Relationship of scattering from the PEC screen with infinite periodicity and its complementary structure

In this paper, the relationship is addressed between the scattering from the perfect electric conductor (PEC) screen with periodicity and its complementary structure. The Babinet´s principle describes the basic relationship of the scattering fields from the PEC screen and its complementary structures. The Babinet´s principle for periodic structures can be simply proved by applying the integral equation (IE) formulation with periodic Green´s function. The details of the proof will be shown in the conference. In addition, the relationship for the reflection and transmission coefficients between the PEC screen with periodicity and its complementary structure is derived in this paper. For periodic apertures perforated from the screen, one can apply integral equations about the electrical current on PEC part of the screen. However, the unknown density near the aperture should be made large enough to achieve the accurate solution for the scattering. In contrast, it will be easier to achieve the convergence of solution if one solves the integral equation for the electrical current on PEC patches in its complementary structure. Then one can find the reflection and transmission coefficients for the original structure by applying the derived relationship to those for its complementary structure.