Beam propagation and the ABCD ray matrices

We have generalized the ABCD propagation law, Q(2) = (AQ(1) + B)/(CQ(1) + D), for an optical system by introducing a generalized complex radius of curvature Q for a general optical beam. The real part of 1/Q is related to the mean radius of curvature of the wave front, while the imaginary part is related to the second moment of the amplitude of the beam.