Diffraction-limited optical focusing with arbitrarily oriented magnetic field

In this paper, an approach to create diffraction-limited optical focal spots with arbitrarily oriented magnetic dipolar field components in 4Pi microscopy configuration is proposed. This is achieved by focusing two counter-propagating modulated vector beams consisting of complex intensity and polarization distribution. Through combining the magnetic dipole radiation pattern and the Richards–Wolf vectorial diffraction method, the required illuminations at the pupil plane of a 4Pi focusing configuration for the reconstruction of magnetic dipole focal field are found analytically. Furthermore, the orientation of the doughnut shape focal field can be rotated arbitrarily by modulating the pupil field distribution carefully. As an extension, a three-dimensional optical bubble encloses a transverse spin magnetic field can be obtained by introducing a second magnetic dipole oriented in the orthogonal plane with appropriate amplitude and phase differences. (paper)