We developed a matrix theory that applies to any cylindrically symmetric fiber surrounded with Bragg cladding, which includes both the Bragg fibers and the recently proposed dielectric coaxial fibers. In this formalism,an arbitrary number of inner dielectric layers are treated exactly and the outside cladding structure is approximated in the asymptotic limit. An estimate of the radiation loss of such fibers is given. We compare the asymptotic results with those obtained from the finite difference time domain (FDTD) calculations and find excellent agreement between the two approaches.
Yong Xu, George X. Ouyang, Reginald K. Lee, and Amnon Yariv, "Asymptotic Matrix Theory of Bragg Fibers," J. Lightwave Technol. 20, 428- (2002)