Quantized optical orbital angular momentum precession and nutation in a twisted light

Abstract

In a subject of ‘optical angular momentum (OAM) and optical vortex’, a twisted light (also referred to as a ‘spiralling optical field’) possesses a helical wavefront. Recently, a new advance in the twisted light is Rego et al's discovery of self-torque effect that can cause an intrinsic angular acceleration (DOI:10.1126/science.aaw9486). Such a self-torque effect gives rise to a time-varying optical orbital angular momentum. Then we believe that the time-dependent OAM of this vortex laser beam can lead to non-trivial evolution of the OAM state vector. It is expected that the information on the self-torque of a twisted optical field might be reflected in an extra phase shift and, based on this, we study the possible precession and nutation evolution of a quantized optical orbital angular momentum in such a twisted light. The relevant effects such as non-cyclic non-adiabatic ‘geometric’ phase and dynamical phase due to the angular momentum precession and nutation in the vortex beam are also included. An effective Hamiltonian characterizing the optical vortex precession and nutation is constructed and the time-dependent wave equation is solved. The result obtained in this paper could be utilized in treating the polarization evolution and possible mechanical (force) effect of twisted optical fields that can exhibit the self-torque phenomenon.