Dipole-wave theory of electromagnetic diffraction

A theory of diffraction is presented which systematically employs the wave approach used in the Kirchhoff method and, unlike the Kirchhoff integral, does not have severe applicability limitations. The diffraction problem is solved by using the Hertz vector instead of the field vector used in the Kirchhoff integral. The basic diffraction problems for linearly, radially, and azimuthally polarized radiation are solved analytically. The key qualitative feature of the solutions is the presence of 'poles' — zero field points within the diffraction pattern of light and dark fringes. The poles lie along the direction of the electric field vector. The solutions obtained satisfy the Maxwell equations and the reciprocity principle.