Efficient calculation of electromagnetic diffraction in optical systems using a multipole expansion

The field distribution in the focal region of a high-aperture optical system is calculated using an expansion into multipole components. For any angular illumination distribution and numerical aperture, the incident field is expanded into spherical harmonics and the field in the focal region is then determined by a sum of multipole fields. These are expressed as analytic expressions in terms of associated Legendre functions and spherical Bessel functions, thus avoiding computational problems in evaluation of diffraction integrals. As a result, focal distributions can be calculated much more efficiently than by using direct quadrature.