A New Method for Calculating Dispersion Curves and Guided Waves of Optical Waveguides

Optical waveguides are dielectric cylindrical structures that can conduct electromagnetic energy in the visible and infrared parts of the spectrum. The waveguides used in optical communication are flexible fibers made of transparent dielectrics. The cross section of a waveguide usually consists of three regions: the central region (core) is surrounded by a cladding which, in turn, is surrounded by a protective coating. The refractive index of the core can be constant or can vary over the cross section; the refractive index of the cladding is usually constant. The coating is optically isolated from the core; for this reason, it is usually neglected in mathematical models, and it is assumed that the cladding is unbounded from the outside. We use the classical model, in which the waveguide is assumed to be unbounded and linearly isotropic; i.e., the refractive index n of the waveguide is invariable along the axis O_x3 and is a piecewise continuous function of the transverse coordinates: n=n(x), where x=(x₁, x₂) isin R²