On the propagation of vector ultra-short pulses

Journal of Nonlinear Mathematical Physics

Volumn 15, Issue 2, 2008, Pages 162-170

  Pietrzyk, Monika ^a   Kanattsikov I ^b,c   Bandelow, Uwe ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49949118495     PISSN: 14029251     EISSN: None     Source Type: Journal    
DOI: 10.2991/jnmp.2008.15.2.4     Document Type: Article

References (40)

1. G.P. Agrawal, Nonlinear Optics, Academic Press, NY 1989;
2. A. Hasegawa and Y.Kodama, Solitons in Optical Communications, Oxford University Press, Oxford 1995.
3. J.E. Rothenberg, Space-time focusing: breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses, Opt. Lett. 17 (1992) 1340-1342;
4. J.K. Ranka and A.L. Gaeta, Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses, Opt. Lett 23 (1998) 534-536;
5. K.E. Oughstun and H. Xiao, Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive, attenuative medium, Phys. Rev. Lett. 78 (1997) 642-645.
6. T. Brabec and F. Krausz, Intense few-cycle laser fields: Frontiers of nonlinear optics Rev. Mod. Phys. 72 (2000) 545-591;
7. A. Baltuska, Th. Udem, M. Uiberacher e.a., Attosecond control of electronic processes by intense light fields, Nature 421 (2003) 611-615.
8. I.V. Mel'nikov, H. Leblond, F. Sanchez and D. Mihaleche, Nonlinear optics of a few-cycle optical pulse: slow envelope approximation revisited, IEEE J. Select. Topics Quant. Electr. 10 (2004) 870-875;
9. A.I. Maimistov, Some models of propagation of extremely short electromagnetic pulses in nonlinear medium, Quant. Electr. 30 (2000) 287-304 (In Russian);
10. P. Kinsler and G.H.C. New, Few-cycle pulse propagation, Phys. Rev. E 67 (2003) 02383;
11. M. Porras, Phys. Rev. E 65 (2002) 026606;
12. E. V. Kazantseva, A. Maimistov and J.-G. Caputo, Reduced Maxwell-Duffing description of extremely short pulses in nonresonant media, Phys. Rev. E 71 (2005) 056622;
13. H. Leblond and F Sanchez, Models for optical solitons in the two-cycle regime, Phys. Rev. A 67 (2003) 013804
14. T. Brabec and F. Krausz, Nonlinear optical pulse propagation in the single-cycle regime, Phys. Rev. Lett. 78 (1997) 3282-3285.
15. A. Demircan, U. Bandelow, Supercontinuum generation by the modulation instability, Opt. Comm. 244 (2005) 181-185
16. T. Schäfer and C.E. Wayne, Propagation of ultra-short optical pulses in cubic nonlinear media, Physica D 196 (2004) 90-105.
17. Y. Chung, C.K.R.T. Jones, T. Schäfer and C.E. Wayne, Ultra-short pulses in linear and nonlinear media, Nonlinearity 18 (2005) 1351-74, nlin.SI/0408020.
18. Y. Chung and T. Schäfer, Nonlocal stabilization of ultra-short pulses in cubic nonlinear media, nlin.SI/0512029
19. A. Sakovich and S. Sakovich, The short pulse equation is integrable, J. Phys. Soc. Japan 74 (2005) 239-241, nlin.SI/0409034.
20. J.C. Brunelli, The short pulse hierarchy, J. Math. Phys. 46 (2005) 123507, nlin.SI/0601015;
21. J.C Brunelli, The bi-Hamiltonian structure of the short pulse equation, Phys. Lett. A 353 (2006) 475-478, nlin.SI/0601014.
22. A. Sakovich and S. Sakovich, Solitary wave solutions of the short pulse equation, J. Phys. A 39 (2006) L361-L367, nlin.SI/0601019.
23. R.E. Slusher and B.J. Eggleton, Nonlinear Photonic Crystals, Springer-Verlag, Berlin 2003.
24. D.N. Payne, A. J. Barlow and J.J. Ramskov Hansen, Development of low- and high-birefringent optical fibers, IEEE J. Quant. Electr. 18 (1982) 477-488.
25. M. H. Jakubowski, Computing with Solitons in Bulk Media, PhD Thesis, Princeton 1999.
26. CR. Menyuk, Nonlinear pulse propagation in biréfringent optical fibers, IEEE J. Quant. Electr. 23 (1987) 174-176;
27. CR. Menyuk, Pulse propagation in an elliptically birefringent Kerr medium, IEEE J. Quant. Electr. 25 (1989) 2674-2682.
28. D.N. Christodoulides and R.I. Joseph, Vector solitons in birefringent nonlinear dispersive media, Opt. Lett. 13 (1988) 53-55.
29. M.J. Ablowitz, B. Prinari and A.D. Trubach, Integrable nonlinear Schrödinger systems and their soliton dynamics, Dynamics of PDE 1 (2004) 239-301.
30. Y.S. Kivshar and G.P. Agrawal, Optical Solitons, Academic Press 2003.
31. D.C. Hutchings, J.M.Arnold and D.F. Parker, Stationary mixed-polarization spatial solitons and their stability in semiconductor waveguides, Phys. Rev. E 58 (1998) 6649-6658;
32. S.B. Leble, Nonlinear waves in optical waveguides and soliton theory applications, in: Optical solitons. Theoretical and experimental challenges, K. Porsezian, V. C Kuriakose (Eds.), Springer-Verlag, Berlin Heidelberg, 2003;
33. M.E. Pietrzyk, On the properties of two pulses propagating simultaneously in different dispersion regimes in a nonlinear planar waveguide, J. Opt. A 1 (1999) 685-696;
34. M. Lakshmanan, T. Kanna and R. Radhakrishnan, Shape-changing collisions of coupled bright solitons in birefringent optical fibers, Rep. Math. Phys. 46 (2000) 143-156;
35. (2) crystals: a (3 + 1)-dimensional model and its reduction to the NLS equation, J.Phys. A 31 (1998) 3041-3066.
36. M.H. Holmes, Introduction to Perturbation Methods, Springer-Verlag, NY 1995.
37. P.D. Maker and R.W. Terhune, Study of optical effects due to an induced polarization third order in the electric field strength, Phys. Rev. 137, (1965) A801-A818.
38. S.V. Popov, Yu. P. Svipko and N.I. Zheludev, Susceptibility Tensors for Nonlinear Optics, IOP Publishing, Bristol 1995.
39. M. Yamashita and K. Torizuka, Numerical study of femtosecond pulse compression by induced phase modulation with group-velocity dispersion effects, Jap. J. Appl. Phys. 29 (1990) 294-298.
40. Pietrzyk M and Kanattšikov I, Multisymplectic analysis of the Short Pulse Equation and numerical applications, to appear in the Proc. 10th Int. Conf. on Differential Geometry and Its Applications, Olomouc, Czech Republic, 2007.