Topology of Surface Plasmon Polaritons with Integer and Fractional Orbital Angular Momentum

The topology of surface plasmon polariton fields (SPPs) with orbital angular momentum (OAM) is characterized by the winding numbers of the phase singularities in the field, also known as topological charges. Using theoretical expressions for the surface plasmon fields, we identify the phase singularities as points where the field is zero and investigate their properties for both integer and noninteger, or fractional, orbital angular momentum. The phase singularities act as vortex centers for the rotating fields. We analyze the behavior of the vortex-antivortex pairs and the breakup of the central vortex and discuss their influence on the measured topology as the orbital angular momentum changes from one integer value l to the next l +1 via the fractional states. Our work highlights the fact that measures of the topological charges do not always equate with the orbital angular momentum and shows how the topology can change discontinuously, even though all of the parameters controlling the fields change smoothly.