Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation

The exact electric field vectors of the higher-order Hermite-Gaussian and Laguerre-Gaussian beams are derived from the transverse component of the electric field given at the z = 0 plane by use of the angular spectrum method and the electric field divergence theorem. The total beam powers are proved to be conserved along the beam propagation direction. The power-series solutions are also obtained from the exact solutions by use of Lommel's lemma. It is shown that the power-series solutions exactly satisfy Lax's equations [Phys. Rev. A 11 (1975) 1365]. (C) 1999 Published by Elsevier Science B.V. All rights reserved.