# Construction of a Propagating Plane Wave using Huygens' Principle

I would like to know how to simply construct a plane wave using Huygens' Principle, that each point on a wavefront can be regarded as a source of waves emanating from that point in every direction. I am okay with it being created in the 'forward' and 'backward' directions, as this can be eliminated using an obliquity factor.

I have seen this question, and am not sure whether or not new sources need to be created at each instant of time. What wavelengths for the sources need to be used?

Do we have infinite lines of sources (wavefronts) moving at the velocity of the plane wave, in the direction of the propagation of the plane wave?

• " I.e the plane wave does not permeate all of space." But by definition, a plane wave $e^{i(kx-\omega t)}$ exists everywhere in space, at any time (past, now, future). So I am not sure what you are really asking. You also seem to be familiar with the obliquity factor, so why can't you accept that the Kirchhoff (or Rayleigh for the mathematically rigorous version) diffraction formula already shows how waves propagate in the spirit of Huygens' principle? – wcc Jul 24 '18 at 2:17
• @IamAStudent You are right, a piecewise function could be used to describe what I'm asking, but I will edit the question to construct a plane wave as you described. I haven't encountered the Kirchhoff formulation yet, but I will be studying that later in the EM course I am taking right now, so I am trying to understand the Huygens principle. I've only encountered the obliquity factor as a fudge-factor to make back propagation go away. – user154080 Jul 24 '18 at 2:32
• Yes, I believe the obliquity factor was originally introduced by Fresnel as a fudge factor and then later mathematically derived by Kirchhoff and others. Chapter 3 in "Introduction to Fourier Optics" by J. Goodman is an excellent material to start learning about scalar diffraction theory. – wcc Jul 24 '18 at 3:53
• See researchgate.net/publication/… This goes over the construction of a plane wave using Huygens principle. – user45664 Jul 24 '18 at 17:03