Vector diffraction theory for electromagnetic waves

Abstract

The scalar Huygens–Fresnel principle is reformulated to take into account the vector nature of light and its associated directed electric and magnetic fields. Based on Maxwell’s equations, a vector Huygens secondary source is developed in terms of the fundamental radiating units of electromagnetism: the electric and magnetic dipoles. The formulation is in terms of the vector potential from which the fields are derived uniquely. Vector wave propagation and diffraction formulated in this way are entirely consistent with Huygens’s principle. The theory is applicable to apertures larger than a wavelength situated in dark, perfectly absorbing screens and for points of observation in the right half-space at distances greater than a wavelength beyond the aperture. Alternatively, a formulation in terms of the fields is also developed; it is referred to as a vector Huygens–Fresnel theory. The proposed method permits the determination of the diffracted electromagnetic fields along with the detected irradiance.