We describe an improved differential method for calculating the leaky modes of finite size microstructured optical fibres. This method, which includes the fast Fourier factorization method, is used here in cylindrical coordinates. The method utilizes a reformulation of the Maxwell equations in a Fourier space taking into account the Fourier expansion truncations and the possible discontinuities of the permittivity. For waveguides fulfilling C_nv symmetries, the symmetry properties of the modes are established in Fourier space for cylindrical coordinates in real space. This result allows us to reduce the required computer resources. The method can deal with arbitrary cross-section microstructured optical fibres made of inhomogeneous inclusions or matrix. We validate the method through several comparisons with the well established multipole method and with other methods. We also illustrate the application of the differential theory to calculate the modal properties of complex microstructured optical fibres that cannot be studied with the multipole method.

42.81.-i Fiber optics

02.30.Uu Integral transforms

Mathematical physics

Optics, quantum optics and lasers

Issue 7 (July 2007)

Received 4 May 2007 , accepted for publication 4 June 2007

Published 25 June 2007