Dynamical characteristics of tightly focused vortex beams with different states of polarization

Abstract

We report a comparative study of the dynamical characteristics, including the energy, momentum, and angular momentum (AM), of tightly focused vortex beams with different states of polarization. Following Richards and Wolf vectorial diffraction formalism, the electric and magnetic field components of focused vortex beams with linear, circular, radial, and azimuthal polarizations are derived. A general theory to characterize the energy, momentum, spin AM (SAM), and orbital AM (OAM) of tightly focused vortex beams is introduced. Numerical simulations are performed on vortex beams with different polarization states focused by a high NA lens into water. These analytical and numerical studies show that the distributions of field, phase, and dynamical quantities depend on the sign and value of the topological charge carried by the focusing vortex beam, and are strongly affected by the states of polarization. For the vortex beams that do not carry SAM, the change of the sign of the topological charge has no effect on the transverse SAM and OAM, but leads to a reversal of the longitudinal SAM and OAM. For circularly polarized vortex beams, which do carry SAM, the change of the sign of the topological charge has no effect on the longitudinal SAM and transverse OAM, but leads to a redistribution of the transverse SAM and longitudinal OAM. Our results will be useful in revealing the mechanism of spin–orbit interaction within the tightly focused beams and providing new insights into the dynamical properties of focused vortex beams that may be important in applications including optical trapping and micro-manipulation.