An electromagnetic theory of dielectric waveguides with multiple embedded cylinders

We consider a dielectric waveguide or optical fiber having a real isotropic ambient refractive index. In addition, several isotropic and uniform embedded cylindrical regions of differing refractive index are considered. The radii, refractive indexes, and positions of the cylindrical subregions are arbitrary. We establish a rigorous method of determining the fields and propagation constants for the vector electromagnetic modes supported by this structure. We verify the accuracy of the method by comparing its results with those of other authors in particular cases, and exhibit direct demonstrations of convergence.< >