SU(N) Representation of Mode Dispersion in a Multimode Optical Fiber: Determining Principal Modes for Mode Division Multiplexing

A method is proposed to experimentally determine principal modes for mode division multiplexing in a multimode optical fiber, i.e., increasing optical fiber information capacity via higher-order transverse eigenmodes. Principal modes are a special linear combination of eigenmodes that do not exhibit mode dispersion up to first order in frequency. This method is based on an SU(N) representation of mode dispersion whereby the generators of the corresponding SU(N) Lie algebra, i.e., generalized Gell-Mann matrices, predict higher-order Stokes parameters which can be used to measure principal modes at the optical fiber input and output. Applications of the SU(N) representation to decoherence free subspaces for single photon entanglement in higher-dimensional Hilbert spaces is discussed.