Far-field method for the characterisation of three-dimensional fields: vectorial polarimetry

Abstract

In the search for increasing the resolution of an optical system it is usually necessary to increase its numerical aperture (NA). For high NA the scalar theory of diffraction is no longer applicable and the vectorial nature of the electromagnetic (EM) field cannot be ignored. In this case, the EM field in the focal region of the system must be described using a vectorial theory of diffraction. An important consequence of focusing with high NA, as predicted by the vectorial theory of diffraction, is the appearance of a longitudinal component of the field, comparable to the transversal components in the focal region. In conventional polarisation microscopy, even when high NAs are used, only the transversal components are considered for the analysis of the specimen. Although this approach has been proved to be adequate in a number of applications, it ignores the potentially valuable information contained in the longitudinal component. The Z-polarized microscope, introduced by Huse et al. [J. Biomed. Opt. 6 (2001) 480], showed the other side of the approach. That is, the Z- polarized microscope only considered the interaction of the longitudinal component with the sample, ignoring the information contained in the transversal components. In this work, we present an alternative far-field method for the anal- ysis of the three-dimensional EM field resulting from the interaction of a tightly focused field and a sub-resolution scatterer. The method proposed here is based on the analysis of the scattering-angle-resolved polarisation state distribution across the exit pupil of a high NA objective lens and it is proved to yield high sensitivity in sub-resolution displacements of a sub-resolution specimen.