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Optics Letters

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  • Editor: Anthony J. Campillo
  • Vol. 32, Iss. 11 — Jun. 1, 2007
  • pp: 1521–1523

Fractionalization of optical beams: I. Planar analysis

Julio C. Gutiérrez-Vega  »View Author Affiliations


Optics Letters, Vol. 32, Issue 11, pp. 1521-1523 (2007)
http://dx.doi.org/10.1364/OL.32.001521


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Abstract

We apply the tools of the fractional calculus to introduce new fractional-order beam solutions to the paraxial wave equation that can be regarded as intermediate solutions between the known integral-order solutions. We restrict our attention to the fractionalization of the elegant and standard Hermite–Gaussian beams.

© 2007 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1960) Diffraction and gratings : Diffraction theory
(260.1960) Physical optics : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Physical Optics

History
Original Manuscript: January 10, 2007
Revised Manuscript: February 25, 2007
Manuscript Accepted: February 26, 2007
Published: May 10, 2007

Citation
Julio C. Gutiérrez-Vega, "Fractionalization of optical beams: I. Planar analysis," Opt. Lett. 32, 1521-1523 (2007)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-11-1521


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References

  1. A. E. Siegman, Lasers (University Science, 1986).
  2. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004). [CrossRef] [PubMed]
  3. A. E. Siegman, J. Opt. Soc. Am. 63, 1093 (1973). [CrossRef]
  4. S. Y. Shin and L. B. Felsen, J. Opt. Soc. Am. 67, 699 (1977). [CrossRef]
  5. S. R. Seshadri, Opt. Lett. 28, 595 (2003). [CrossRef] [PubMed]
  6. J. Enderlein and F. Pampaloni, J. Opt. Soc. Am. A 21, 1553 (2004). [CrossRef]
  7. I. Podlubny, Fractional Differential Equations (Academic, 1999).
  8. K. Oldham and J. Spanier, The Fractional Calculus (Academic, 1974).
  9. N. Engheta, IEEE Antennas Propag. Mag. 39, 35 (1997). [CrossRef]
  10. N. Engheta, IEEE Trans. Antennas Propag. 44, 554 (1996). [CrossRef]
  11. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform (Wiley, 2001).
  12. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, Prog. Opt. 38, 265 (1998).
  13. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1964), Chap. 13.

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