Transformation properties of a Cosine-Gaussian beam in fractional Fourier transform plane

By using the Wigner distribution function(WDF) method, the transformation properties of a Cosine-Gaussian beam in the fractional Fourier transform plane are studied. Closed-form expressions for the intensity distribution and beam widths of Cosine-Gaussian beams in the FRFT's plane are derived and changes in the intensity distribution of Cosine-Gaussian beams with the order of the FRFT are illustrated with numerical examples. It is shown that the intensity in the FRFT plane depends on the fractional order, the variation of the on-axis intensity and beam width with fractional order are periodic, and the period is 2. A flat-topped beam can be achieved by a suitable choice of the transform order for the Cosine-Gaussian beams with the modulation parameter.