Modes of a Bragg fiber with a cladding made of delta functions

The Bragg fibers have been extensively developed for the last 20 years. However, to improve understanding of their properties, a simple analytical theory of them is necessary. A theory based on the approximation of thin fuzzy layers by delta functions in the scalar wave equation has been developed. Two models are discussed: a plane waveguide model, and a realistic cylindrical fiber model. The former leads to simple formulas for the guided (Bragg) modes, which can be used to estimate qualitively the main properties of the Bragg fibers (including radiative losses) and optimize their structure. The latter is to be applied to calculations of parameters of realistic fiber structures. The developed theory can be useful for designing Bragg fibers, because it is simpler and in many respects closer to real fibers than the widely used model with sharply bounded homogeneous layers.