抄録
An accurate numerical solution is presented for the excitation problem of guided modes of a slab waveguide at a plane wave incidence, where a finite periodic array of strips is used for excitation. This system is one of the typical models of grating couplers. The problem is two-dimensional and only the TE mode is treated. We derive a set of singular integral equations and solve it by the moment method, where the Chebyshev polynomials are successfully used as the basis and the testing functions. Numerical calculations are carried out under the condition that the error on the optical theorem is less than 0.1%. It is shown that the frequency which yields maximum excitation efficiency is somewhat different from one predicted by the Bragg condition. We also confirm that too many strips lead to deterioration of the efficiency. The calculations predict that the efficiency of the first even mode at its maximum is 37%.
