Modeling of photonic crystal fibers

This paper presents an analysis and an overview of characteristics and possible applications of periodic and quasi-periodic photonic crystal fibers (PCF). The analysis is based on the decomposition of the transverse electric field into a series of orthogonal modes which are used to solve the vector wave equation for optical fibers. Two different sets of orthogonal functions are used and compared. The first are Hermite-Gaussian functions which are localized and a small number of terms is needed to describe the field in the observed fiber. The second choice is cosine functions which are not localized and therefore allow the extension of this approach to the calculation of the external field. The results of the analysis are also used to describe the characteristics of PCF and demonstrate the possibilities of custom tailoring some of the fiber properties.