İyonlaştırıcı kısa lazer atımlarının doğrusal olmayan ortamda yayılımı

Using a pseudo-spectral method that is split step Fourier method, obtaining a solution for propagation of ionizing short Gaussian pulse would be computationally inexpensive and practical. For a solution obtained by using split step Fourier method, the most important parameter to choose is step size. However, using either large or small step size may yield different numerical errors in the final result. For a large step size, general evolution of the Gaussian pulse could be predicted well but small changes might be neglected. for a small step size, small changes could be indicated well but there would be a prone to error in general pulse evolution. Furthermore, using a generic method of undetermined coefficients that could be utilized for every differential equation would yield a high accuracy solution in order to check the validity of split-step Fourier method. The aim of this study is to examine the evolution of the ionizing short Gaussian pulse lasers in a non-linear medium in both low intensity propagation regime and high intensity propagation regime via various methods to solve the propagation equation i.e split-step Fourier method and method of undetermined coefficients. Similarity of two solutions arising from split-step Fourier method and method of undetermined coef ficients would evolve in a similar trend. Comparison of solutions for both gathered from split-step Fourier method and method of undetermined coefficients with the previous solutions from the literature in the low intensity propagation regime are behave similar except some pulse parameters. Difference between in the parameters of the Gaussian pulse in low intensity propagation regime and high intensity propagation regime has been shown. Results would be given in terms of the pulse parameters i.e spot size, pulse length, intensity, power, electron number density, field amplitude and energy. These results would be used for whether split-step Fourier method and method of undetermined coefficients match the expectancy. Evolution that could be derived by these two different methods fulfill the expectancy, that is expected power loss, expected energy loss and shorter focus length.