## Propagation of broadband Gaussian Schell-model beams in the apertured fractional Fourier transformation systems |

JOSA A, Vol. 28, Issue 6, pp. 976-982 (2011)

http://dx.doi.org/10.1364/JOSAA.28.000976

Enhanced HTML Acrobat PDF (952 KB)

### Abstract

On the basis of the fact that a hard-edged aperture function can be expressed as finite matrices with different weighting coefficients, we obtain the analytical formula for the propagation of the broadband Gaussian Schell- model (BGSM) beam through the apertured fractional Fourier transformation (AFrFT) system. It is shown by numerical examples that the intensity distribution in the plane of a small fractional order is obviously influenced by the bandwidth when the BGSM beams propagate through the AFrFT system. Further extensions are also pointed out.

© 2011 Optical Society of America

**OCIS Codes**

(050.1220) Diffraction and gratings : Apertures

(070.2590) Fourier optics and signal processing : ABCD transforms

(350.5500) Other areas of optics : Propagation

(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

(140.3295) Lasers and laser optics : Laser beam characterization

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: January 10, 2011

Revised Manuscript: March 18, 2011

Manuscript Accepted: March 18, 2011

Published: May 9, 2011

**Citation**

Haidan Mao, Xinyue Du, Linfei Chen, and Daomu Zhao, "Propagation of broadband Gaussian Schell-model beams in the apertured fractional Fourier transformation systems," J. Opt. Soc. Am. A **28**, 976-982 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-6-976

Sort: Year | Journal | Reset

### References

- A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186(1993). [CrossRef]
- D. M. Zhao, H. D. Mao, H. J. Liu, S. M. Wang, F. Jing, and X. F. Wei, “Propagation of Hermite-cosh-Gaussian beams in apertured fractional Fourier transforming systems,” Opt. Commun. 236, 225–235 (2004). [CrossRef]
- X. Y. Du and D. M. Zhao, “Fractional Fourier transform of truncated elliptical Gaussian beams,” Appl. Opt. 45, 9049–9052(2006). [CrossRef] [PubMed]
- F. Wang, Y. J. Cai, and Q. Lin, “Experimental observation of truncated fractional Fourier transform for a partially coherent Gaussian Schell-model beam,” J. Opt. Soc. Am. A 25, 2001–2010(2008). [CrossRef]
- Y. Q. Gao, B. Q. Zhu, D. Z. Liu, and Z. Q. Liu, “Fractional Fourier transform of flat-topped multi-Gaussian beams,” J. Opt. Soc. Am. A 27, 358–365 (2010). [CrossRef]
- Y. J. 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]
- J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as a superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988). [CrossRef]
- H. D. Mao and D. M. Zhao, “Three models for a hard aperture function and corresponding approximate analytical propagation equations of a Gaussian beam through an apertured optical system,” J. Opt. Soc. Am. A 22, 647–653 (2005). [CrossRef]
- X. Deng, W. Yu, S. Chen, L. Ding, and W. Tan, “Output power increase of high power Nd: glass laser by bandwidth,” Acta Optica Sinica 3, 97–101 (1983) (in Chinese). [CrossRef]
- I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985). [CrossRef]
- M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999). [CrossRef]
- F. Simin and G. W. Herbert, “Spatiotemporal structure of isodiffracting ultrashort electromagnetic pulses,” Phys. Rev. E 61, 862–873 (2000). [CrossRef]
- M. A. Porras, “Diffraction effects in few-cycle optical pulses,” Phys. Rev. E 65, 026606 (2002). [CrossRef]
- R. W. Peng, Y. X. Ye, Z. X. Tang, and D. Y. Fan, “Transverse intensity distributions of a broadband laser modulated by a hard-edged aperture,” J. Opt. Soc. Am. A 22, 1903–1908 (2005). [CrossRef]
- Q. Cao and X. M. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997). [CrossRef]
- H. D. Mao and D. M. Zhao, “Parametric characteristics for a broadband Gaussian beam in free space,” Appl. Phys. B 100, 611–616 (2010). [CrossRef]
- H. D. Mao and D. M. Zhao, “Second-order intensity-moment characteristics for broadband partially coherent flat-topped beams in atmospheric turbulence,” Opt. Express 18, 1741–1755(2010). [CrossRef] [PubMed]
- L. Z. Pan and B. D. Lu, “Spectral switches of polychromatic Gaussian beams passing through an astigmatic aperture lens,” Opt. Commun. 234, 13–22 (2004). [CrossRef]
- S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).
- S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. A 60, 1168–1170(1970). [CrossRef]
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
- I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965). [CrossRef]
- A. Erdelyi, Tables of Integral Transforms (McGraw-Hill, 1954).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.