SCALING LAW AND SIMULTANEOUS OPTICAL IMPLEMENTATION OF VARIOUS ORDER FRACTIONAL FOURIER TRANSFORMS

The optical implementation of fractional Fourier transforms (FractFT’s) of different orders usually requires different geometric configurations. I obtain a scaling relation for optical implementation of the FractFt that allows one to do the 1/Q1-order FractFT on the 1/Q-order optical FractFt setup, except for the usual Fourier transform. With the scaling relation, FractFt’s of different orders can be optically implemented simultaneously. The optical implementation of a FractFT in the frequency domain is also suggested.