title: Optical fractional Fourier transforms with complex orders.
abstract: A definition of real and complex domains for the order of fractional Fourier transforms is introduced in association with diffraction either in free space or through real and complex lenses. The geometrical and the optical conditions that lead to real and complex orders of the fractional Fourier transforms and their relevance to cascading optical systems are discussed.
authors.forename: L M
authors.initials: LM
authors.lastname: Bernardo
authors.forename: O D
authors.initials: OD
authors.lastname: Soares