K. Wang and C. Zhao, “Analytical solution for an anomalous hollow beam in a fractional Fourier transforming optical system with a hard aperture,” Opt. Laser Technol. 44, 1232–1239 (2012).

[CrossRef]

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).

[CrossRef]

Y. Gao, B. Zhu, D. Liu, and Z. Lin, “Fractional Fourier transform of flat-topped multi-Gaussian beams,” J. Opt. Soc. Am. A 27, 358–365 (2010).

[CrossRef]

C. Zhao and Y. Cai, “Propagation of a general-type beam through a truncated fractional Fourier transform optical system,” J. Opt. Soc. Am. A 27, 637–647 (2010).

[CrossRef]

C. Zhao, K. Huang, and X. Lu, “Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system,” Opt. Laser Technol. 42, 280–284 (2010).

[CrossRef]

B. Tang and M. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276–1282 (2009).

[CrossRef]

G. Zhou, “Fractional Fourier transform of Lorentz-Gaussian beams,” J. Opt. Soc. Am. A 26, 350–355 (2009).

[CrossRef]

K. Wang and C. Zhao, “Fractional Fourier transform for an anomalous hollow beam,” J. Opt. Soc. Am. A 26, 2571–2576 (2009).

[CrossRef]

G. Zhou, “Fractional Fourier transform of Ince-Gaussian beams,” J. Opt. Soc. Am. A 26, 2586–2591 (2009).

[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik 119, 477–480 (2008).

[CrossRef]

X. Ji and B. Lü, “Focal shift and focal switch of Bessel-Gaussian beams passing through a lens system with or without aperture,” Opt. Laser Technol. 39, 562–568 (2007).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

Y. Cai and Q. Lin, “Fractional Fourier transform for elliptical Gaussian beam,” Opt. Commun. 217, 7–13 (2003).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

Y. Cai and Q. Lin, “Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane,” J. Opt. Soc. Am. A 20, 1528–1536 (2003).

[CrossRef]

A. Torre, “The fractional Fourier transform and some of its applications to optics,” Prog. Opt. 43, 531–596 (2002).

[CrossRef]

V. Bagini, F. Frezza, and M. Santarsiero, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

[CrossRef]

D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).

[CrossRef]

H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

J. J. Wen and M. A. Breazeale, “Diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).

[CrossRef]

V. Bagini, F. Frezza, and M. Santarsiero, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

[CrossRef]

J. J. Wen and M. A. Breazeale, “Diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1953).

V. Bagini, F. Frezza, and M. Santarsiero, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).

[CrossRef]

C. Zhao, K. Huang, and X. Lu, “Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system,” Opt. Laser Technol. 42, 280–284 (2010).

[CrossRef]

X. Ji and B. Lü, “Focal shift and focal switch of Bessel-Gaussian beams passing through a lens system with or without aperture,” Opt. Laser Technol. 39, 562–568 (2007).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

J. Zhang, X. Lu, and Z. Lin, “Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures,” Optik 122, 307–310 (2011).

[CrossRef]

Y. Gao, B. Zhu, D. Liu, and Z. Lin, “Fractional Fourier transform of flat-topped multi-Gaussian beams,” J. Opt. Soc. Am. A 27, 358–365 (2010).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

J. Zhang, X. Lu, and Z. Lin, “Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures,” Optik 122, 307–310 (2011).

[CrossRef]

C. Zhao, K. Huang, and X. Lu, “Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system,” Opt. Laser Technol. 42, 280–284 (2010).

[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik 119, 477–480 (2008).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

X. Ji and B. Lü, “Focal shift and focal switch of Bessel-Gaussian beams passing through a lens system with or without aperture,” Opt. Laser Technol. 39, 562–568 (2007).

[CrossRef]

A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1953).

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).

[CrossRef]

A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1953).

P. Pääkkönen and J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).

[CrossRef]

V. Bagini, F. Frezza, and M. Santarsiero, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

[CrossRef]

B. Tang and M. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276–1282 (2009).

[CrossRef]

A. Torre, “The fractional Fourier transform and some of its applications to optics,” Prog. Opt. 43, 531–596 (2002).

[CrossRef]

P. Pääkkönen and J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).

[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik 119, 477–480 (2008).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

J. J. Wen and M. A. Breazeale, “Diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

B. Tang and M. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276–1282 (2009).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

J. Zhang, X. Lu, and Z. Lin, “Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures,” Optik 122, 307–310 (2011).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

K. Wang and C. Zhao, “Analytical solution for an anomalous hollow beam in a fractional Fourier transforming optical system with a hard aperture,” Opt. Laser Technol. 44, 1232–1239 (2012).

[CrossRef]

C. Zhao, K. Huang, and X. Lu, “Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system,” Opt. Laser Technol. 42, 280–284 (2010).

[CrossRef]

C. Zhao and Y. Cai, “Propagation of a general-type beam through a truncated fractional Fourier transform optical system,” J. Opt. Soc. Am. A 27, 637–647 (2010).

[CrossRef]

K. Wang and C. Zhao, “Fractional Fourier transform for an anomalous hollow beam,” J. Opt. Soc. Am. A 26, 2571–2576 (2009).

[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik 119, 477–480 (2008).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

D. Deng, “Propagation of Airy beams through a hard-edged aperture,” Appl. Phys. B 107, 195–200 (2012).

[CrossRef]

X. Lu, X. Chen, L. Zhang, and D. Xue, “High-order Bessel-Gaussian beam and its propagation properties,” Chin. Phys. Lett. 20, 2155–2157 (2003).

[CrossRef]

J. J. Wen and M. A. Breazeale, “Diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).

[CrossRef]

V. Namias, “The fractional order Fourier transform and its applications to quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).

[CrossRef]

B. Tang and M. Xu, “Fractional Fourier transform for beams generated by Gaussian mirror resonator,” J. Mod. Opt. 56, 1276–1282 (2009).

[CrossRef]

V. Bagini, F. Frezza, and M. Santarsiero, “Generalized Bessel-Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).

[CrossRef]

A. April, “Bessel-Gauss beams as rigorous solutions of the Helmholtz equation,” J. Opt. Soc. Am. A 28, 2100–2107 (2011).

[CrossRef]

C. Zhao and Y. Cai, “Propagation of a general-type beam through a truncated fractional Fourier transform optical system,” J. Opt. Soc. Am. A 27, 637–647 (2010).

[CrossRef]

Y. Gao, B. Zhu, D. Liu, and Z. Lin, “Fractional Fourier transform of flat-topped multi-Gaussian beams,” J. Opt. Soc. Am. A 27, 358–365 (2010).

[CrossRef]

D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).

[CrossRef]

Y. Zhang, B. Dong, B. Gu, and G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

Y. Cai and Q. Lin, “Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane,” J. Opt. Soc. Am. A 20, 1528–1536 (2003).

[CrossRef]

G. Zhou, “Fractional Fourier transform of Lorentz-Gaussian beams,” J. Opt. Soc. Am. A 26, 350–355 (2009).

[CrossRef]

G. Zhou, “Fractional Fourier transform of Ince-Gaussian beams,” J. Opt. Soc. Am. A 26, 2586–2591 (2009).

[CrossRef]

K. Wang and C. Zhao, “Fractional Fourier transform for an anomalous hollow beam,” J. Opt. Soc. Am. A 26, 2571–2576 (2009).

[CrossRef]

Y. Cai and Q. Lin, “Fractional Fourier transform for elliptical Gaussian beam,” Opt. Commun. 217, 7–13 (2003).

[CrossRef]

D. Zhao, H. Mao, H. Liu, S. Wang, F. Jing, and X. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004).

[CrossRef]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).

[CrossRef]

P. Pääkkönen and J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).

[CrossRef]

K. Wang and C. Zhao, “Analytical solution for an anomalous hollow beam in a fractional Fourier transforming optical system with a hard aperture,” Opt. Laser Technol. 44, 1232–1239 (2012).

[CrossRef]

X. Ji and B. Lü, “Focal shift and focal switch of Bessel-Gaussian beams passing through a lens system with or without aperture,” Opt. Laser Technol. 39, 562–568 (2007).

[CrossRef]

C. Zhao, K. Huang, and X. Lu, “Propagation properties of Bessel and Bessel-Gaussian beams in a fractional Fourier transform optical system,” Opt. Laser Technol. 42, 280–284 (2010).

[CrossRef]

J. Zhang, X. Lu, and Z. Lin, “Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures,” Optik 122, 307–310 (2011).

[CrossRef]

D. Zhao, H. Mao, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of Hermite-Gaussian beams in apertured fractional Fourier transforming systems,” Optik 114, 504–508 (2003).

[CrossRef]

C. Zhao, L. Wang, and X. Lu, “Radiation forces of highly focused Bessel-Gaussian beams on a dielectric sphere,” Optik 119, 477–480 (2008).

[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

[CrossRef]

A. Torre, “The fractional Fourier transform and some of its applications to optics,” Prog. Opt. 43, 531–596 (2002).

[CrossRef]

A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1953).