OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 7 — Jul. 1, 2001
  • pp: 1579–1587

High-aperture beams

Colin J. R. Sheppard  »View Author Affiliations


JOSA A, Vol. 18, Issue 7, pp. 1579-1587 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001579


View Full Text Article

Acrobat PDF (306 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Beams of a high angle of convergence and divergence are called high-aperture beams. Different ways of defining high-aperture generalizations to paraxial beams are reviewed for both scalar beams and electromagnetic beams. The different approaches are divided into three types. The particular examples of Gaussian beams and Bessel beams are discussed. For Gaussian beams, beams that exhibit a Gaussian variation in the waist necessarily include evanescent components, which rules out their use in describing propagation over all space. Generalizations of the definitions of beam width and the beam-propagation factor M2 for high-aperture beams are described. The similarities among the three types of high-aperture beams and the different models of ultrashort-pulsed beams are discussed.

© 2001 Optical Society of America

OCIS Codes
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(140.3410) Lasers and laser optics : Laser resonators
(140.4780) Lasers and laser optics : Optical resonators
(230.5750) Optical devices : Resonators
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

Citation
Colin J. R. Sheppard, "High-aperture beams," J. Opt. Soc. Am. A 18, 1579-1587 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-7-1579


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. A. G. van Nie, “Rigorous calculation of the electromagnetic field of a wave beam,” Philips Res. Rep. 19, 378–394 (1964).
  2. G. D. Boyd and J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength lasers,” Bell Syst. Tech. J. 40, 489–508 (1960).
  3. G. Goubau and F. Schwering, “On the guided propagation of electromagnetic wave beams,” IEEE Trans. Antennas Propag. 9, 248–256 (1961).
  4. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
  5. H. G. Booker and P. C. Clemmow, “The concept of an angular spectrum of plane waves and its relation to that of polar diagrams and aperture distributions,” Proc. Inst. Electr. Eng. 97 III, 11–17 (1950).
  6. E. Wolf, “Electromagnetic diffraction in optical systems 1. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
  7. C. J. R. Sheppard and K. G. Larkin, “Vectorial pupil functions and vectorial transfer functions,” Optik 107, 79–87 (1997).
  8. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
  9. C. J. R. Sheppard and K. G. Larkin, “Optimal concentration of electromagnetic radiation,” J. Mod. Opt. 41, 1495–1505 (1994).
  10. C. J. R. Sheppard, “Electromagnetic field in the focal region of wide-angular annular lens and mirror systems,” IEE J. Microwaves, Opt. Acoust. 2, 163–166 (1978).
  11. C. J. R. Sheppard and P. Török, “Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion,” J. Mod. Opt. 44, 803–818 (1997).
  12. A. Yoshida and T. Asakura, “Electromagnetic field near the focus of Gaussian beams,” Optik 41, 281–291 (1974).
  13. C. J. R. Sheppard and M. Gu, “Imaging by a high aperture optical system,” J. Mod. Opt. 40, 1631–1651 (1993).
  14. K. B. Wolf, M. A. Alonso, and G. W. Forbes, “Wigner functions for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999).
  15. A. W. Lohmann, “Three-dimensional properties of wave fields,” Optik 51, 105–117 (1978).
  16. N. Streibl, “Fundamental restrictions for 3-D light distributions,” Optik 66, 341–354 (1984).
  17. K. G. Larkin and C. J. R. Sheppard, “Direct method for phase retrieval from the intensity of cylindrical wave fronts,” J. Opt. Soc. Am. A 16, 1838–1844 (1999).
  18. M. Lax, W. H. Louisel, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
  19. G. P. Agrawal and D. N. Pattanayck, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575–578 (1979).
  20. G. P. Agrawal and M. Lax, “Free-space wave propagation beyond the paraxial approximation,” Phys. Rev. A 27, 1693–1695 (1983).
  21. S. Nemoto, “Nonparaxial Gaussian beams,” Appl. Opt. 29, 1940–1946 (1990).
  22. L. Cicchitelli, H. Hora, and R. Postle, “Longitudinal components for laser beams in vacuum,” Phys. Rev. A 41, 3727–3732 (1990).
  23. A. Wünsche, “Transition from the paraxial approximation to exact solutions of the wave equation and application to Gaussian beams,” J. Opt. Soc. Am. A 9, 765–774 (1992).
  24. Q. Cao and X. Deng, “Corrections to the paraxial approximation of an arbitrary free-propagation beam,” J. Opt. Soc. Am. A 15, 1144–1148 (1998).
  25. T. Takenaka, M. Yokota, and O. Fukumitsu, “Propagation of light beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 2, 826–829 (1985).
  26. E. Zauderer, “Complex argument Hermite–Gaussian and Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 3, 465–469 (1986).
  27. H. Laabs, “Propagation of Hermite–Gaussian beams beyond the paraxial approximation,” Opt. Commun. 147, 1–4 (1998).
  28. R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Gaussian–Maxwell beams,” J. Opt. Soc. Am. A 3, 536–540 (1986).
  29. R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Cross polarization in laser beams,” Appl. Opt. 26, 1589–1593 (1987).
  30. W. H. Carter, “Electromagnetic beam fields,” Opt. Acta 21, 871–892 (1974).
  31. S. R. Seshadri, “Electromagnetic Gaussian beam,” J. Opt. Soc. Am. A 15, 2712–2719 (1998).
  32. C. J. R. Sheppard, “Polarization of almost-plane waves,” J. Opt. Soc. Am. A 17, 335–341 (2000).
  33. L. W. Davis and G. Patsakos, “TM and TE electromagnetic beams in free space,” Opt. Lett. 6, 22–23 (1981).
  34. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
  35. P. Varga and P. Török, “Exact and approximate solutions of Maxwell’s equations for a confocal cavity,” Opt. Lett. 21, 1523–1525 (1996).
  36. P. Varga and P. Török, “Gaussian wave solution of Maxwell’s equations and the validity of the scalar wave equation,” Opt. Commun. 152, 108–118 (1998).
  37. J. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 360.
  38. E. T. Whittaker, “On an expression of the electromagnetic field due to electrons by means of two scalar potential functions,” Proc. London Math. Soc. 1, 367–372 (1904).
  39. E. Wolf, “A scalar representation of electromagnetic fields: II,” Proc. Phys. Soc. London 74, 269–280 (1959).
  40. A. Nisbet, “Hertzian electromagnetic potentials and associated gauge transformations,” Proc. R. Soc. London Ser. A 231, 250–263 (1955).
  41. D. Pattanayak and G. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980).
  42. L. W. Davis and G. Patsakos, “Comment on ‘Representation of vector electromagnetic beams,’” Phys. Rev. A 26, 3702–3703 (1982).
  43. C. J. R. Sheppard, “Focal distributions and Hertz potentials,” Opt. Commun. 160, 191–194 (1999).
  44. M. Couture and P.-A. Belanger, “From Gaussian beam to complex-source-point spherical wave,” Phys. Rev. A 24, 355–359 (1981).
  45. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
  46. A. L. Cullen and P. K. Yu, “Complex source-point theory of the electromagnetic open resonator,” Proc. R. Soc. London Ser. A 366, 155–171 (1979).
  47. C. J. R. Sheppard and S. Saghafi, “Electromagnetic Gaussian beams beyond the paraxial approximations,” J. Opt. Soc. Am. A 16, 1381–1386 (1999).
  48. C. J. R. Sheppard and S. Saghafi, “Electric and magnetic dipole beam modes beyond the paraxial approximation,” Optik 110, 487–491 (1999).
  49. C. J. R. Sheppard and S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett. 24, 1543–1545 (1999).
  50. M. V. Berry, “Evanescent and real waves in quantum billiards and Gaussian beams,” J. Phys. A 27, L391–L398 (1994).
  51. C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
  52. E. Heyman and L. B. Felson, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
  53. L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, Colo., 1969).
  54. G. Toraldo di Francia, “Optical resonators,” Opt. Acta 13, 323–342 (1966).
  55. J. B. Keller and S. I. Rubinow, “Asymptotic solution of eigenvalue problems,” Ann. Phys. (Leipzig) 9, 24–75 (1960).
  56. J. F. Nye and M. Berry, “Dislocations of wave fronts,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
  57. G. B. Airy, “The diffraction of an annular aperture,” Philos. Mag. Ser. 3 18, 1–10 (1841).
  58. Lord Rayleigh, “On the diffraction of object glasses,” Mon. Not. R. Astron. Soc. 33, 59–63 (1872).
  59. E. H. Linfoot and E. Wolf, “Diffraction images in systems with an annular aperture,” Proc. Phys. Soc. London Ser. B 66, 145–149 (1953).
  60. G. C. Steward, “IV Aberration diffraction effects,” Proc. R. Soc. London Ser. A 225, 131 (1928).
  61. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
  62. W. H. Steel, “Axicons with spherical surfaces,” in Optics in Metrology, P. Mollet, ed. (Pergamon, New York, 1960), pp. 181–193.
  63. C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves, Opt. Acoust. 2, 105–112 (1978).
  64. S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991).
  65. Z. Bouchal and M. Olivík, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
  66. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
  67. F. Gori, G. Guatteri, and C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987).
  68. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996).
  69. H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators,” Opt. Lett. 19, 1678–1680 (1994).
  70. C. J. R. Sheppard and K. G. Larkin, “Similarity theorems for fractional Fourier transforms and fractional Hankel transforms,” Opt. Commun. 154, 173–178 (1998).
  71. I. S. Gradstein and I. M. Ryshik, Tables of Series, Products, and Integrals (Harri Deutsch, Frankfurt, Germany, 1981).
  72. P. Pääkkönen and J. Turunen, “Resonators with Bessel–Gauss modes,” Opt. Commun. 156, 359–366 (1998).
  73. A. Papoulis, “Ambiguity function in Fourier optics,” J. Opt. Soc. Am. A 64, 779–788 (1974).
  74. C. J. R. Sheppard and K. G. Larkin, “Focal shift, optical transfer function, and phase-space representations,” J. Opt. Soc. Am. A 17, 772–779 (2000).
  75. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE 1224, 2–14 (1990).
  76. X. D. Zeng, C. H. Liang, and Y. Y. An, “Far-field radiation of planar Gaussian sources and comparison with solutions based on the parabolic approximation,” Appl. Opt. 36, 2042–2047 (1997).
  77. M. A. Porras, “The best optical beam beyond the paraxial approximation,” Opt. Commun. 111, 338–349 (1994).
  78. C. W. McCutchen, “Two families of apodization problems,” J. Opt. Soc. Am. 59, 1163–1171 (1969).
  79. A. Papoulis, “Apodization for optimum imaging of smooth objects,” J. Opt. Soc. Am. 62, 1423–1429 (1972).
  80. P. Jacquinot and M. B. Roizen-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3, pp. 29–186.
  81. P. S. Carney and G. Gbur, “Optimal apodizations for finite apertures,” J. Opt. Soc. Am. A 16, 1638–1640 (1999).
  82. D. Slepian, “Analytic solution of two apodization problems,” J. Opt. Soc. Am. 55, 1110–1115 (1965).
  83. J. C. Heurtley and W. Streifer, “Optical resonator modes—circular reflectors of spherical curvature,” J. Opt. Soc. Am. 65, 1472–1479 (1965).
  84. M. A. Alonso and G. W. Forbes are preparing a paper titled “Uncertainty products for nonparaxial wave fields” for publication.
  85. C. J. R. Sheppard and X. Gan, “Free-space propagation of femtosecond light pulses,” Opt. Commun. 133, 1–6 (1997).
  86. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
  87. C. F. R. Caron and R. M. Potvliege, “Free-space propagation of ultrashort pulses: space–time couplings in Gaussian pulse beams,” J. Mod. Opt. 45, 1881–1892 (1999).
  88. M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).

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