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

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 w0, 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 w0 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.