Analytical non-paraxial TM polarized Gaussian beam in the source region

Abstract

The non-paraxial TM polarized Gaussian beam, which approximately reduces to be a Gaussian TEM00 mode at the paraxial case, is the rigorous solution of Maxwell's equations for a confocal resonator. By means of mathematical techniques, the analytical expression in the source region has been derived without any approximation and expressed as a sum of the propagating part and the evanescent part. With some certain given values of the initial Gaussian half width w 0, the distributions of the squared modulus of the propagating part, the evanescent part, and the whole beam are depicted in the reference plane close to the source. When w 0 is small enough, the squared modulus of the non-paraxial TM polarized Gaussian beam is composed of two lobes, which results from the contribution of the evanescent wave. This research further reveals the difference of a non-paraxial TM polarized Gaussian beam from a non-paraxial Gaussian beam.