By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.
