High-aperture Gaussian beams

Gaussian beams are an important fundamental concept of optics. They occur naturally in the treatment of laser beams and resonators, and can also be used as a basis for study of general diffraction problems. However, a limitation of the usual formulation of Gaussian beams is that they are derived using a paraxial approximation. This breaks down when beam divergence is large. Moreover, for investigation of the polarization properties of beams a vectorial treatment is necessary. Numerous authors have considered correction terms which extend the validity of the beams to higher divergence angles. An alternative is to derive a form of beam which is an exact solution of the wave equation for the scalar case or Maxwell's equations for the vectorial case. This can be accomplished using the complex source point method. However, this leads to the presence of unphysical singularities. These can be avoided by introducing complex sink-source pairs. The resulting solution is a rigorous solution of Maxwell's equations which reduces to a conventional Gaussian beam for small angles of divergence. The resonance conditions for a resonator can be derived. Various different polarizations can also be considered, including plane polarized, transverse electric and transverse magnetic modes.