Nested SU(2) symmetry of photonic orbital angular momentum - Saito, Shinichi (Frontiers in Physics, 2023)
The polarisation state is described by a quantum mechanical 2 level system, which is known as special unitary group of degree 2, SU(2). Polarisation is coming from an internal spin degree of freedom inherent to photons, while photons also have orbital degree of freedom. Fundamental understanding on the nature of spin and orbital angular momentum of photons is very important to utilise the degrees of freedom for various applications in optical communications, computations, sensing, and laser-patterning. Here, we show orbital angular momentum of coherent photons emitted from a laser diode can be incremented by a vortex lens, and the magnitude of orbital angular momentum is increased upon an increase of the topological charge inside the mode. The superposition state of left and right vortices is described by the SU(2) state, similar to polarisation, however, the radius of the corresponding Poincar é sphere depends on the topological charge.Consequently, we expect a nested SU(2) structure to describe various states with different magnitude in orbital angular momentum. We have experimentally developed a simple system to realise an arbitrary SU(2) state of orbital angular momentum by controlling both amplitudes and phases of left and right vortices using spin degree of freedom, whose interplays were confirmed by expected far-field images of dipoles and quadruples.