ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Melnikov L. A., Konjuhov A. I., Veshneva I. V., Derbov V. L., Serov V. V. Nonlinear dynamics of spatial and temporal patterns in lasers and atom optics: Kerr-lens mode-locked laser, Zeeman laser and Bose-Einstein atomic condensate. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 3, pp. 40-62. DOI: 10.18500/0869-6632-2002-10-3-40-62

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2002-3_melnikov_etal.pdf
(downloads: 0)
Language: 
English
Heading: 
Nonlinear Waves. Solitons
Article type: 
Article
UDC: 
621.373.826
DOI: 
10.18500/0869-6632-2002-10-3-40-62

Nonlinear dynamics of spatial and temporal patterns in lasers and atom optics: Kerr-lens mode-locked laser, Zeeman laser and Bose-Einstein atomic condensate

Autors: 
Melnikov Leonid Arkadevich, Yuri Gagarin State Technical University of Saratov
Konjuhov Andrej Ivanovich, Saratov State University
Veshneva Irina Vladimirovna, Saratov State University
Derbov Vladimir Leonardovich, Saratov State University
Serov Vladislav Victorovich, Saratov State University
Abstract: 

Nonlinear dynamics оf spatial and temporal behaviour of laser and atom optical systems is investigated numerically. Systems with nearly one scalar transverse mode (Kerr-lens mode-locked laser), with large number of vectorial transverse modes (Zeeman laser with large Fresnel number and anisotropic cavity), and non-ground collective states of Bose-Einstein condensate of trapped neutral atoms are considered. Attempts to classify the complex transverse polarization pattern dynamics are made basing on the vectorial Karhunen-Loeve modes and their singularity points character, including catastrophes and Newton diagrams. Excitation оf non-ground states оf atomic Bose-Einstein condensate via resonant perturbation is analyzed.

Key words: 
-
Acknowledgments: 
This work was supported in part by grant REC-006 of the US Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF).
Reference: 
  1. Krausz F, Fermann ME, Brabec T, Curley PF, Hofer M, Ober MH, Spielman C, Winter Е, Schmidt AJ. Femtosecond solid-state lasers. IЕЕЕ J. оf Quantum Electron. 1992;28(10):2097-2122. DOI: 10.1109/3.159520.
  2. Akhmanov SA, Vysloukh VA, Chirkin АS. Optics of Femtosecond Laser Pulses. New York: Springer; 1992. 366 p.
  3. Brabec Т‚ Spielmann С, Krausz Е. Mode locking in solitary lasers. Opt. Lett. 1991;16(24):1961-1963.
  4. Haus HA, Fujimoto JG, Ippen EP. Structures for additive pulse mode locking. J.0pt. Soc.Am. B. 1991;8(10):2069-2076. DOI: 10.1364/JOSAB.8.002068.
  5. Magni V, Cerullo С‚ De Silvesrtri S. Closed form gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers. Opt. Commun. 1993;101(5-6):365-370. DOI: 10.1016/0030-4018(93)90731-J.
  6. Cerullo G, De Silvesrtri S, Magni V. Opt. Letters. 1994;19(14):1040-1042.
  7. Krausz Р, Brabec T, Spielman C. Self-starting passive mode locking. Opt. Lett. 1991;16(4):235-236. DOI: 10.1364/OL.16.000235.
  8. Haus HA, Fujimoto JG, Ippen EP. Analytic theory of additive pulse and Kerr lens mode locking. IEEE J. оf Quantum Electron. 1992;28(10):2086-2096. DOI: 10.1109/3.159519.
  9. Воumа BE, Ramaswamy-Paye M, Fujimoto JG. Compact resonator designs for mode-locked solid-state lasers. Appl. Phys. В. 1997;65(2):213-220. DOI: 10.1007/s003400050266.
  10. Barbosa EA, Vierra ND. Kerr-lens mode locking resonator calculation with two nonlinear elements. Optics Commun. 2001;188(1-4):205-211. DOI: 10.1016/S0030-4018(00)01092-0.
  11. Bohn MJ, Jones RJ, Diels J-C. Mutual Kerr-lens mode-locking. Optics Communications. 1999;170(1-3):85-92. DOI: 10.1016/S0030-4018(99)00441-1.
  12. Cerullo G, De Silvesrtri S, Magni, Pallaro L. Opt. Letters. 1994;19(11):807-809.
  13. Alfrey AJ. Modeling of longitudinally pumped CW Ti:sapphire laser oscillators. IЕЕЕ J. of Quantum Electron. 1989;25(4):760-766. DOI: 10.1109/3.17342.
  14. Hermann J. J.Opt.Soc.Am.B. 1994;11(3):498-512, (1994).
  15. Garduno-Mejia J, Mohebi M, Jamasbi М. Opt. Comm. 1999;171:263-269.
  16. Kalashnikov VL, Sorokin E, Sorokina IT. Spectral characteristics of ultrashort pulses in kerr-lens mode-locked lasers. 2001. e-print arXiv: physics/0101004.
  17. Kalashnikov V, Sorokin E, Sorokina IТ. J. Opt. Soc. Am. В. 2001;18(11):1732-1739.
  18. Kalashnikov VL. Theory of sub-10 fs-generation in Kerr-lens mode-locked solid-state lasers with a coherent semiconductor absorber. Optics Communications. 2001;192(3-6):323-331. DOI: 10.1016/S0030-4018(01)01168-3.
  19. Haus HA, Sorokina I, Sorokin Е. Raman-induced redshift of ultrashort mode-locked laser pulses. J. Opt. Soc. Am. В. 1998;15(1):223-231. DOI: 10.1364/JOSAB.15.000223.
  20. Kutz JN, Collings BC, Bergman K, Knox WH. Stabilized pulse spacing in soliton lasers due to gain depletion and recovery. IEEE Journal of Quant. Electron. 1998;34(9):1749-1757. DOI: 10.1109/3.709592.
  21. Xing Q, Chai L, Zhang М, Wang С. Opt.Comm. 1999;162:71.
  22. Kovalsky MG, Hnilo AA, Gonzlez Inchauspe CMF. Hidden instabilities in the Ti:sapphire Kerr lens mode-locked laser. Opt. Lett. 1999;24(22):1638-1640. DOI: 10.1364/OL.24.001638.
  23. Соte Р, van Dier HM. Period doubling of a femtosecond Ti:sapphire laser by total mode locking. Opt. Lett 1998;23(9):715-717. DOI: 10.1364/OL.23.000715.
  24. Bolton SR, Jenks RA, Elknton CN, Sucha G. J.Opt.Soc.Am. В. 1999;16:339.
  25. Spence DE, Kean PN, Sibbet W. 60-fsec pulse generation from a self-mode-locked Ti:sapphire laser. Opt. Lett. 1991;16(1):42-44. DOI: 10.1364/OL.16.000042.
  26. Kalashnikov VL, Poloyko IG, Mikhailov VP, von der Linde D. Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers. 0pt.Soc.Am В. 1997;14(10):2691-2695. DOI: 10.1364/JOSAB.14.002691.
  27. Wei M-D, Hsieh W-F. Opt. Comm. 1999;168:161-166.
  28. Melnikov LА, Veshneva IМ, Konukhov AI. Transverse pattern dynamics in a short-pulse mode-locked solid state laser. Chaos, Solitons & Fractals 1994;4(8-9):1535-1546. DOI: 10.1016/0960-0779(94)90095-7.
  29. Nakazawa M, Kubota H, Tamura K. Time-domain ABCD matrix formalism for laser mode-locking and optical pulse transmission. IEEE J. Quant. Electron. 1998;34(7):1075-1081. DOI: 10.1109/3.687847.
  30. Bolton SR, Acton MR. Quasiperiodic route to chaos in the Kerr-lens mode-locked Ti:sapphire laser. Phys. Rev. А. 2000;62(6):063803. DOI: 10.1103/PhysRevA.62.063803.
  31. Konstenbauder AG. Ray-pulse matrices: a rational treatment for dispersive optical systems. IEEE J. Quant. Electron. 1990;26(6):1148-1157. DOI: 10.1109/3.108113.
  32. Dijaili S, Dienes А, Smith JS. IEEE J. Quant. Electron. 1990;26:1158.
  33. Sanchez LM, Hnilo AA. Description of Kerr lens mode-locked lasers with Poincaré maps in the complex plane. Opt. Comm. 2001;199(1-4):189-199. DOI: 10.1016/S0030-4018(01)01569-3.
  34. Borisevich NA, Buganov ОМ, Tikhomirov SA, Tolstorozhev GB, Shkred GL. Quantum Electronics. 1999;29(9):780-786.
  35. Brambilla M, Lugiato LA, Penna V, Prati F, Tamm C, Weiss СО. Transverse laser patterns. I. Phase singularity crystals. Phys. Rev. A. 1991;43(9):5090-5113. DOI: 10.1103/PhysRevA.43.5090.
  36. Martin-Regalado J, Prati F, San Miguel M, Abraham NB. Polarization properties of vertical-cavity surface-emitting lasers. IEEE J. of Quantum Electron. 1997;33(5):765-783. DOI: 10.1109/3.572151.
  37. Abraham NB, Arimondo E, San Miguel M. Polarization state selection and stability in a laser with a polarization-isotropic resonator; an example of no lasing despite inversion above threshold. Opt. Comm. 1995;117(3-4):344-356. DOI: 10.1016/0030-4018(95)00151-W.
  38. Serrat C, Abraham NB, San Miguel M, Vilaseca R, Martin-Regalado J. Polarization dynamics in a vertical-cavity laser with an axial magnetic field. Phys. Rev. А. 1996;53(6):R3731-R3733. DOI: 10.1103/PhysRevA.53.R3731.
  39. Freund I. Optics Communications. 1999;159(1-3):99-117.
  40. Freund I. Saddle point wave fields. Optics Communications. 1999;163(4-6):230-242. DOI: 10.1016/S0030-4018(99)00142-X.
  41. Lugiato LA, Орро GL, Pernigo MA, Tredicci JR, Narducci LM, Bandy DK. Optics Communications. 1988;68:63.
  42. Green C, Mindlin GB, D’Angelo EJ, Solari HG, Tredicce JR. Spontaneous symmetry breaking in a laser: The experimental side. Phys.Rev.Lett. 1990;65(25):3124-3127. DOI: 10.1103/PhysRevLett.65.3124.
  43. Stanley WD. // Digital Signal Processing. Reston Publishing Company, Inc.; 1975. 323 p.
  44. Rееd IS, Lan LS. A fast approximate Karhunen-Loève transform (AKLT) for Data Compression. Journal оf Visual Communication and Image Representation. 1994;5(4):304-316. DOI: 10.1006/jvci.1994.1029.
  45. Carevic Р, Caelli Т. Region-based coding of color images using Karhunen–Loeve transform. Graphical Models and Image Processing. 1997;59(1):27-38. DOI: 10.1006/gmip.1996.0402.
  46. Wolf SG, Ginosar R, Zeevi YY. Spatio-chromatic image enhancement based on a model of human visual information processing. Journal оf Visual Communication and Image Representation. 1998;9(1):25-37. DOI: 10.1006/jvci.1998.0371.
  47. Alessandro G, Орро GL. Optics Communications. 1992;88(2-3):130-136.
  48. Konukhov АL, Ryabinina MV, Veshneva V, Melnikov LA. 1999. Proc. SPIE. 3726. P. 237.
  49. Konukhov AL, Ryabinina MV, Veshneva LV, Melnikov LA. Journal оf Optics В: Quantum & Semicl. Optics. 2001;3:S209-S214.
  50. Gilmore R. Catastrophe Theory for Scientists and Engineers. A WileyInterscience Publication John Wiley & Sons; 1981. 666 p.
  51. Melnikov LA, Konukhov AL, Ryabinina MV. Quantum and Semiclassical Optics. 1998;10:167.
  52. Moser JK. Lectures оn Hamiltonian Systems. Мет. Amer. Math. Soc.; 1968. 60 p.
  53. Bruno AD. Local Method of Nonlinear Analysis of Differential Equations. Moscow: Nauka; 1979. 256 p.
  54. Parkins AS, Walls DF. The physics of trapped dilute-gas Bose-Einstein condensates. Phys. Reports. 1998;303(1):1-80. DOI: 10.1016/S0370-1573(98)00014-3.
  55. Dalfovo F, Giorgini S, Pitaevskii LP, Stringari S. Theory оf Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 1999;71(3):463-512. DOI: 10.1103/RevModPhys.71.463.
  56. Courteille PW‚ Bagnato VS, Yukalov VI. Bose-Einstein condensation оf trapped atomic gases. Laser Physics. 2001;11:659-800.
Received: 
19.06.2002
Accepted: 
28.07.2002
Available online: 
11.01.2024
Published: 
30.09.2002
  • 218 reads