© 2007 Optical Society of America

1. I. Podlubny, Fractional Differential Equations (Academic Press, 1999).
2. K. Oldham and J. Spanier, The Fractional Calculus (Academic Press, 1974).
3. Y. A. Rossikhin and M. V. Shitikova, "Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids," Appl. Mech. Rev. 50, 15-67 (1997). [CrossRef]
4. N. Engheta, "On the role of fractional calculus in electromagnetic theory," IEEE Antennas Propag. Mag. 39, 35-46 (1997). [CrossRef]
5. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with applications in Optics and signal processing (Wiley, 2001). [PubMed]
6. A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, "Fractional transformation in Optics," Prog. Opt. 38, 265-342 (1998).
7. N. Engheta, "Fractional curl operator in electromagnetics," Microwave Opt Technol Lett. 17, 86-91 (1998). [CrossRef]
8. Q.A. Naqvi and M. Abbas, "Fractional duality and metamaterials with negative permittivity and permeability," Opt. Commun. 227, 143-146 (2003). [CrossRef]
9. J. C. Gutiérrez-Vega, "Fractionalization of optical beams: I. Planar analysis,"Opt. Lett. 32, (2007) To be published. [CrossRef] [PubMed]
10. A. E. Siegman, Lasers (University Science, 1986).
11. J. Enderlein and F. Pampaloni, "Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes," J. Opt. Soc. Am A 21, 1553-1558 (2004). [CrossRef]
12. E. Zauderer, "Complex argument Hermite-Gaussian and Laguerre-Gaussian beams," J. Opt. Soc. Am. A 3, 465-469 (1986). [CrossRef]
13. M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, 1964) Ch. 13.
14. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2000) 6th ed.
15. S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher order Gaussian beams," Opt. Commun. 153, 207-210 (1998). [CrossRef]
16. M. A. Porras, R. Borghi, and M. Santarsiero, "Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams," J. Opt. Soc. Am. A 18, 177-184 (2001). [CrossRef]
17. S. R. Seshadri, "Complex-argument Laguerre-Gauss beams: transport of mean-squared beam width," Appl. Opt. 44, 7339-7343 (2005). [CrossRef] [PubMed]
18. M. A. Bandres and J. C. Gutiérrez-Vega, "Higher-order complex source for elegant Laguerre-Gaussian waves,"Opt. Lett. 29, 2213-2215 (2004). [CrossRef] [PubMed]
19. L. Allen, S. M. Barnett, and M. J. Padgett, Orbital Angular Momentum (Institute of Optics Publishing, 2003). [CrossRef]

Appl. Mech. Rev.

• Y. A. Rossikhin and M. V. Shitikova, "Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids," Appl. Mech. Rev. 50, 15-67 (1997). [CrossRef]

Appl. Opt.

• S. R. Seshadri, "Complex-argument Laguerre-Gauss beams: transport of mean-squared beam width," Appl. Opt. 44, 7339-7343 (2005). [CrossRef] [PubMed]

IEEE Antennas Propag. Mag.

• N. Engheta, "On the role of fractional calculus in electromagnetic theory," IEEE Antennas Propag. Mag. 39, 35-46 (1997). [CrossRef]

J. Opt. Soc. Am A

• J. Enderlein and F. Pampaloni, "Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes," J. Opt. Soc. Am A 21, 1553-1558 (2004). [CrossRef]

J. Opt. Soc. Am. A

• E. Zauderer, "Complex argument Hermite-Gaussian and Laguerre-Gaussian beams," J. Opt. Soc. Am. A 3, 465-469 (1986). [CrossRef]
• M. A. Porras, R. Borghi, and M. Santarsiero, "Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams," J. Opt. Soc. Am. A 18, 177-184 (2001). [CrossRef]

Microwave Opt Technol Lett.

• N. Engheta, "Fractional curl operator in electromagnetics," Microwave Opt Technol Lett. 17, 86-91 (1998). [CrossRef]

Opt. Commun.

• Q.A. Naqvi and M. Abbas, "Fractional duality and metamaterials with negative permittivity and permeability," Opt. Commun. 227, 143-146 (2003). [CrossRef]
• S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher order Gaussian beams," Opt. Commun. 153, 207-210 (1998). [CrossRef]

Opt. Lett.

• M. A. Bandres and J. C. Gutiérrez-Vega, "Higher-order complex source for elegant Laguerre-Gaussian waves,"Opt. Lett. 29, 2213-2215 (2004). [CrossRef] [PubMed]
• J. C. Gutiérrez-Vega, "Fractionalization of optical beams: I. Planar analysis,"Opt. Lett. 32, (2007) To be published. [CrossRef] [PubMed]

Prog. Opt.

• A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, "Fractional transformation in Optics," Prog. Opt. 38, 265-342 (1998).

Other

• L. Allen, S. M. Barnett, and M. J. Padgett, Orbital Angular Momentum (Institute of Optics Publishing, 2003). [CrossRef]
• M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, 1964) Ch. 13.
• I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2000) 6th ed.
• A. E. Siegman, Lasers (University Science, 1986).
• H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with applications in Optics and signal processing (Wiley, 2001). [PubMed]
• I. Podlubny, Fractional Differential Equations (Academic Press, 1999).
• K. Oldham and J. Spanier, The Fractional Calculus (Academic Press, 1974).

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