volume | PIER Journals

Abstract

The effect of Kerr nonlinearity on a Lorentz beam is investigated by using the nonlinear Schrődinger (NLS) equation. Based on the variational method, the evolution of a Lorentz beam in a Kerr medium is demonstrated and the critical collapse powers of the Lorentz beam are derived. Numerical simulations of the propagation of a Lorentz beam in a Kerr medium show that the beam becomes quasi-circular in a very short distance. Although the beam width of the Lorentz beam broadens, the central part of the beam give rise to a partial collapse.

1. Gawhary, O. E. and S. Severini, "Lorentz beams and symmetry properties in paraxial optics," J. Opt. A, Pure Appl. Opt., Vol. 8, 409-414, 2006. Google Scholar

2. Naqwi, A. and F. Durst, "Focusing of diode laser beams: A simple mathematical model," Appl. Opt., Vol. 29, 1780-1785, 1990. Google Scholar

3. Dumke, W. P., "The angular beam divergence in double-heterojunction lasers with very thin active regions," J. Quantum Electron., Vol. 11, 400-402, 1975. Google Scholar

4. Zhou, G., "Nonparaxial propagation of a Lorentz-Gauss beam," J. Opt. Soc. Am. A, Vol. 25, 2594-2599, 2008. Google Scholar

5. Zhou, G., "Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system," Opt. Express, Vol. 18, 4637-4643, 2010. Google Scholar

6. Jiang, Y., K. Huang, and X. Lu, "Radiation force of highly focused Lorentz-Gauss beams on a Rayleigh particle," Opt. Express, Vol. 19, 9708-9713, 2011. Google Scholar

7. Biswas, A., "Temporal-soliton solution of the complex Ginzburg-Landau equation with power law nonlinearity," Progress In Electromagnetics Research, Vol. 96, 1-7, 2009. Google Scholar

8. Mitatha, S., "Dark soliton behaviors within the nonlinear micro and nanoring resonators and applications," Progress In Electromagnetics Research, Vol. 99, 383-404, 2009. Google Scholar

9. Gharakhili, F. G., M. Shahabadi, and M. Hakkak, "Bright and dark soliton generation in a left-handed nonlinear transmission line with series nonlinear capacitors," Progress In Electromagnetics Research, Vol. 96, 237-249, 2009. Google Scholar

10. Khalique, C. M. and A. Biswas, "Optical solitons with parabolic and dual-power nonlinearity via lie symmetry analysis," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 7, 963-973, 2009. Google Scholar

11. Gross, B. and J. T. Manassah, "Numerical solution for the propagation of elliptic Gaussian beam in a Kerr medium," Phys. Lett. A, Vol. 169, 371-378, 1992. Google Scholar

12. Barthelemy, A., C. Froehly, S. Maneuf, and E Reynaud, "Experimental observation of beams' self-deflection appearing with two-dimensional spatial soliton propagation in bulk Kerr material," Opt. Lett., Vol. 17, 844-846, 1992. Google Scholar

13. Crosignani, B. and P. D. Porto, "Nonlinear propagation in Kerr media of beams with unequal transverse widths," Opt. Lett., Vol. 18, 1394-1396, 1993. Google Scholar

14. Biswas, A., R. Kohl, M. E. Edwards, and E. Zerrad, "Soliton parameter dynamics in a non-Kerr law media," Progress In Electromagnetics Research C, Vol. 1, 1-35, 2008. Google Scholar

15. Xu, J., W.-X. Wang, L.-N. Yue, Y.-B. Gong, and Y.-Y. Wei, "Electromagnetic wave propagation in an elliptical chiroferrite waveguide," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14-15, 2010-2030, 2009. Google Scholar

16. Topa, A. L., C. R. Paiva, and A. M. Barbosa, "Electromagnetic wave propagation in chiral H-guides," Progress In Electromagnetics Research, Vol. 103, 285-303, 2010. Google Scholar

17. Choudhury, P. K. and W. K. Soon, "TE mode propagation through tapered core liquid crystal optical fibers," Progress In Electromagnetics Research, Vol. 104, 449-463, 2010. Google Scholar

18. Wei, H.-Y., Z.-S. Wu, and Q. Ma, "Log-amplitude variance of laser beam propagation on the slant path through the turbulent atmosphere," Progress In Electromagnetics Research, Vol. 108, 277-291, 2010. Google Scholar

19. Costa-Quintana, J. and F. Lopez-Aguilar, "Propagation of electromagnetic waves in material media with magnetic monopoles," Progress In Electromagnetics Research, Vol. 110, 267-295, 2010. Google Scholar

20. Apostol, M. and G. Vaman, "Plasmons and diffraction of an electromagnetic plane wave by a metallic sphere," Progress In Electromagnetics Research, Vol. 98, 97-118, 2009. Google Scholar

21. Cao, P., X. Zhang, L. Cheng, and Q. Meng, "Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination," Progress In Electromagnetics Research, Vol. 98, 283-298, 2009. Google Scholar

22. Aberg, I., "High-frequency switching and Kerr effect-nonliear problems solved with nonstationary time domain techniques," Progress In Electromagnetics Research, Vol. 17, 185-235, 1997. Google Scholar

23. Zamani, A. K. and M. Shahabadi, "Multiple-scale analysis of plane wave refraction at a dielectric slab with Kerr-type nonlinearity ," Progress In Electromagnetics Research, Vol. 56, 81-92, 2006. Google Scholar

24. Konar, S. and A. Biswas, "Intra-channel collision of Kerr law optical solitons," Progress In Electromagnetics Research, Vol. 53, 55-67, 2005. Google Scholar

25. Benson, T. M. and P. C. Kendall, "Variational techniques including effective and weighted index methods," Progress In Electromagnetics Research, Vol. 10, 1-40, 1995. Google Scholar

26. Green, P. D., D. Milovic, D. A. Lott, and A. Biswas, "Optical solitons with higher order dispersion by semi-inverse variational principle," Progress In Electromagnetics Research, Vol. 102, 337-350, 2010. Google Scholar

27. Anderson, D. and M. Bonnedal, "Variational approach to nonlinear self-focusing of Gaussian laser beams," Phys. Fluids, Vol. 22, 105-109, 1979. Google Scholar

28. Anderson, D., "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A, Vol. 27, 3135-3145, 1983. Google Scholar

29. Malomed, B., "Variational methods in nonlinear fiber optics and related fields," Prog. Opt., Vol. 43, 70-191, 2002. Google Scholar

30. Pérez-Garcia, V. M., P. Torres, and G. D. Montesinos, "The method of moments for nonlinear Schrödinger equations: Theory and applications," SIAM J. Appl. Math., Vol. 67, 990-1015, 2007. Google Scholar

31. Pérez-Garcia, V. M., "Self-similar solutions and collective coordinate methods for nonlinear SchrÄodinger equations," Phys. D, Vol. 191, 211-218, 2004. Google Scholar

32. Vlasov, S. N., V. A. Petrishchev, and V. I. Talanov, "Averaged description of wave beams in linear and nonlinear media (the method of moments)," Radio. Quan. Electron., Vol. 14, 1062-1070, 1971. Google Scholar

33. Fibich, G. and G. Papanicolau, "Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension," SIAM J. Appl. Math., Vol. 60, 183-240, 1999. Google Scholar

34. Vlasov, S. N., S. N. Gurbatov, and L. V. Piskunov, "Self-focusing of wave beams having an elliptical cross section," Radiofizika, Vol. 17, 1805-1811, 1974. Google Scholar

35. Johannisson, P., D. Anderson, M. Lisak, and M. Marklund, "Nonlinear Bessel beams," Opt. Commun., Vol. 222, 107-115, 2003. Google Scholar

36. Chen, R. P., C. F. Yin, X. X. Chu, and H. Wang, "Effect of kerr nonlinearity on an Airy beam," Phys. Rev. A, Vol. 82, 043832, 2010. Google Scholar

37. Chen, R. P., Y. Z. Ni, and X. X. Chu, "Propagation of a cos-Gaussian beam in a kerr medium," Opt. Laser Tech., Vol. 43, 483-487, 2011. Google Scholar

38. Grow, T. D., A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, "Collapse dynamics of super-Gaussian beams," Opt. Express, Vol. 14, 5468-5475, 2006. Google Scholar

39. Moll, K. D., A. L. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes profile," Phys. Rew. Lett., Vol. 90, 203902, 2003. Google Scholar

40. Feit, M. D. and J. A. Fleck, "Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams," J. Opt. Soc. Am. B, Vol. 5, 633-640, 1988. Google Scholar

41. Fibich, G. and B. Ilan, "Self-focusing of elliptic beams: An example of the failure of the aberrationless approximation," J. Opt. Soc. Am. B, Vol. 17, 1749-1758, 2000. Google Scholar

42. Fibich, G. and A. L. Gaeta, "Critical power for self-focusing in bulk media and in hollow waveguides," Opt. Lett., Vol. 25, 335-337, 2000. Google Scholar

Professor Rui Pin Chen

Professor Chong Heng Raymond Ooi