Complex order fractional Fourier transforms and their use in diffraction theory. Application to optical resonators
Résumé
The electromagnetic field transfer by diffraction from a spherical emitter to a spherical receiver is expressed by a fractionalFourier transform whose order depends on the distance between the emitter and the receiver and their curvatureradii. Special attention is paid to complex order transforms: scaled variables and scaled field amplitudes are defined bycomplying with mathematical consistency. For a given distance of observation, a simple geometrical condition is set upto determine whether the corresponding transform order is a real or a complex number. The result is applied to checkthe stability of optical resonators.