Fields of a Gaussian beam beyond the paraxial approximation

Analytic expressions for the fields of a tightly focused Gaussian laser beam are derived, accurate to epsilon(11), where epsilon is the diffraction angle. It is found that, for example, using the derived fields, the calculated power can be about 25% more accurate than when calculated using the paraxial approximation for a beam focused down to a waist radius w(0) similar to 0.4 lambda, where lambda is the wavelength.