# Huygens Principle, what's the benefit to this interpretation?

I don't understand what's the point in interpreting a wavefront as point sources emitting spherical waves. You then need to use magnetic and electric currents to explain away how there are not backwards emitted waves.

My interpretation has always been that a wavefront spreads out, so considering a circular wave, one small portion of the wave will contribute to a larger portion of the wave at a further distance, which seems like a perfectly reasonable intuitive explanation, yet I'm not understanding why you need Huygens principle.

• interference and diffraction – hyportnex May 1 '18 at 22:32
• According to wikipedia, Huygen's came before Thomas Young. Huygens was one of the first to promote the wave theory of light. Also unlike a water wave in which you can see the medium oscillating up and down, I can't see the medium that light oscillates in. In order to do physics theory, you need some mathematical foothold to get you started. Huygens provided this – DWade64 May 2 '18 at 1:45
• See the Q&A's under the 'Related' list on the right side of the screen. – user45664 May 2 '18 at 17:24

## 1 Answer

Here is a perspective from optical engineering.

The major intuition comes from linearity.

Huygens principle says, the waves are superposition: the optical propagation is a linear system, and you can add up the waves to finish the propagation. Say the incoming wave is $x$, output wave $y$, the they are related as:

$$y = Ax$$

Where $A$ represents the propagation, and the specific form depends on propagation distance $z$ and wavelength $\lambda$.

One good thing about free space propagation is, it is space-invariant. Consequently you can express the system using convolutions: use a convolution kernel to represent the propagation. One example of this propagation kernel is the Rayleigh Sommerfeld formula. This simply says, matrix $A$ is a Toeplitz matrix, and can be diagonalized in Fourier domain. One eigenvector of $A$ is the planar wavefront, which has the form of the Fourier basis.

You can further simplify this relationship. For example if the propagation is large compared to wavelength, and paraxial, matrix $A$ reduces to the form of the Fresnel formula (a fractional Fourier matrix). In far field, it further reduces to the Fraunhofer formula, and $A$ is now a Fourier matrix.

So to summarize, Huygens principle formulates the propagation problem as a linear system. This greatly simplifies our model and helps us understand the optical waves, in an easy yet mostly accurate way.

Edits:

See this very helpful link http://www.mit.edu/~birge/diffraction/ for visualization of the above mentioned diffraction kernels.