OPTICAL INTERPRETATION OF A COMPLEX-ORDER FOURIER-TRANSFORM

It is demonstrated that the definition of a fractional-order Fourier t ransform can be extended into the complex-order regime. A complex-orde r Fourier transform deals with the imaginary part as well as the real part of the exponential function in the integral. As a result, while t he optical implementation of fractional-order Fourier transform involv es gradient-index media or spherical lenses, the optical interpretatio n of complex-order Fourier transform is practically based on the convo lution operation and Gaussian apertures. The beam width of a Gaussian beam subjected to the complex-order Fourier transform is obtained anal ytically with the ABCD matrix approach.