On Diffraction and Radiation of Electromagnetic Waves

Inasmuch as it is rarely possible to treat diffraction of electromagnetic waves exactly, the Kirchhoff formulation of Huygens' Principle has been frequently used in approximate calculations. If the Kirchhoff formula is applied directly to the field intensities of the incident wave over the aperture, the diffracted field is found to be inconsistent with Maxwell's equations. If, on the other hand, this formula is applied to some auxiliary vector potential from which the diffracted field is subsequently deduced by differentiation, the result (although consistent with Maxwell's equations) depends on the particular choice of the auxiliary vector and in some instances, at least, is obviously unreasonable (Appendix III). The calculations of diffracted fields and radiation fields, based either on the Equivalence Principle or on the more general Induction Theorem, depend upon a priori verifiable approximations to the actual fields in the neighborhoods of the sources of the diffracted and radiated waves. For this reason we feel that these methods are preferable to those based on the Kirchhoff formula.