A vector Huygens-Fresnel model of the diffraction of electromagnetic waves

Abstract

The scalar Huygens-Fresnel Principle describing the propagation of light is reformulated to take into account the vector nature of light and the associated directed electric and magnetic fields. A vector Huygens secondary source is developed in terms of the fundamental radiating units of electromagnetism: the electric and magnetic dipoles. The vector Huygens wavelets are incorporated into a computer model that calculates the resulting vector fields after light passes through a diffracting system by a wavefront reconstruction process similar to that originally proposed by Huygens himself in 1687. Fresnel and Fraunhofer diffraction patterns are computed for common apertures such as rectangles and circles where theoretical results are available for comparison and validation of the model. However, irregular apertures not easily described in closed mathematical form are studied as well. Both completely absorbing and infinitely conducting screens are considered as well as plane wave and spherical illumination.