  We theoretically investigate a nanoscale mode-division multiplexing scheme
based on parity-time (PT) symmetric coaxial plasmonic waveguides. Coaxial
waveguides support paired degenerate modes corresponding to distinct orbital
angular momentum states. PT symmetric inclusions of gain and loss break the
degeneracy of the paired modes and create new hybrid modes without orbital
angular momentum. This process can be made thresholdless by matching the mode
order with the number of gain and loss sections within the coaxial ring. Using
both a Hamiltonian formulation and degenerate perturbation theory, we show how
the wavevectors and fields evolve with increased loss/gain and derive
sufficient conditions for thresholdless transitions. As a multiplexing filter,
this PT symmetric coaxial waveguide could help double density rates in on-chip
nanophotonic networks.
