Decomposition techniques of exponential operators and paraxial light optics

The evolution operator formalism, combined with appropriate decomposition techniques of exponential operators, has revealed an effective strategy to treat evolution-like problems in both classical and quantum context. The continuous original equation is turned into a set of finite-difference equations, which preserve at a discrete level the basic features of the corresponding continuous model. The resulting scheme is easy to be encoded and demands for less computer time. The method can be applied to the paraxial gaussian optics, described by the one-dimensional parabolic wave equation. Within this contest, the formalism generates an explicit difference scheme, which provides a flexible numerical integration procedure, accounting for higher-order aberrations as well.