We have generalized the ABCD propagation law, Q2 = (AQ1 + B)/(CQ1 + 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.
© 1991 Optical Society of America
P. A. Bélanger, "Beam propagation and the ABCD ray matrices," Opt. Lett. 16, 196-198 (1991)