Full text of article: Russian language.

 PDF

Abstract:
Results of the numerical calculation of the envelope and frequency profile of a pulse propagating in a dispersive medium, exemplified by the propagation of a femtosecond pulse in the plasma, are presented. The explanation for the appearance of modulation in the odd orders of approximation of the theory of dispersion and for the extinction of modulation in the even orders is given. Taking into account the fourth-order term of the approximate dispersion theory is shown to be sufficient in the majority of cases when calculating the ultrashort pulse propagation.

Keywords:
ultrashort pulse, dispersion theory, pulse envelope, Fourier transforms, chirping.

Citation:
Zakharov NS, Kholod SV. Influence of higher-order terms of the approximate dispersion theory on the pulse envelope profile in a dispersive medium. Computer Optics 2017; 41(5): 636-644. DOI: 10.18287/2412-6179-2017-41-5-636-644.

References:

1. Kozlov SA, Samartsev VV. Fundamentals of femtosecond optics. Cambridge: Woodhead Publishing; 2013. ISBN: 978-1-7824-2128-3.
2. Zakharov NS, Kholod SV. Interaction of ultrashort laser pulses with matter [In Russian]. Sergiev Posad: “12 CSRI MоD RF” Publisher; 2012.
3. Geints YuE, Zemlyanov AA, Kabanov AM, Matvienko GG. Nonlinear Femtosecond Atmospheric Optics [In Russian]. Tomsk: Publishing House of IAO SB RAS; 2010.
4. Ginzburg VL. The propagation of electromagnetic waves in plasmas. Oxford: Pergammon Press; 1964.
5. Vainshtein LA. Propagation of pulses. Soviet Physics Uspekhi 1976; 19(2): 189-205. DOI: 10.1070/PU1976v019n02ABEH005138.
6. Vainshtein LA, Vakman DE. Frequency separation in the theory of oscillations and waves [In Russian]. Moscow: “Nauka” Publisher; 1983.
7. Akhmanov SA, Vysloukh VA, Chirkin AS. Optics of femtosecond lаser pulses [In Russian]. Moscow: “Nauka” Publisher; 1988. ISBN: 5-02-013838-Х.
8. Bespalov VG, Kozlov SA, Shpolyanskiy YuA, Walmsley IA. Simplified field wave equations for the nonlinear propagation of extremely short light pulses. Phys Rev A 2002; 66(1): 013811. DOI: 10.1103/PhysRevA.66.013811.
9. Brabec Th, Krausz F. Nonlinear optical pulse propagation in the single-cycle regime. Phys Rev Lett 1997; 78(17): 3282-3285. DOI: 10.1103/PhysRevLett.78.3282.
10. Brabec Th, Krausz F. Intence few-cycle laser Fields: Frontiers of nonlinear optics. Rev Mod Phys 2000; 72(2): 545-591. DOI: 10.1103/RevModPhys.72.545.
11. Ranka JK, Gaeta AL. Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses. Opt Lett 1998; 23(7): 534-536. DOI: 10.1364/OL.23.000534.
12. Shtumpf SA, Korolev AA, Kozlov SA. Dynamics of the strong field of a few-cycle optical pulse in a dielectric medium. Bulletin of the Russian Academy of Sciences: Physics 2007. 71(2): 147-150. DOI: 10.3103/S1062873807020013.
13. Vinogradova MB, Rudenko OV, Sukhorukov AP. Wave theory [in Russian]. Moscow: “Nauka” Publisher; 1979.
14. Akhmanov SA, Vysloukh VA, Chirkin AS. Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation. Soviet Physics Uspekhi 1986; 29(7): 642-647. DOI: 10.1070/PU1986v029n07ABEH003462.
15. Gromov EM, Talanov VI. The higher-order approximati­ons of the nonlinear dispersion wave theory in both the homogeneous and inhomogeneous media [In Russian]. Bulletin of the Russian Academy of Sciences: Physics 1996; 60(12): 1836-1848.
16. Klovskii DD, Sisakyan IN, Shvartsburg AB, Sherman AYu. Shirikiv SM. Nonlinear evolution of diverse pulse shapes in an optical fibre. Computer Optics 1989; 1(1): 85-88.
17. Alimenkov IV, Pchelkina YuG. Solution of pulse – propagation equation for optical fiber in quadratures [In Russian]. Computer Optics 2013; 37(3): 294-296.
18. Alimenkov IV, Pchelkina YuG. Solution of expanded pulse – propagation equation for optical fiber [In Russian]. Computer Optics 2014; 38(1): 28-30.
19. Mohamadou A, Tiofack CGL, Kofane TC, Ekogo TB, Atangana J, Porsezian K. Higher order dispersion effects in the noninstantaneous nonlinear Schrödinger equation. Journal of Modern Optics 2011; 58(11): 924-931. DOI: 10.1080/09500340.2011.582963.
20. Liu W-J, Tian B, Zhang H-Q, Xu T, Li H. Solitary wave pulses in optical fibers with normal dispersion and higher-order effects. Phys Rev A 2009; 79(6): 063810. DOI: 10.1103/PhysRevA.79.063810.
21. He F-T, Wang X-L, Duan Z-L. The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber. The Scientific World Journal 2013; 2013: 130734. DOI: 10.1155/2013/130734.
22. Marfice JP, Baiocchi OR. Dispersion approximation using higher-order Taylor series terms. Applied Optics 1987; 26(19): 4043-4045. DOI: 10.1364/AO.26.004043.
23. Beech R, Osman F. Effects of higher order dispersion terms in the nonlinear Schrodinger equation. American Journal of Applied Sciences 2005; 2(9): 1356-1369. DOI: 10.3844/ajassp.2005.1356.1369.
24. Kholod SV. The program for calculating the parameters of propagation ultrashort laser pulse in dispersive medium (Fourier 2.0) [In Russian]. Cert RF of Computer Programs N2016661466 of November 20, 2016, Russian Bull of Computer Programs N11, 2016. – Source: áhttp://www1.fips.ru/Archive/EVM/2016/2016.11.20/DOC/RUNW/000/002/016/661/466/document.pdfñ.
25. Zakharov NS, Kholod SV. Diagnostics of plasma by ultrashort laser pulses [In Russian]. Appl Phys 2005; 6: 80-83.
26. Zakharov NS, Kholod SV. Influence of the processes of ionization on frequency modulated wave packets propagation in the rarefied gases [In Russian]. Appl Phys 2009; 4: 81-85.
27. Zheltikov AM. Let there be white light: supercontinuum generation by ultrashort laser pulses. Physics-Uspekhi 2006; 49(6): 605-628. DOI: 10.1070/PU2006v049n06ABEH005975.

---

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: journal@computeroptics.ru ; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20