We study fractional Fourier transformation in the metaxial regime of geometric optics. Two commonly used optical arrangements that perform fractional Fourier transformation are a symmetric thick lens and a length of graded-index waveguide. By means of Lie methods in phase space, we can correct some of their aberrations: for the first, through deforming the lens surfaces to a polynomial shape, and for the second, by warping the output screen at the end of the waveguide. We correct the planar cases to third, fifth, and seventh aberration orders; checks are provided on the convergence of aberration series in phase space. We add some comments on the usefulness of these corrected devices for fractional transformers in scalar wave optics.
© 1999 Optical Society of America
Original Manuscript: June 29, 1998
Revised Manuscript: October 8, 1998
Manuscript Accepted: November 13, 1998
Published: April 1, 1999
Kurt Bernardo Wolf and Guillermo Krötzsch, "Metaxial correction of fractional Fourier transformers," J. Opt. Soc. Am. A 16, 821-830 (1999)