Abstract
Fields in free space are able to carry orbital angular momentum, which may arise when a system is invariant under rotations. Such systems favour a description in cylindrical polar coordinates. Solutions of the wave equation in these coordinates are Bessel beams, invariant under propagation in the longitudinal direction.Some fields also possess spin angular momentum, such as the optical vector field and the electron spinor field. These fields are described by multicomponent wavefunctions, in contrast to a scalar (spinless) field. The resulting spin degree of freedom can be quantized by either the longitudinal direction (spin) or the momentum vector (helicity). Differences between helicity and spin states are in general small and disappear in suitable limits.
Spin and orbital angular momentum couple to each other, yielding fields that are eigenstates of the total angular momentum. The effects of this coupling can be studied by considering the mechanical properties of the fields. There is an orbital contribution, arising from the multicomponent nature of the wavefunctions, and a spin contribution.
Combining fields with circular polarization gives rise to states with linear polarization, analogous to constructing standing waves from travelling waves, or creating a real Majorana field from two complex spinor fields. Fermionic Majorana modes, rather than particles, can be constructed with equal contributions of positive and negative frequencies. These modes carry no charge and are invariant under charge conjugation, conditions optical modes satisfy trivially. However, symmetry considerations lead to the conclusion that optical Majorana modes are linearly polarized. There exist bound optical modes analogous to fermionic Majorana modes, but there are also photonic Majorana modes possible that do not have fermionic counterparts.
The coupling between orbital and spin angular momentum changes considerably in systems described in parabolic coordinates, as the basis states are eigenstates of the parabolic momentum instead. There is only an effective spintoorbital angular momentum coupling and a spintoparabolicmomentum coupling close to one Cartesian coordinate axis.
Date of Award  23 Jan 2019 

Original language  English 
Awarding Institution 

Supervisor  Mark Dennis (Supervisor) 