Computer Simulation of Transition Regimes of Solitons in Stimulated Raman Scattering with Excitation of Polar Optical Phonons

DOI: 10.4236/ajcm.2015.53031   PDF   HTML     3,969 Downloads   4,344 Views   Citations


The system of nonlinear equations modeling the process of nonstationary stimulated Raman scattering (SRS) in noncentrosymmetric crystals for the waves on laser, Stokes, polariton, and phonon frequencies is investigated by using the numerical methods. The general case for amplitudes of waves that resulted in doubling of the number of equations is considered. It is shown that the application of the methods of finite differences to the computer simulation of transition regimes is completely consistent with the analytical results found for the asymptotical solutions in form of solitons. The obtained results also indicate that the laser pulses of Gaussian shape appearing at the boundary of nonlinear medium tend to become solitons of Lorentzian shape. It was also found that the formation of solitons occurs when the vibrations of optical phonons and that of electromagnetic wave were either in or out of phase. It is shown that all electromagnetic waves entering the medium with different speeds become solitons having the same speed. In the second part of the paper we considered the computer simulation of soliton stability with respect to small (weak) perturbations of all interacting waves. In the present paper we considered the case of evolution of those disturbances in the vicinity of peaks of solitons. The numerical analysis showed that in wide range of parameters the solitons were stable.

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Feshchenko, G. and Feshchenko, V. (2015) Computer Simulation of Transition Regimes of Solitons in Stimulated Raman Scattering with Excitation of Polar Optical Phonons. American Journal of Computational Mathematics, 5, 336-344. doi: 10.4236/ajcm.2015.53031.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Rolle, J., Berge, L., Duchateau, G. and Skupin, S. (2014) Filamentation of Ultrashort Laser Pulses in Silica Glass and KDP Crystal: A Comparative Study. Physical Review A, 90, 1-8.
[2] Chen, Z., Segev, M. and Christodoulides, D.N. (2012) Optical Spatial Solitons: Historical Overview and Recent Advances. Reports on Progress in Physics, 75, 1-20.
[3] Prokopovich, I.P. and Khrushchinskii, A.A. (1997) Highly Efficient Generation of Attosecond Pulses in Coherent Stimulated Raman Self-Scattering of Intense Femtosecond Laser Pulses. Laser Physics, 7, 305-308.
[4] Prokopovich, I.P. and Peatross, J. (1999) Direct Shaping and Amplifying of High-Intense Single Attosecond Pulses from High-Intense Femtosecond Optical Pulses in Inert Gases. Laser Physics, 9, 588-591.
[5] Kaplan, A.E. and Shkolnikov, P.L. (1996) Subfemtosecond Pulses in the Multicascade Stimulated Raman Scattering. Journal of the Optical Society of America B, 13, 347-354.
[6] Makhviladze, T.M. and Sarychev, M.E. (1976) Soliton Regimes of Stimulated Raman Scattering. Soviet Physics— JETP, 44, 471-477.
[7] Makhviladze, T.M., Sarychev, M.E. and Shelepin L.A. (1975) Raman Scattering of Light by an Excited Medium. Soviet Physics—JETP, 42, 255-261.
[8] Kivshar, Y. and Agrawal, G. (2003) Optical Solitons: From Fibers to Photonic Crystals. Academic Press, Waltham.
[9] Ames, W. (1992) Numerical Methods for Partial Differential Equations. 3rd Edition, Academic Press, Waltham.
[10] Farlow, S. (1993) Partial Differential Equations for Scientists and Engineers. Dover Books, Mineola.
[11] Kreyszig, E. (1993) Advanced Engineering Mathematics. 7th Edition, John Wiley & Sons Ltd., Hoboken.
[12] Marchevskii, F.N., Strizhevskii, V.L. and Feshchenko, V.P. (1984) Soliton Generation by Stimulated Raman Scattering with Excitation of Polar Optical Phonons. Quantum Electronics, 11, 277-282.
[13] Boyd, R. (2008) Nonlinear Optics. 3rd Edition, Academic Press, Waltham.

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