An analytical solution for electromagnetic wave scattering by multiple wedges

In this work an analytical solution to the problem of electromagnetic wave diffraction by multiple coplanar wedges is found by means of an infinite-order discrete superposition of non-integer cylindrical waves, i.e. products of a non-integer order Bessel function times an exponential factor. The evaluation of the expansion coefficients is accomplished by imposing the boundary conditions on every side of the geometry; the corresponding equations are solved in a ‘weak form’, i.e. by representing the dependence of the boundary fields with respect to the radial abscissa in terms of an expansion over a set of Laguerre orthogonal polynomials. A detailed study is carried out for estimating accuracy performances relevant to the finite-order numerical implementation of the method.