## Propagation of Laguerre–Gaussian and elegant Laguerre–Gaussian beams in apertured fractional Hankel transform systems

JOSA A, Vol. 21, Issue 12, pp. 2375-2381 (2004)

http://dx.doi.org/10.1364/JOSAA.21.002375

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### Abstract

On the basis of the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, approximate analytical expressions for the output field distribution of a Laguerre-Gaussian beam and an elegant Laguerre-Gaussian beam passing through apertured fractional Hankel transform systems are derived. Some numerical simulation comparisons are done, by using the approximate analytical formulas and diffraction integral formulas, and it is shown that our method can significantly improve the numerical calculation efficiency.

© 2004 Optical Society of America

**OCIS Codes**

(050.1220) Diffraction and gratings : Apertures

(050.1940) Diffraction and gratings : Diffraction

(070.2590) Fourier optics and signal processing : ABCD transforms

(140.3300) Lasers and laser optics : Laser beam shaping

**Citation**

Zhangrong Mei and Daomu Zhao, "Propagation of Laguerre–Gaussian and elegant Laguerre–Gaussian beams in apertured fractional Hankel transform systems," J. Opt. Soc. Am. A **21**, 2375-2381 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-12-2375

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### References

- V. Namias, “The fractional Fourier transform and its application in quantum mechanics,” J. Inst. Math. Appl. 25, 241–265 (1980).
- A. C. McBride and F. H. Kerr, “On Namias’s fractional Fourier transform,” IMA J. Appl. Math. 39, 159–175 (1987).
- D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).
- H. M. Ozaktas and D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).
- A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
- A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, “Fractional transformations in optics,” in Progress in Optics Vol. XXXVIII, E. Wolf, ed. (Elsevier, Amsterdam, 1998).
- H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, New York, 2001).
- A. Torre, “The fractional Fourier transform and some of its applications to optics,” in Progress in Optics Vol. XLIII, E. Wolf, ed. (Elsevier, Amsterdam, 2002).
- V. Namias, “Fractionalization of Hankel transforms,” J. Inst. Math. Appl. 26, 187–197 (1980).
- L. Yu, X. Lu, Y. Zeng, M. Huang, M. Chen, W. Huang, and Z. Zhu, “Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform,” Opt. Lett. 23, 1158–1160 (1998).
- D. Zhao, “Collins formula in frequency-domain described by fractional Fourier transforms or fractional Hankel transforms,” Optik (Stuttgart) 111, 9–12 (2000).
- D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Graded index fibers, Wigner-distribution functions, and the fractional Fourier transforms,” Appl. Opt. 33, 6188–6193 (1994).
- J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1998).
- D. Zhao, H. Mao, W. Zhang, and S. Wang, “Propagation of off-axial Hermite–cosine–Gaussian beams through an apertured and misaligned ABCD optical system,” Opt. Commun. 224, 5–12 (2003).
- D. Zhao, H. Mao, M. Shen, H. Liu, F. Jing, Q. Zhu, and X. Wei, “Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems,” J. Opt. A, Pure Appl. Opt. 6, 148–154 (2004).
- S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
- B. Lu and R. Peng, “Relative phase shift in Laguerre-Gaussian beams propagating through an apertured paraxial ABCD system,” J. Mod. Opt. 50, 857–865 (2003).
- A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, New York, 1954).
- S. Saghafi and C. J. R. Sheppard, “Near field and far field of elegant Hermite–Gaussian and Laguerre–Gaussian modes,” J. Mod. Opt. 45, 1999–2009 (1998).

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