Propagation properties of a non-canonical vortex beam in a high numerical aperture system

A non-canonical vortex is an optical helical phase structure with the same topological charge of a canonical vortex but different phase distributions. Based on the Richards&Wolf vectorial diffraction theory, the expression for the strongly focused, linearly polarized non-canonical vortex beam is derived, and its propagation properties are studied numerically in the focal region. It is that the transverse focal shift does not only occur in the strongly focused, off-axis (or on-axis) canonical vortex beams, but also can be seen in a strongly focused, non-canonical vortex beam. The transverse focal shift in these two fields have the same form, but the factors influencing them are quite different. It is also demonstrated that because of the transverse focal shift, if both the semi-aperture angle and the phase distribution factor meet a certain requirement, the total field intensity pattern in the focus region can rotate clockwise in the propagation direction, while the intensity maxima will also rotate 180° from the negative half space to the positive half space. The result will provide a new way for controlling the field distribution in structured fields, which may be applied in optical tweezers.