The paraxial wave equation in one space dimension is reconsidered from the viewpoint of the Lie algebra formalism, according to a method which is well documented in the literature (Kalnins and Miller Jr 1974 J. Math. Phys. 15 1728). As a result, we obtain the expression of the general solution of the wave equation in Cartesian coordinates. Although such a solution is not new, being recently reported (Bandres and Gutiérrez-Vega 2007 Opt. Lett. 32 3459), the formalism applied here may give a deeper insight into the nature of such a solution, also revealing interesting relationships between apparently unrelated formulations. © IOP Publishing Ltd.
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics