The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.
© 1994 Optical Society of America
Original Manuscript: April 28, 1994
Published: November 1, 1994
Haldun M. Ozaktas and David Mendlovic, "Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators," Opt. Lett. 19, 1678-1680 (1994)