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 inc ident field is expanded into spherical harmonics and the held in the f ocal region is then determined by a sum of multipole fields. These are expressed as analytic expressions in terms of associated Legendre fun ctions and spherical Bessel functions, thus avoiding computational pro blems in evaluation of diffraction integrals. As a result, focal distr ibutions can be calculated much more efficiently than by using direct quadrature.