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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 6 — Jun. 1, 2003
  • pp: 1111–1119

Decentered elliptical Hermite–Gaussian beam

Yangjian Cai and Qiang Lin  »View Author Affiliations

JOSA A, Vol. 20, Issue 6, pp. 1111-1119 (2003)

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A new kind of laser beam called the decentered elliptical Hermite–Gaussian beam (DEHGB) is defined by use of a tensor method. The propagation formula of the DEHGB passing through a nonsymmetrical paraxial optical system is derived through vector integration. The derived formula can be easily reduced to the propagation formula of an aligned elliptical Hermite–Gaussian beam and that of a decentered elliptical Gaussian beam under certain conditions. By use of this formula, the propagation characteristics of the DEHGB through free space are presented graphically. As application examples, we construct a generalized laser array using the DEHGB as the fundamental mode. We also obtain the decentered elliptical flattened Gaussian beam by expressing it as superposition of a series of DEHGBs by using polynomial expansion.

© 2003 Optical Society of America

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(140.3300) Lasers and laser optics : Laser beam shaping
(350.5500) Other areas of optics : Propagation

Original Manuscript: September 4, 2002
Revised Manuscript: February 3, 2003
Manuscript Accepted: February 3, 2003
Published: June 1, 2003

Yangjian Cai and Qiang Lin, "Decentered elliptical Hermite–Gaussian beam," J. Opt. Soc. Am. A 20, 1111-1119 (2003)

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  1. A. E. Siegman, “Hermite–gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973). [CrossRef]
  2. W. H. Carter, “Spot size and divergence for Hermite Gaussian beams of any order,” Appl. Opt. 19, 1027–1029 (1980). [CrossRef] [PubMed]
  3. P. A. Belanger, “Packetlike solutions of the homogeneous-wave equation,” J. Opt. Soc. Am. A 1, 723–724 (1984). [CrossRef]
  4. V. N. Smirnov, G. A. Strokovskii, “On diffraction of optical Hermite–Gaussian beams from a diaphragm,” Opt. Spectrosc. 76, 912–919 (1994).
  5. E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3, 465–469 (1986). [CrossRef]
  6. S. Saghafi, C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998). [CrossRef]
  7. S. Saghafi, C. J. R. Sheppard, J. A. Piper, “Characteris-ing elegant and standard Hermite–Gaussian beam modes,” Opt. Commun. 191, 173–179 (2001). [CrossRef]
  8. A. A. Tovar, L. W. Casperson, “Production and propagation of Hermite–sinusoidal-Gaussian laser beams,” J. Opt. Soc. Am. A 15, 2425–2432 (1998). [CrossRef]
  9. H. Laabs, C. Gao, H. Weber, “Twisting to three-dimensional Hermite–Gaussian beams,” J. Mod. Opt. 46, 709–719 (1999).
  10. Y. Cai, Q. Lin, “The elliptical Hermite–Gaussian beam and its propagation through paraxial systems,” Opt. Commun. 207, 139–147 (2002). [CrossRef]
  11. L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2423–2441 (1973). [CrossRef]
  12. A. R. Al-Rashed, B. E. A. Saleh, “Decentered Gaussian beams,” Appl. Opt. 34, 6819–6825 (1995). [CrossRef] [PubMed]
  13. C. Palma, “Decentered Gaussian beams, ray bundles, and Bessel Gauss beams,” Appl. Opt. 36, 1116–1120 (1997). [CrossRef] [PubMed]
  14. B. Lü, H. Ma, “Coherent and incoherent combinations of off-axis Gaussian beams with rectangular symmetry,” Opt. Commun. 171, 185–194 (1999). [CrossRef]
  15. B. Lü, H. Ma, “Coherent and incoherent off-axis Hermite–Gaussian beam combinations,” Appl. Opt. 39, 1279–1289 (2000). [CrossRef]
  16. M. L. Luis, M. Y. Omel, J. J. D. Joris, “Incoherent su-perposition of off-axis polychromatic Hermite–Gaussian modes,” J. Opt. Soc. Am. A 19, 1572–1582 (2002). [CrossRef]
  17. P. J. Cronin, P. Török, P. Varga, C. Cogswell, “High-aperture diffraction of a scalar, off-axis Gaussian beam,” J. Opt. Soc. Am. A 17, 1556–1564 (2000). [CrossRef]
  18. J. A. Arnaud, H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969). [CrossRef] [PubMed]
  19. W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. 62, 1195–1201 (1972). [CrossRef]
  20. Q. Lin, Y. Cai, “Decentered elliptical Gaussian beam,” Appl. Opt. 41, 4336–4340 (2002). [CrossRef] [PubMed]
  21. Q. Lin, S. Wang, J. Alda, E. Bernabeu, “Transformation of non-symmetric Gaussian beam into symmetric one by means of tensor ABCD law,” Optik (Stuttgart) 85, 67–72 (1990).
  22. J. Alda, S. Wang, E. Bernabeu, “Analytical expression for the complex radius of curvature tensor Q for generalized Gaussian beams,” Opt. Commun. 80, 350–352 (1991). [CrossRef]
  23. P. Baues, “Huygens’ principle in homogeneous, isotropic media and a general integral equation applicable to optical resonators,” Opto-electronics 1, 37–44 (1969). [CrossRef]
  24. K. M. Abramski, A. D. Colley, H. J. Baker, D. R. Hall, “High-power two-dimensional waveguide CO2 laser arrays,” IEEE J. Quantum Electron. 32, 340–349 (1996). [CrossRef]
  25. H. J. Baker, D. R. Hall, A. M. Hornby, R. J. Morley, M. R. Taghizadeh, E. F. Yelden, “Propagation characteristics of coherent array beam from carbon dioxide waveguide lasers,” IEEE J. Quantum Electron. 32, 400–407 (1996). [CrossRef]
  26. W. D. Bilida, J. D. Strohschein, H. J. J. Seguin, “High-power 24-channel radial array slab rf-excited carbon dioxide laser,” in Gas and Chemical Lasers and Applications II, R. C. Sze, E. A. Dorko, eds., Proc. SPIE2987, 13–21 (1997). [CrossRef]
  27. J. D. Strohschein, H. J. J. Seguin, C. E. Capjack, “Beam propagation constants for a radial laser array,” Appl. Opt. 37, 1045–1048 (1998). [CrossRef]
  28. B. Lü, H. Ma, “Beam propagation properties of radial lasers arrays,” J. Opt. Soc. Am. A 17, 2005–2009 (2000). [CrossRef]
  29. B. Lü, H. Ma, “Beam combination of a radial laser array: Hermite–Gaussian model,” Opt. Commun. 15, 395–403 (2000).
  30. F. Gori, M. Santarsiero, R. Borghi, G. Guattari, “Intensity-based model analysis of partially coherent beams with Hermite–Gaussian modes,” Opt. Lett. 23, 989–991 (1998). [CrossRef]
  31. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994). [CrossRef]
  32. V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, “Propagation of axially symmetric flattened Gaussian beams,” J. Opt. Soc. Am. A 13, 1385–1394 (1996). [CrossRef]

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