Beam-mode expansion applied to focal-region fields

Propagation properties of elementary beam modes are derived and used to examine the structure of the focal region of a focused aperture. Some general features of the field structure are obtained by approximating the field with a suitable fundamental Gaussian beam. The parameters governing the beam are found to be closely related to the Fresnel number of the system. It is then shown how the equations describing the fundamental mode are also applicable to a complete set of modes. The relationship between an analysis based on beam modes and a Fourier treatment is shown. Numerical results are presented which show the accuracy of field reconstruction for finite numbers of modes