The fundamental solution to Laplace equation can be given by a basis of Theta functions. This means that the Theta functions are the eigenvectors of the eigenvalue problems for Laplace operator. In this way the solutions for laser equation present a representation of a semi-simple Lie algebra. This analogy have been explained in the works of Kac, and specially in a short article by him on Laplace operators associated to Kac-Moody algebras. There is also a short explanation in his famous book; infinite dimensional Lie algebras. I believe that this insight can explain some perspectives to physicists or the people who work in optic.

Mohammad