The Gaussian wave solution of Maxwell's equations and the validity of scalar wave approximation

We present an exact solution of Maxwell's equations for a non-paraxial Gaussian wave. Paraxial vectorial and paraxial scalar approximations of the exact solution are also obtained. We examine in detail, via several numerical examples, the validity conditions for the paraxial scalar and paraxial vectorial approximations when compared to the exact solution. Our findings show that when the half width of the beam waist is greater than 10 lambda the paraxial scalar approximation yields accurate results. When, however, the half width of the beam waist is comparable to the wavelength the exact solution predicts significant deviations from the paraxial scalar approximation. These results might prove important in semiconductor laser research. (C) 1998 Elsevier Science B.V. All rights reserved.