Far-field structure of a linearly polarized plane wave diffracted by a rectangular aperture

A description of a linearly polarized plane wave diffracted by a rectangular aperture is directly derived from the Maxwell's equations. Based on the vector angular spectrum representation of the Maxwell's equations, the diffracted plane wave is decomposed into the TE and TM terms. By means of the method of stationary phase, the analytical expressions for the TE and TM terms are presented in the far field. As the TE and TM terms are orthogonal to each other in the far field, their sum constitutes the physical pattern of Fraunhofer diffraction. The influence of the linearly polarized angle on the far field structure is also investigated with a numerical example.