Evaluation of periodic Green function and its derivations by interpolation polynomial in diffraction problems

Consider multielement d-periodic grating in homogeneous isotropic media with wave number X. One (curvilinear) period of the grating contains N cylindrical perfectly conducting screens with generatrices parallel to Oz axis. Cross-sections of the screens by xOy plane are open smooth Lyapunov type contours. The grating is illuminated by a unit amplitude plane electromagnetic wave. Such structure may serve as one of the models for scatterers system, which has resonance features.