obtained statistical characteristics similar to those that were assumed in advance. At the same time, the most adequate variant of the pair correlation coefficient is obtained in the case of applying the algorithm proposed by us for its calculation.