Green's function approach to propagation in fibres of arbitrary cross section

Abstract

An attempt has been made to obtain a formally exact solution, based on Green's function of the scalar wave equation for step-index fibres of arbitrary cross-sectional shape. The wave functions in the core and cladding are expanded in a series of basis functions (appropriate to cylindrical coordinates), and the expansion coefficients along with the characteristic equation of the problem are derived in a matrix notation. Compared with the earlier similar treatments of the problems, the present formalism is very general in the sense that it does not assume any special symmetry property of the cross-sectional curve or of the underlying solutions. The theory is applied to fibres that are only slightly deformed about a circular shape. Explicit algebraic and (or) numerical results are obtained for the allowed propagation constants, fields, and the group delay of a few low-ordered modes.