  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.
