Section 6: The Huygens-Fresnel Principle

Christian Huygens wrote a treatise in 1678 on the wave theory of light. The ideas that he put forth were rooted in some very deep mathematics, well beyond the scope of the present discussion. It is important, however, to understand what Huygens postulated since it has been since proven to be a valid representation of a tremendously complex physical reality. Does electromagnetic wave propagation really work exactly as Huygens explained? No, electromagnetic wave propagation obeys quantum mechanical rules that allow superposed possibilities with only probability

amplitude to describe whether or not some particular “reality” will be the one thatʼs observed. Does electromagnetic wave propagation work in accordance with Huygensʼexplanations? Yes, in classical physics Huygensʼequations correctly describe certain aspects of the behavior of a propagating field. Unfortunately, Huygensʼprinciples have some shortcomings which were corrected later by Augustine Fresnel and then applied to Maxwellʼs equations by Gustav Kirchoff. Understanding Huygensʼwave theory for electromagnetic field propagation provides the basis for not only formulating a better mental picture of whatʼs actually going on in the air in an 802.11 environment but for understanding signal obstruction in accordance with an aspect of field diffraction known as the Fresnel Zone, which will be discussed.

Huygens wrote in the language of mathematics and appreciating his equations with any clarity requires the use of advanced calculus. Nonetheless, a model of what he described will be sufficient to understand his principles. Consider a source of an electromagnetic field (like an antenna) as shown below. For an isotropic radiator the field propagates outwards in a spherical manner and the figure (6.1 below) shows the spherical wavefront at some moment in time as itʼs moving outwards from the source.

Figure 6.1 A Spherical Wavefront from an Isotropic Radiator

Huygens said that the wavefront itself could be considered to be a set of new source points, each one being the center of a new radiating field. For example, the figure below (6.2) shows one of the new source points (A) on the current wavefront and that point has generated a new spherical wavefront (B), called a wavelet.

Figure 6.2 Each New Point Source Generates a Wavelet

Copyright 2003 - Joseph Bardwell