Universal Characteristic Equation for Multi-Layer Optical Fibers

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.