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Journal of the Optical Society of America A

Classical versus complex fractional Fourier transformation

Daniela Dragoman

Published Jan 23, 2009• 11 citations
Publisher

Abstract

The quantum optical complex fractional Fourier transform (FRFT) has been related to the classical FRFT using both classical and quantum formalisms. In particular, it was shown that the kernel of the complex FRFT can be classically produced with rotated astigmatic optical systems that mimic the quantum entanglement property.
DOI
10.1364/josaa.26.000274

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In a recent paper of Optics Letter (Fan Hongyi and Lu Hailiang, Optics Letters 28 (2003) 680) the complex fractional Fourier transform (CFFRT) is introduced, which is different from the usual two-dimensional real fractional Fourier transforms. In the present work we illuminate its definition from the point of view of rotation of the complex form of Wigner distributions as well as from the view of optical propagation mechanism in graded-index medium. The newly constructed quantum mechanical entangled state representations are used to link CFFRT to the Wigner distributions.