Systematic approach to connect density-matrix formalism and Stokes formalism for modal analysis in mode-division multiplexing optical-fiber communication systems

Based on some general properties of the Gell-Mann operators, we establish systematic connections between the density-matrix formalism and the Stokes formalism for modal analysis of mode-division multiplexing optical-fiber communication systems. We present analytical formulas to connect key quantities, differential evolution equations, transformations, concatenation rules, and observable information in the two formalisms, such that researchers employing different formalisms can handily communicate with each other. The underlying approach offers a more regular and concise way to derive existing formulas in the Stokes formalism, and more importantly, it also allows for acquiring useful new formulas in the Stokes formalism. With the formal connections, we examine the equivalence of statistical models in the two formalisms, and conduct numerical simulations on the modal properties of a randomly-perturbed 4-mode fiber. The numerical results suggest that the conditions for treating different mode groups separately in modal analysis could be more stringent than previously conceived in literature. Also, the agreement in numerical results obtained from the two formalisms verifies the applicability of the theoretical connections.