Spatial principal states and vortex modes in optical fiber for communications

Abstract

Using SU(N) group theory, we develop a formalism to superimpose N vortex modes and form N orthogonal principal states in fiber. These principal states provide a means to overcome the detrimental effects of mode coupling that occur in optical communications links. This formalism reduces to the Jones matrix eigenanalysis when N equals 2, which has been studied extensively to characterize polarization mode dispersion. Specifically we use the 4 vortex modes of the LP11 modal group to establish the principal states and we graphically display them using the higher order Poincare sphere, HOPS. For polarization mode dispersion and N = 2, we require 3 Pauli spin matrices and consequently 3 mux demux components to generate the Principal states. For N = 3, we use the 8 Gell Mann matrices and 8 components. For N = 4 as is the case for 4 the vortex modes of the LP11 modal group, we require 15 generators and 15 physical components, since these systems scale as N^2-1. The LP11 modal group includes the HE21 horizontal and vertical vortex modes as well as the transvers electric and transverse magnetic vortex modes. As an example, we describe in some detail a link with 3 and separately one with 4 principal states, which are superimposed from the vortex modes. We also show schematically the active and passive components required to multiplex and demultiplex the principal states.