ALGEBRAIC APPROACH TO CHARACTERIZING PARAXIAL OPTICAL-SYSTEMS

The paraxial propagation formalism for ABCD systems is reviewed and wr itten in terms of quantum mechanics. This formalism shows that the pro pagation based on the Collins integral can be generalized so that, in addition, the problem of beam quality degradation that is due to aberr ations can be treated in a natural way. Moreover, because this formali sm is well elaborated and reduces the problem of propagation to simple algebraic calculations, it seems to be less complicated than other ap proaches. This can be demonstrated with an easy and unitary derivation of several results, which were obtained with different approaches, in each case matched to the specific problem. It is first shown how the canonical decomposition of arbitrary (also complex) ABCD matrices intr oduced by Siegman [Lasers, 2nd ed. (Oxford U. Press, London, 1986)] ca n be used to establish the group structure of geometric optics on the space of optical wave functions. This result is then used to derive th e propagation law for arbitrary moments in general ABCD systems. Final ly a proper generalization to nonparaxial propagation operators that a llows us to treat arbitrary aberration effects with respect to their i nfluence on beam quality degradation is presented.