The fractional Fourier transform (FRFT) for quasi-periodic Bloch functions is studied. An isomorphism between square-integrable functions on the real line and quasi-periodic Bloch functions is used to extend existing work on the fractional Fourier transform for the former functions to the latter. The properties of the FRFT for quasi-periodic Bloch functions are discussed, and various numerical examples are presented.
© 2001 Optical Society of America
Original Manuscript: November 27, 2000
Revised Manuscript: April 2, 2001
Manuscript Accepted: April 17, 2001
Published: October 1, 2001
Chee Ching Chong, Apostolos Vourdas, and Cherif Bendjaballah, "Fractional Fourier transform for quasi-periodic Bloch functions," J. Opt. Soc. Am. A 18, 2478-2485 (2001)