Generation of tunable three-dimensional polarization in 4Pi focusing system

We show that, by uniformly modulating the amplitude or polarization of one half of the input beam, a tunable three-dimensional (3D) polarization field near the focus of a 4Pi focusing system can be generated. If the input field is radially polarized and modulated by an amplitude-phase modulator, the longitudinal component of the focused field will partially convert to the transversal one according to the modulation factor and a 3D linear polarization state is created. If the input field is circularly polarized in one half and elliptically polarized in another half, the focal field will have elliptical polarization with the normal to the polarization ellipse being 3D controllable, corresponding to a 3D controllable spin angular momentum.