Analysis of the electromagnetic wave diffraction by 2D micro-optics objects using the decomposition in terms of cylindrical functions

We propose a method to calculate the intensity distribution resulting from the diffraction of plane TE- or TM-waves by a dielectric homogeneous cylinder of arbitrary cross-section. With this method, the field within and outside the cylinder is decomposed into a series in terms of cylindrical functions, representing the partial solutions of the Helmholtz's equation. The series coefficients are being found from the condition that the internal and outside fields should be conjugate on the cylindrical object interface. A method for calculating the field of a plane wave diffraction by a multi-layer dielectric cylinder of circular cross-section is also proposed. For the number of homogeneous layers greater than two the problem is reduced to solving a linear set of algebraic equations, while with only two layers the analytical relationships for the diffraction field have been derived. The intensity distribution resulting from diffraction of the plane TE-wave by a two-layer dielectric cylinder is numerically simulated using two methods - a finite elements method and via analytical formulae.