Tightly focused field modulated by spiral phase with an off-axis singularity

We examine the influences of an off-axis singularity in spiral phase on the tightly focused field. Through vectorial diffraction theory, the tightly focused fields modulated by the off-axis singularity displacements and polarization states have been presented and analyzed. The results demonstrate that, the intensity patterns in the focal plane transform along the direction determined by the off-axis singularity displacement and handedness of spiral phase. The off-axis singularity induces the transverse intensity patterns rotate along the propagation, and the direction of rotation is corresponding to the handedness of spiral phase. The profiles and transformation degree of all intensity patterns are dependent on off-axis singularity displacement, polarization state and amplitude distribution of incident light beam. Collaborating with polarization and amplitude modulation, the off-axis singularity in spiral phase is helpful to construct various tightly focused fields potentially applied in these areas, such as optical imaging, manipulation or measurement.