Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By R. P. Chen and C. H. R. Ooi

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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.

R. P. Chen and C. H. R. Ooi, "Evolution and Collapse of a Lorentz Beam in Kerr Medium," Progress In Electromagnetics Research, Vol. 121, 39-52, 2011.

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.

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

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.

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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

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

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

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.

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

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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