OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1572–1582

Incoherent superposition of off-axis polychromatic Hermite-Gaussian modes

Luis Martí-López, Omel Mendoza-Yero, and Joris J. J. Dirckx  »View Author Affiliations

JOSA A, Vol. 19, Issue 8, pp. 1572-1582 (2002)

View Full Text Article

Acrobat PDF (208 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We study a statistical ensemble of multimode laser beams. Each beam is made up of an incoherent superposition of off-axis polychromatic Hermite–Gaussian modes. We obtain analytic expressions for the squared beam radius, the waist position, the Rayleigh range, the skewness parameter, the kurtosis parameter, and the squared beam-propagation factor. We demonstrate that the squared beam radius has a quadratic dependence on the distance from the waist plane. The skewness parameter may be different from zero in the near-field zone, but it tends to zero in the far-field zone. The kurtosis parameter in the far-field zone coincides with the kurtosis parameter of the incoherent superposition of on-axis modes.

© 2002 Optical Society of America

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(140.3300) Lasers and laser optics : Laser beam shaping
(350.5500) Other areas of optics : Propagation

Luis Martí-López, Omel Mendoza-Yero, and Joris J. J. Dirckx, "Incoherent superposition of off-axis polychromatic Hermite-Gaussian modes," J. Opt. Soc. Am. A 19, 1572-1582 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1560 (1966).
  2. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  3. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
  4. C. Martínez, J. Serna, F. Encinas-Sanz, R. Martínez-Herrero, and P. M. Mejías, “Time-resolved spatial structure of TEA CO2 laser pulses,” Opt. Quantum Electron. 32, 17–30 (2000).
  5. S. Wang, Q. Lin, and X. Jiang, “Axial superposition of Gaussian spherical beams,” Opt. Laser Technol. 31, 151–155 (1999).
  6. Z. Y. Wang, T. Chen, P. He, and T. C. Zuo, “Calculation of mode contents of high-power CO2 laser beam according to the changes of transverse intensity distribution,” Opt. Commun. 175, 215–220 (2000).
  7. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
  8. F. Encinas-Sanz, J. M. Guerra, and I. Pastor, “Transverse pattern morphogenesis in a CO2 laser,” Opt. Lett. 21, 1153–1155 (1996).
  9. J. Merlin, C. Oliveira, and J. Dietz, “Energy distribution analysis of high-power laser beam from spots on paper,” in Laser Technologies in Industry, S. P. Almeida, L. M. Bernardo, and O. D. Soares, eds., Proc. SPIE 952, 731–735 (1988).
  10. E. Louvergneaux, D. Hennequin, D. Dangoisse, and P. Glorieux, “Transverse mode competition in a CO2 laser,” Phys. Rev. A 53, 4435–4438 (1996).
  11. B. Lü and H. Ma, “Coherent and incoherent combinations of off-axis Gaussian beams with rectangular symmetry,” Opt. Commun. 171, 185–194 (1999).
  12. Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
  13. O. E. Martínez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988).
  14. O. E. Martínez, “Matrix formalism for disperse laser cavities,” IEEE J. Quantum Electron. 25, 296–300 (1989).
  15. A. G. Kostenbauder, “Ray-pulse matrices: a rotational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26, 1148–1157 (1990).
  16. C. J. R. Sheppard and X. Gan, “Free-space propagation of femto-second light pulses,” Opt. Commun. 133, 1–6 (1997).
  17. M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
  18. M. A. Porras, “Propagation of single-cycle pulsed light beams in dispersive media,” Phys. Rev. A 60, 5069–5073 (1999).
  19. L. Martí-López and O. Mendoza-Yero, “Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators,” Opt. Laser Technol. 31, 239–245 (1999).
  20. L. Martí-López and O. Mendoza-Yero, “Polychromatic Gaussian beams emitted by dispersive laser resonators,” Opt. Laser Technol. 33, 1–5 (2001).
  21. L. Martí-López, O. Mendoza-Yero, and J. A. Ramos-de-Campo, “Propagation of polychromatic Gaussian beams through thin lenses,” J. Opt. Soc. Am. A 18, 1348–1356 (2001).
  22. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  23. R. Borghi, G. Piquero, and M. Santarsiero, “Use of biorthogonal functions for the modal decomposition of multimode beams,” Opt. Commun. 194, 235–242 (2001).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited