Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states

Physica D: Nonlinear Phenomena

Volumn 176, Issue 3-4, 2003, Pages 181-211

  Berge L ^a   Gouedard C ^a   Schjodt Eriksen J ^b   Ward, H ^a  

^a CEA DIF   (France)

^b TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Filamentation; Kerr media; Polarization

Indexed keywords

DIFFRACTION; LIGHT POLARIZATION; NONLINEAR EQUATIONS; OPTICAL KERR EFFECT;

FILAMENTATION PATTERNS;

NONLINEAR OPTICS;

EID: 0037367198     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00740-6     Document Type: Article

References (55)

1. Kaw P.K., Schmidt G., Wilcox T., Filamentation and trapping of electromagnetic radiation in plasmas. Phys. Fluids. 16:1973;1522-1525.
2. Labaune C., Baton S., Jalinaud T., Baldis H.A., Pesme D., Filamentation in long scale length plasmas: experimental evidence and effects of laser spatial incoherence. Phys. Fluids B. 4:1992;2224-2231.
3. V.I. Bespalov, V.I. Talanov, Filamentary structure of light beams in nonlinear media, Zh. Eksp. Teor. Fiz.-Pis'ma Red. 3 (1966) 471-476 [JETP Lett. 3 (1966) 307-310].
4. Marburger J.H., Dawes E., Dynamical formation of small-scale filaments. Phys. Rev. Lett. 21:1968;556-558.
5. Campillo A.J., Shapiro S.L., Suydam B.R., Periodic breakup of optical beams due to self-focusing. Appl. Phys. Lett. 23:1973;628-630.
6. Braun A., Korn G., Liu X., Du D., Squier J., Mourou G., Self-channeling of high-peak-power femtosecond laser pulses in air. Opt. Lett. 20:1995;73-75.
7. Brewer R.G., Lifsitz J.R., Narrow optical waveguides and instabilities induced in liquids. Phys. Lett. 23:1966;79-81.
8. Brodeur A., Ilkov F.A., Chin S.L., Kosareva O.G., Kandidov V.P., Moving focus in the propagation of ultrashort laser pulses in air. Opt. Lett. 22:1997;304-306.
9. V.V. Korobkin, R.V. Serov, Investigation of self-focusing of neodymium-laser radiation, Zh. Eksp. Teor. Fiz.-Pis'ma Red. 6 (1967) 642-644 [JETP Lett. 6 (1967) 135-137].
10. Lord G.J., Small-scale filaments in liquids and tracks of moving foci. Phys. Rev. Lett. 22:1969;994-997.
11. 6 Opt. Lett. 6:1981;185-187.
12. Mamaev A.V., Saffman M., Anderson D.Z., Zozulya A.A., Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence. Phys. Rev. A. 54:1996;870-879.
13. Schwartz J., Rambo P., Diels J.C., Kolesik M., Wright E.M., Moloney J.V., Ultraviolet filamentation in air. Opt. Commun. 180:2000;383-390.
14. Mlejnek M., Kolesik M., Moloney J.V., Wright E.M., Optically turbulent femtosecond light guide in air. Phys. Rev. Lett. 83:1999;2938-2941.
15. Tzortzakis S., Bergé L., Couairon A., Franco M., Prade B., Mysyrowicz A., Break-up and fusion of self-guided femtosecond light pulses in air. Phys. Rev. Lett. 86:2001;5470-5473.
16. Tikhonenko V., Christou J., Luther-Davies B., Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium. Phys. Rev. Lett. 76:1996;2698-2701.
17. Konno K., Suzuki H., Self-focusing of laser beam in nonlinear media. Phys. Scripta. 20:1979;382-386.
18. Soto-Crespo J.M., Wright E.M., Akhmediev N.N., Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium. Phys. Rev. A. 45:1992;3168-3175.
19. Kuznetsov E.A., Rubenchik A.M., Zakharov V.E., Soliton stability in plasmas and hydrodynamics. Phys. Rep. 142:1986;103-165.
20. N.G. Vakhitov, A.A. Kolokolov, Stationary solutions of the wave equation in a medium with nonlinearity saturation, Izv. Vyssh. Uchebn. Zavect. Radiofiz. 16 (1973) 1020-1028 [Sov. Radiophys. 16 (1975) 783-789].
21. A.A. Kolokolov, Stability of stationary solutions of nonlinear wave equations, Izv. Vyssh. Uchebn. Zavect. Radiofiz. 17 (1974) 1332-1336 [Sov. Radiophys. 17 (1976) 1016-1020].
22. Bergé L., Wave collapse in physics: principles and applications to light and plasma waves. Phys. Rep. 303:1998;259-370. references therein.
23. Juul Rasmussen J., Rypdal K., Blow-up in nonlinear Schrödinger equations. I. A general review. Phys. Scripta. 33:1986;481-497.
24. Vidal F., Johnston T.W., Asymptotic behavior of radially symmetric self-focused beams. Phys. Rev. E. 55:1997;3571-3580.
25. Gatz S., Herrmann J., Propagation of optical beams and the properties of two-dimensional spatial solitons in media with a local saturable nonlinear refractive index. J. Opt. Soc. Am. B. 14:1997;1795-1806.
26. Bergé L., Schmidt M.R., Juul Rasmussen J., Christiansen P.L., Rasmussen K.Ø., Amalgamation of interacting light beamlets in Kerr-type media. J. Opt. Soc. Am. B. 14:1997;2550-2562.
27. Fibich G., Ilan B., Vectorial and random effects in self-focusing and in multiple filamentation. Physica D. 157:2001;112-146 Fibich G., Ilan B., Deterministic vectorial effects lead to multiple filamentation. Opt. Lett. 26:2001;840-842 Fibich G., Ilan B., Multiple filamentation of circularly polarized beams. Phys. Rev. Lett. 89:2002;013901.
28. Fibich G., Ilan B., Vectorial and random effects in self-focusing and in multiple filamentation. Physica D. 157:2001;112-146 Fibich G., Ilan B., Deterministic vectorial effects lead to multiple filamentation. Opt. Lett. 26:2001;840-842 Fibich G., Ilan B., Multiple filamentation of circularly polarized beams. Phys. Rev. Lett. 89:2002;013901.
29. Fibich G., Ilan B., Vectorial and random effects in self-focusing and in multiple filamentation. Physica D. 157:2001;112-146 Fibich G., Ilan B., Deterministic vectorial effects lead to multiple filamentation. Opt. Lett. 26:2001;840-842 Fibich G., Ilan B., Multiple filamentation of circularly polarized beams. Phys. Rev. Lett. 89:2002;013901.
30. Marburger J.H., Self-focusing: theory. Prog. Quant. Electron. 4:1975;35-110.
31. Vidal F., Johnston T.W., Electromagnetic beam breakup: multiple filaments, single beam equilibria, and radiation. Phys. Rev. Lett. 77:1996;1282-1285.
32. Rypdal K., Juul Rasmussen J., Stability of solitary structures in the nonlinear Schrödinger equation. Phys. Scripta. 40:1989;192-201.
33. Akhmediev N.N., Korneev V.I., Nabiev R.F., Modulational instability of the ground state of the nonlinear wave equation: optical machine gun. Opt. Lett. 17:1992;393-395.
34. Atai J., Chen Y., Soto-Crespo J.M., Stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity. Phys. Rev. A. 49:1994;R3170-R3173.
35. Weinstein M.I., Nonlinear Schrödinger equations and sharp interpolation estimates. Commun. Math. Phys. 87:1983;567-576.
36. Fibich G., Gaeta A.L., Critical power for self-focusing in bulk media and in hollow waveguides. Opt. Lett. 25:2000;335-337.
37. Anderson D., Bonnedal M., Variational approach to nonlinear self-focusing of Gaussian laser beams. Phys. Fluids. 22:1979;105-109.
38. V.E. Zakharov, V.V. Sobolev, V.C. Synakh, Behavior of light beams in nonlinear media, Zh. Eksp. Teor. Fiz. 60 (1971) 136-145 [Sov. Phys. JETP 33 (1971) 77-81].
39. Malkin V.M., On the analytical theory for stationary self-focusing of radiation. Physica D. 64:1993;251-266.
40. LeMesurier B.J., Papanicolaou G., Sulem C., Sulem P.L., Focusing and multi-focusing solutions of the nonlinear Schrödinger equation. Physica D. 31:1988;78-102.
41. Borghi R., Santarsiero M., Vilcalvi S., Focal shift of focused flat-topped beams. Opt. Commun. 154:1998;243-248.
42. Santarsiero M., Borghi R., Correspondence between super-Gaussian and flattened Gaussian beams. J. Opt. Soc. Am. A. 16:1999;188-190.
43. G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego, CA, 1989 R.W. Boyd, Nonlinear Optics, Academic Press, Boston, MA, 1992.
44. G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego, CA, 1989 R.W. Boyd, Nonlinear Optics, Academic Press, Boston, MA, 1992.
45. Menyuk C.R., Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quant. Electron. QE-23:1987;174-176.
46. Menuyk C.R., Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes. J. Opt. Soc. Am. B. 5:1988;392-402.
47. Akhmediev N., Soto-Crespo J.M., Dynamics of pulse propagation in birefringent optical fibers. Phys. Rev. E. 49:1994;5742-5754.
48. Schjødt-Eriksen J., Moloney J.V., Wright E.M., Feng Q., Christiansen P.L., Polarization instability of femtosecond pulse splitting in normally dispersive self-focusing media. Opt. Lett. 26:2001;78-80.
49. Maker P.D., Terhune R.W., Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. 137:1965;A801-A819.
50. J. Schjødt-Eriksen, Arresting of collapse in inhomogeneous and ultrafast Kerr media, Ph.D. Dissertation, Danish Technical University, Lyngby, February 2001.
51. Bergé L., Coalescence and instability of copropagating nonlinear waves. Phys. Rev. E. 58:1998;6606-6625.
52. Feit M.D., Fleck J.A., Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams. J. Opt. Soc. Am. B. 5:1988;633-640.
53. McKinstrie C.J., Bingham R., The modulational instability of coupled waves. Phys. Fluids B. 1:1989;230-237.
54. Kandidov V.P., Kosareva O.G., Tamarov M.P., Brodeur A., Chin S.L., Nucleation and random movement of filaments in the propagation of high-power laser radiation in a turbulent atmosphere. Quant. Electron. 29:1999;911-915.
55. Chin S.L., Talebpour A., Yang J., Petit S., Kandidov V.P., Kosareva O.G., Tamarov M.P., Filamentation of femtosecond laser pulses in turbulent air. Appl. Phys. B. 74:2002;64-76.