## Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics

JOSA A, Vol. 24, Issue 7, pp. 1937-1944 (2007)

http://dx.doi.org/10.1364/JOSAA.24.001937

Enhanced HTML Acrobat PDF (379 KB)

### Abstract

We report the experimental observation of the fractional Fourier transform (FRT) for a partially coherent optical beam with Gaussian statistics [i.e., partially coherent Gaussian Schell-model (GSM) beam]. The intensity distribution (or beam width) and the modulus of the square of the spectral degree of coherence (or coherence width) of a partially coherent GSM beam in the FRT plane are measured, and the experimental results are analyzed and agree well with the theoretical results. The FRT optical system provides a convenient way to control the properties, e.g., the intensity distribution, beam width, spectral degree of coherence, and coherence width, of a partially coherent beam.

© 2007 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.2590) Fourier optics and signal processing : ABCD transforms

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: November 22, 2006

Revised Manuscript: February 3, 2007

Manuscript Accepted: February 28, 2007

Published: June 13, 2007

**Citation**

Fei Wang and Yangjian Cai, "Experimental observation of fractional Fourier transform for a partially coherent optical beam with Gaussian statistics," J. Opt. Soc. Am. A **24**, 1937-1944 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-7-1937

Sort: Year | Journal | Reset

### References

- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
- Q. S. He, J. Turunen, and A. T. Friberg, "Propagation and imaging experiments with Gaussian Schell-model beams," Opt. Commun. 67, 245-250 (1988). [CrossRef]
- E. Tervonen, A. T. Friberg, and J. Turunen, "Gaussian Schell-model beams generated with synthetic acousto-optic holograms," J. Opt. Soc. Am. A 9, 796-803 (1992). [CrossRef]
- A. Belendez, L. Carretero, and A. Fimia, "The use of partially coherent light to reduce the efficiency of silver-halide noise gratings," Opt. Commun. 98, 236-240 (1993). [CrossRef]
- Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, and C. Yamanaka, "Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression," Phys. Rev. Lett. 53, 1057-1060 (1984). [CrossRef]
- J. C. Ricklin and F. M. Davidson, "Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication," J. Opt. Soc. Am. A 19, 1794-1802 (2002). [CrossRef]
- E. Wolf, "Non-cosmological redshifts of spectral lines," Nature 326, 363-365 (1987). [CrossRef]
- J. Pu, H. Zhang, and S. Nemoto, "Spectral shifts and spectral switches of partially coherent light passing through an aperture," Opt. Commun. 162, 57-63 (1999). [CrossRef]
- S. Anand, B. K. Yadav, and H. C. Kandpal, "Experimental study of the phenomenon of 1×N spectral switch due to diffraction of partially coherent light," J. Opt. Soc. Am. A 19, 2223-2228 (2002). [CrossRef]
- Y. Cai and S. Zhu, "Ghost interference with partially coherent radiation," Opt. Lett. 29, 2716-2718 (2004). [CrossRef] [PubMed]
- Y. Cai and S. Zhu, "Ghost imaging with incoherent and partially coherent light radiation," Phys. Rev. E 71, 056607 (2005). [CrossRef]
- R. Simon, E. C. G. Sudarshan, and N. Mukunda, "Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants," Phys. Rev. A 31, 2419-2434 (1985). [CrossRef] [PubMed]
- R. Simon and N. Mukunda, "Twisted Gaussian Schell-model beams," J. Opt. Soc. Am. A 10, 95-109 (1993). [CrossRef]
- M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light," J. Opt. Soc. Am. A 3, 1227-1238 (1986). [CrossRef]
- Q. Lin and Y. Cai, "Tensor ABCD law for partially coherenttwisted anisotropic Gaussian Schell-model beams," Opt. Lett. 27, 216-218 (2002). [CrossRef]
- Y. Cai and Q. Lin, "Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space," Opt. Commun. 204, 17-23 (2002).
- Y. Cai and Q. Lin, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media," J. Opt. Soc. Am. A 19, 2036-2042 (2002). [CrossRef]
- Y. Cai and L. Hu, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system," Opt. Lett. 31, 685-687 (2006). [CrossRef] [PubMed]
- Y. Cai and S. He, "Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere," Appl. Phys. Lett. 89, 041117 (2006). [CrossRef]
- A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993). [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, D. Medlovic, and Z. Zalevsky, "Fractional transformations in optics," in Progress in Optics, Vol. XXXVIII, E.Wolf, ed. (Elsevier, 1998). [CrossRef]
- H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).
- A. Torre, "The fractional Fourier transform and some of its applications to optics," in Progress in Optics, E.Wolf, ed. (Elsevier, 2002), Vol. 43. [CrossRef]
- D. Mendlovic, Z. Zalevsky, R. G. Dorsch, Y. Bitran, A. W. Lohmann, and H. Ozaktas, "New signal representation based on the fractional Fourier transform: definitions," J. Opt. Soc. Am. A 12, 2424-2431 (1995). [CrossRef]
- S. C. Pei, M. H. Yeh, and T. L. Luo, "Fractional Fourier series expansion for finite signals and dual extension to discrete-time fractional Fourier transform," IEEE Trans. Signal Process. 47, 2883-2888 (1999). [CrossRef]
- B. Zhu, S. Liu, and Q. Ran, "Optical image encryption based on multi-fractional Fourier transforms," Opt. Lett. 25, 1159-1161 (2000). [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]
- X. Xue, H. Q. Wei, and A. G. Kirk, "Beam analysis by fractional Fourier transform," Opt. Lett. 26, 1746-1748 (2001). [CrossRef]
- Q. Lin and Y. Cai, "Fractional Fourier transform for partially coherent Gaussian-Schell model beams," Opt. Lett. 27, 1672-1674 (2002). [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]
- C. Zheng, "Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam," J. Opt. Soc. Am. A 23, 2161-2165 (2006). [CrossRef]
- Y. Cai, Q. Lin, and S. Zhu, "Coincidence fractional Fourier transform with entangled photon pairs and incoherent light," Appl. Phys. Lett. 86, 021112 (2005). [CrossRef]
- Y. Cai and S. Zhu, "Coincidence fractional Fourier transform with partially coherent light radiation," J. Opt. Soc. Am. A 22, 1798-1804 (2005). [CrossRef]
- Y. Cai, Q. Lin, and S. Zhu, "Coincidence subwavelength fractional Fourier transform," J. Opt. Soc. Am. A 23, 835-841 (2006). [CrossRef]
- Y. Cai and F. Wang, "Lensless optical implementation of the coincidence fractional Fourier transform," Opt. Lett. 31, 2278-2280 (2006). [CrossRef] [PubMed]
- F. Wang, Y. Cai, and S. He, "Experimental observation of coincidence fractional Fourier transform with a partially coherent beam," Opt. Express 14, 6999-7004 (2006). [CrossRef] [PubMed]
- R. Simon, E. C. G. Sudarshan, and N. Mukunda, "Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields," Phys. Rev. A 29, 3273-3279 (1984). [CrossRef]

## 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.