A new differential theory is developed for studying mode propagation in microstructured optical fibers (MOFs) with arbitrary cross section. The present method called Fast Fourier Factorization initially applied on gratings has been generalized to anisotropic and/or inhomogeneous media described in cylindrical coordinates. Thus, a new formulation of Maxwell equations are written in a truncated Fourier space taking account to the development truncations and discontinuities of opto-geometrical quantities. In the case of isotropic and homogeneous medium, the achieved first order differential set may be resolved with suitable algorithm which changes the boundary-value problem into an initial-value problem. To avoid numerical contaminations, the S-propagation algorithm is used. The numerical implementation of the FFF method is validated by comparison with the results computed with the Multipole Method for a six hole MOF. Then, new results for a MOF profile that cannot be directly studied with the Multipole Method are given.