The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the <i>ABCD</i> matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths.
© 2004 Optical Society of America
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
Bryan Hennelly, Damian Kelly, and John T. Sheridan, "Wavelength-controlled variable-order optical fractional Fourier transform," Opt. Lett. 29, 427-429 (2004)