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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: 3317–3325

Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space

Dongmei Deng, Qi Guo, Sheng Lan, and Xiangbo Yang  »View Author Affiliations


JOSA A, Vol. 24, Issue 10, pp. 3317-3325 (2007)
http://dx.doi.org/10.1364/JOSAA.24.003317


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Abstract

Starting from the vector Maxwell’s equations and applying the multiscale singular perturbation method, the nonparaxial beam propagation is studied in free space. Two new equations have been derived for transverse and longitudinal electric fields of an arbitrary polarized electromagnetic wave even in the case of tightly focused nonparaxial laser beams. By using the analogy of the optical beam in the space domain and the optical pulse in the time domain, the higher-order diffraction term is introduced. For strongly nonparaxial beams that are characterized by large values of the perturbative parameter, our correction solutions yield an accurate description of the field in the near-field region and are consistent with all other correction results obtained by others in the far-field region. For weakly nonparaxial beams, our correction solutions can be expressed in a very simple form that is proved to be exactly consistent with the solutions obtained by Cao and Deng [J. Opt. Soc. Am. A 15, 1144 (1998) ]. In addition, the lowest-order correction to the paraxial approximation can be found to be in good agreement with the results of Lax et al. [Phys. Rev. A 11, 1365 (1975) ] and Seshadri [J. Opt. Soc. Am. A 19, 2134 (2002) ].

© 2007 Optical Society of America

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: March 22, 2007
Revised Manuscript: June 26, 2007
Manuscript Accepted: June 26, 2007
Published: September 24, 2007

Citation
Dongmei Deng, Qi Guo, Sheng Lan, and Xiangbo Yang, "Application of the multiscale singular perturbation method to nonparaxial beam propagations in free space," J. Opt. Soc. Am. A 24, 3317-3325 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-10-3317

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