By means of matrix optics technique the beam transfer matrix for one round trip in a spheric a l mirror resonator can be decomposed into two matrix product,it is shown that ea ch one corresponds to the fractional Fourier transform.The beam oscillator in a resonator can be regarded as a continually implementing fractional Fourier trans f orm process.The stability condition and the beam waist position for a resonator a re described by the fractional order.The fractional order can be complex.Proper extension is given. -