Exact solution of the plane wave diffraction by multiple rectangular holes in a thin screen

The KP method is applied to rigorously formulate an electromagnetic field diffracted by multiple rectangular apertures in an infinite conducting screen with an infinitesimal thickness. The diffracted field is expanded in terms of the Weber-Schafheitlin (WS) integrals and the expansion coefficients are given in the form of the matrix equation whose elements consist of double infinite integrals that include the Bessel functions and trigonometric functions. Since the KP method yields a solution that satisfies all boundary conditions and the proper edge condition, we can obtain highly accurate and fast convergent numerical results. Therefore, the derived expression serves as the reference solution to evaluate the accuracy of conventional numerical techniques, such as the FDTD method.