Analytical Formulation of Supermodes in Multicore Fibers With Hexagonally Distributed Cores

The supermodes in 19-core multicore fibers (MCFs) with identical hexagonally distributed cores are analyzed in detail by using the coupled mode theory and matrix operation. The analytical formulations for both the propagation constants and modal distribution vectors of the supermodes are derived. Simulation results show that the analytical results agree well with the numerical results. In addition, the features of the effective indices and modal distributions of the supermodes are discussed by using the analytical expressions combined with the applications. The analytical expressions provide a fast and accurate method to reveal the properties and characteristics of the supermodes for MCFs and are helpful for the design and applications of MCFs.