Universal Characteristic Equation for Multi-Layer Optical Fibers

[EN] Optical fibers featuring multi-layer refractive index profiles have been widely investigated and developed in a variety of scenarios, including space-division multiplexing transmission, fiber sensing, loss and dispersion management, as well as high-power amplifiers and lasers. For the first time to our knowledge, we present in this paper a general model deriving the universal characteristic equation for multi-layer optical fibers that comprise a set of concentric layers with arbitrary radial dimensions and refractive index values, considering both stepped (as step-index) or continuous (as graded-index) profiles. Expressions for the main fiber propagation parameters are also derived. We validate the model by comparing our results to the ones provided by numerical software tools with excellent matching for a series of particular optical fibers comprising step-index trench-assisted, ring-core, triangular-index and four-cladding profiles. This compact universal characteristic equation serves as a useful tool for optical fiber designers, where one can get valuable physical insights without the need to resort to numerical software tools, and even evaluate the effect of a single layer in isolation without the need to evaluate the whole refractive index structure.
This work was supported in part by the European Research Council (ERC) under Consolidator Grant Project 724663, and in part by the Spanish MINECO under TEC2016-80150-R project, BES-2015-073359 scholarship for S. Garcia and Ramon y Cajal fellowship RYC-2014-16247 for I. Gasulla.