Applied Physics B

, 93:891

Analytical vectorial structure of a Lorentz–Gauss beam in the far field



A description of a Lorentz–Gauss beam is made directly starting with the Maxwell equations. Based on the vector angular spectrum representation of the Maxwell equations and the method of stationary phase, the analytical TE and TM terms of a Lorentz–Gauss beam have been presented in the far field. The TE and TM terms are orthogonal to each other in the far field. The energy flux distributions of a Lorentz–Gauss beam and its TE and TM terms are depicted in the far field reference plane. The influences of the different parameters on the energy flux distributions of a Lorentz–Gauss beam and its TE and TM terms are discussed. Moreover, the vectorial structure of a Lorentz–Gauss beam is also compared with that of a Gaussian beam. This research is useful to the descriptions and applications of highly divergent laser beams.


41.85.Ew 42.25Bs 


  1. 1.
    O.E. Gawhary, S. Severini, J. Opt. A Pure Appl. Opt 8, 409–414 (2006) CrossRefADSGoogle Scholar
  2. 2.
    A. Naqwi, F. Durst, Appl. Opt. 29, 1780–1785 (1990) ADSCrossRefGoogle Scholar
  3. 3.
    W.P. Dumke, J. Quantum Electron. QE-11, 400–402 (1975) CrossRefADSGoogle Scholar
  4. 4.
    R. Martínez-Herrero, P.M. Mejías, S. Bosch, A. Carnicer, J. Opt. Soc. Am. A 18, 1678–1680 (2001) CrossRefADSGoogle Scholar
  5. 5.
    P.M. Mejías, R. Martínez-Herrero, G. Piquero, J.M. Movilla, Prog. Quantum Electron. 26, 65–130 (2002) CrossRefADSGoogle Scholar
  6. 6.
    H. Guo, J. Chen, S. Zhuang, Opt. Express 14, 2095–2100 (2006) CrossRefADSGoogle Scholar
  7. 7.
    G. Zhou, Opt. Lett. 31, 2616–2618 (2006) CrossRefADSGoogle Scholar
  8. 8.
    G. Zhou, Opt. Express 16, 3504–3514 (2008) CrossRefADSGoogle Scholar
  9. 9.
    C.G. Chen, P.T. Konkola, J. Ferrera, R.K. Heilmann, M.L. Schattenburg, J. Opt. Soc. Am. A 19, 404–412 (2002) CrossRefADSGoogle Scholar
  10. 10.
    G. Zhou, X. Chu, L. Zhao, Opt. Laser Technol. 37, 470–474 (2005) CrossRefADSGoogle Scholar
  11. 11.
    G. Zhou, Opt. Commun. 265, 39–46 (2006) CrossRefADSGoogle Scholar
  12. 12.
    J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968) Google Scholar
  13. 13.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972) MATHGoogle Scholar
  14. 14.
    W.H. Carter, J. Opt. Soc. Am. 62, 1195–1201 (1972) CrossRefADSGoogle Scholar
  15. 15.
    L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995) Google Scholar
  16. 16.
    M. Born, E. Wolf, Principles of Optics, 4th edn. (Pergamon, Elmsford, 1970) Google Scholar
  17. 17.
    O.E. Gawhary, S. Severini, Opt. Lett. 33, 1360–1362 (2008) CrossRefADSGoogle Scholar
  18. 18.
    P. Paakkonen, J. Tervo, P. Vahimaa, J. Turunen, F. Gori, Opt. Express 10, 949–959 (2002) ADSGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of SciencesZhejiang Forestry UniversityLin’anChina

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