Fractional Fourier transform of Ince-Gaussian beams.

Ince-Gaussian beams are introduced to describe the natural resonating modes produced by stable resonators, and they form the third completely orthogonal family of exact solutions of the paraxial wave equation. The fractional Fourier transform (FRFT) is applied to treat the propagation of Ince-Gaussian beams, and an analytical expression for an Ince-Gaussian beam passing through a FRFT system is derived. The normalized intensity distribution of an Ince-Gaussian beam in the FRFT plane is graphically illustrated with numerical examples, and the influences of the different parameters on the normalized intensity distribution are discussed in detail.