  The paper aims at presenting a didactic and self-contained overview of
Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach
for deriving these modes is to solve the Helmoltz electromagnetic wave equation
within the paraxial approximation. Here, a different technique is presented:
Using the plane wave representation of the fundamental Gaussian mode as seed
function, all higher-order beam modes are derived by acting with differential
operators on this fundamental solution. Even special beam modes as the recently
introduced Bessel beams are easily described within that framework.
