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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 6 — Jun. 1, 2001
  • pp: 1348–1356

Propagation of polychromatic Gaussian beams through thin lenses

Luis Martı́-López, Omel Mendoza-Yero, and José A. Ramos-de-Campos  »View Author Affiliations

JOSA A, Vol. 18, Issue 6, pp. 1348-1356 (2001)

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The transformation by a lens of a polychromatic laser beam composed of on-axis superposed monochromatic TEM00 Gaussian modes in the paraxial approximation is studied. The chromatic aberrations are described by allowing the waist position on the z axis and the Rayleigh range to depend on wavelength. The beam radius, the far-field divergence, the Rayleigh range, the beam product, the beam propagation factor, and the kurtosis parameter are calculated. The relationship between the fourth-order and the second-order moments of Hermite–Gaussian and Laguerre–Gaussian modes is obtained and is used for calculating kurtosis parameter. The results are generalized to polychromatic modes of higher orders. It is shown that the on-axis superposition of monochromatic TEM00 modes with no chromatic aberration is leptokurtic.

© 2001 Optical Society of America

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

Original Manuscript: March 7, 2000
Revised Manuscript: November 27, 2000
Manuscript Accepted: December 11, 2000
Published: June 1, 2001

Luis Martı́-López, Omel Mendoza-Yero, and José A. Ramos-de-Campos, "Propagation of polychromatic Gaussian beams through thin lenses," J. Opt. Soc. Am. A 18, 1348-1356 (2001)

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  1. R. Simon, N. Mukunda, G. C. E. Sudarshan, “Partially coherent beams and a generalized ABCD-law,” Opt. Commun. 65, 322–328 (1988). [CrossRef]
  2. L. Shimon, R. Prochaska, E. Keren, “Generalized beam parameters and transformation laws for partially coherent light,” Appl. Opt. 27, 3696–3703 (1988). [CrossRef]
  3. J. Serna, R. Martı́nez-Herrero, P. M. Mejı́as, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991). [CrossRef]
  4. Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of pulsed nonideal beams in a four-dimension domain,” Opt. Lett. 18, 669–671 (1993). [CrossRef] [PubMed]
  5. P. M. Mejı́as, R. Martı́nez-Herrero, “Time-resolved spatial parametric characterization of pulsed light beams,” Opt. Lett. 20, 660–662 (1995). [CrossRef] [PubMed]
  6. Q. Cao, D. Ximing, “Spatial parametric characterization of general polychromatic beams,” Opt. Commun. 142, 135–145 (1997). [CrossRef]
  7. C. J. R. Sheppard, X. Gan, “Free-space propagation of femtosecond light pulses,” Opt. Commun. 133, 1–6 (1997). [CrossRef]
  8. M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998). [CrossRef]
  9. O. E. Martı́nez, “Matrix formalism for pulse compressors,” IEEE J. Quantum Electron. 24, 2530–2536 (1988). [CrossRef]
  10. O. E. Martı́nez, “Matrix formalism for dispersive laser cavities,” IEEE J. Quantum Electron. 25, 296–300 (1989). [CrossRef]
  11. A. G. Kostenbauder, “Ray-pulse matrices: a rotational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26, 1148–1157 (1990). [CrossRef]
  12. M. A. Porras, “Propagation of single-cycle pulsed light beams in dispersive media,” Phys. Rev. A 60, 5069–5073 (1999). [CrossRef]
  13. L. Martı́-López, O. Mendoza-Yero, “Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators,” Opt. Laser Technol. 31, 239–245 (1999). [CrossRef]
  14. A. E. Siegman, “Defining, measuring, and optimizing laser beam quality,” in Laser Resonators and Coherent Optics: Modeling, Technology and Applications, A. Bhowmik, ed., Proc. SPIE1868, 2–12 (1993). [CrossRef]
  15. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), p. 1267.
  16. W. H. Carter, “Spot size and divergence for Hermite–Gaussian beams of any order,” Appl. Opt. 19, 1027–1029 (1980). [CrossRef] [PubMed]
  17. H. P. Kortz, R. Iffländer, H. Weber, “Stability and beam divergence of multimode lasers with internal variable lenses,” Appl. Opt. 20, 4124–4134 (1981). [CrossRef] [PubMed]
  18. M. Y. Klimkov, Osnovy Rasschiota Optiko-Elektronikh Priborov s Lazerami (Fundamentals of Calculus of Optical and Electronic Devices with Lasers) (Sovietskoye Radio, Moscow, 1978), p. 264.
  19. S. A. Self, “Focussing of spherical Gaussian beams,” Appl. Opt. 22, 658–660 (1983). [CrossRef] [PubMed]
  20. H. Kogelnik, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966). [CrossRef]
  21. L. Marti-López, O. Mendoza-Yero, “Polychromatic Gaussian beams emitted by dispersive laser resonators,” Opt. Laser Technol. 33, 1–5 (2001). [CrossRef]
  22. R. D. Bock, Multivariate Statistical Methods in Behavioral Research (McGraw-Hill, New York, 1975), p. 623.
  23. G. Piquero, P. M. Mejı́as, R. Martı́nez-Herrero, “Sharpness changes of Gaussian beams induced by spherically aberrated lenses,” Opt. Commun. 107, 179–183 (1994). [CrossRef]
  24. R. Martı́nez-Herrero, G. Piquero, P. M. Mejı́as, “On the propagation of the kurtosis parameter of general beams,” Opt. Commun. 115, 225–232 (1995). [CrossRef]
  25. S. Saghafi, C. J. R. Sheppard, “The beam propagation factor for higher order Gaussian beams,” Opt. Commun. 153, 207–210 (1998). [CrossRef]
  26. U. Vokinger, R. Dändliker, P. Blattner, H. P. Herzig, “Unconventional treatment of focal shift,” Opt. Commun. 157, 218–224 (1998). [CrossRef]

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