Abstract

The fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the effects on the FRT action of such a medium that are due to small random inhomogeneities in the longitudinal direction, the direction of propagation, and we formulate the random fractional Fourier transform (RFRT). Applying the RFRT to a self-fractional Fourier function, a Gaussian function, we discuss both the total power and the variance. The random Fourier transform is examined as a special limiting case.

© 1999 Optical Society of America

Metaxial correction of fractional Fourier transformers

Kurt Bernardo Wolf and Guillermo Krötzsch
J. Opt. Soc. Am. A 16(4) 821-830 (1999)

Extended fractional Fourier transforms

Jianwen Hua, Liren Liu, and Guoqiang Li
J. Opt. Soc. Am. A 14(12) 3316-3322 (1997)

Fractional Fourier transform description with use of differential operators

B. Ruiz and H. Rabal
J. Opt. Soc. Am. A 14(11) 2905-2913 (1997)

Characterization of chirped pulses with the fractional-order Fourier transformation

Sébastien Coëtmellec, Marc Brunel, Denis Lebrun, and Cafer Özkul
J. Opt. Soc. Am. A 18(11) 2754-2759 (2001)

Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam

Chongwei Zheng
J. Opt. Soc. Am. A 23(9) 2161-2165 (2006)