This work is positioned at the junction of optical communication in particular and communication theory of large. From an optical transmission point of view it ddresses the issue of efficiently uti­lizing the available optical resources of polarization, phase, amplitude, time and wavelength. From an abstract communication theory point of view, it brings a physically-inspired Stokes parameters outlook to the general problem of quadratic detection.  A novel generalization applica­ble to arbitrary dimensions is developed for the four real-valued parameters introduced into optics by Stokes in 1853 to characterize  the State-Of-Polarization of an optical beam, in effect extend­ing the Poincare sphere description of polarization and its Mueller matrix transformation to multi­ple arbitrary dimensions,  leading to optimal non-coherent receiver structures consisting of a bank of correlators against the transmitted Stokes vectors, followed by non-linear post processing. The union bound probability of error performance of the optimal Stokes parameters Shift Keying (SPSK) receiver is derived for arbitrary constellations of Stokes vectors yielding closed-form formulae. Novel extensions of POLSK and DPSK optical transmission are proposed and ana­lyzed, considering transmission blocks containing multiple symbols and/or combined simulta­neous modulation of amplitude and differential phase.

The optimal ML/MAP detector for the vector incoherent channel was alternatively formulated in the Jones, Coherency Matrix and Stokes signal spaces. All systems came to be viewed in a novel unified framework - multi-dimensional Stokes Signal Space. We provide ample evidence indicat­ing that Stokes space is the natural domain to represent incoherent transmission constellations over the vector incoherent channel.