Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section.

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.