Abstract
Electric and magnetic fields of the Gaussian beam of light are analyzed on the basis of Maxwell's equations without using scalar wave approximation. Field components of the planepolarized electric (or magnetic) mode or the TE (or TM) mode are explicitly described in terms of solutions of a Helmholtz equation.
Generalized solutions of the Helmholtz equation are derived and two sets of Hermite-Gaussian functions are analyzed: one is a concise form of mode functions with complex variables of Hermite polynomials, and the other is a conventional form which is expressed with real variables. Transformation between these two sets of mode functions is given.
