Fourier Mode Analysis Microstructured Optical Fibers

We formulate in a nonsimplified form a method for calculating modes of microstructured optical fibers based on the representation of the longitudinal components of field modes at the interfaces of media in the cross section of a fiber by Fourier polynomials in angular coordinates. The Fourier harmonic amplitudes are determined from the homogeneous algebraic system. Its matrix elements are determined based on the Green's theorem and are represented by the integrals of regular functions. The applicability of the method is limited by the only requirements that the contours of inclusions and of the external boundary of a fiber must be described by single-valued functions of angular coordinates. In the particular case of a circular dielectric waveguide, the method gives an exact analytic solution of the waveguide problem. We have obtained the estimates of the intrinsic convergence of the method relative to the order of Fourier polynomials in the calculation of modes of a dielectric elliptical waveguide and microstructured fibers with elliptical inclusions. It is found that damping factors of the modes are determined to a considerable extent by the internal microstructure and the outer boundary of the fiber.