# Applying Huygens's principle to light propagation

• m.e.t.a.
In summary, according to Miller's paper, Huygens's principle accurately describes the way light propagates, but it also has the ability to describe directional propagation of light.
m.e.t.a.
I was taught that Huygens's principle is an accurate description of the way light propagates. Something like: "All points along a wave front can be modeled as point-sources for new waves having the same phase and frequency." This appears to be a good model to explain phenomena such as diffraction.

From my limited understanding, Huygens's principle also explains why light* travels in approximately straight lines: all possible photon paths cancel destructively except for those in a narrow central ~cylindrical beam. (Not sure about the exact "shape" of the beam. I assume a cylinder or cone as an approximation.)

The above explanation is well and good, and I understand some parts of it to a limited degree, but there is one point that I don't understand at all. If Hugens's principle explains why light travels in a straight line, does it also explain why light travels in (apparently) only the positive or negative direction along that line--but not both? My interpretation of Huygens's principle, when applied to a photon, is that the photon has equal probability to travel forwards (along its straight-line path/cylinder) as backwards. Furthermore, the photon need not travel only in the positive direction, or only in the negative, but could alternate between the two directions anywhere up to an infinite number of times between its emission and eventual absorption--if absorption ever occurred--and could hence be inferred to have traveled at any speed < c.

What is wrong with this reasoning?

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* Further question: does a photon have to be coming from an extended source in order to have directionality? By "extended source" I mean something like a slit or hole; and by "having directionality" I mean that the photon propagates in a manner other than symmetrically in all directions, as an expanding sphere. For example, a photon from a laser would be "highly directional".

Thank you, jtbell, that is just what I needed!

So, if I understand the gist of Miller's paper (http://www-ee.stanford.edu/~dabm/146.pdf) whenever light propagates, there is not just one wave front, but two closely spaced wave fronts. The second wave front chases the first, trailing behind it by an infinitesimal distance, and is also phase-shifted by 180º w.r.t. the first wave front. This phase shift causes total constructive phase interference in one direction ("forwards") and total destructive interference in the opposite direction ("backwards"). The result is a zero probability of the photon traveling "backwards". This is a fairly neat explanation. Is it the accepted model?

## 1. What is Huygens's principle?

Huygens's principle is a theory that describes how light propagates through space. It states that every point on a wavefront can be considered as a source of secondary spherical wavelets that spread out in all directions. These wavelets then combine to form the new wavefront at the next point in space.

## 2. How does Huygens's principle apply to light propagation?

Huygens's principle can be used to explain the phenomena of reflection, refraction, and diffraction of light. It states that at any point in space, the light behaves as if it were coming from all directions, which allows us to predict and understand how light will interact with different surfaces and mediums.

## 3. What are the limitations of Huygens's principle?

While Huygens's principle is a useful tool for understanding light propagation, it has some limitations. It does not take into account the wave nature of light and cannot fully explain the behavior of light in certain situations, such as near sharp edges or with very small particles.

## 4. Can Huygens's principle be applied to other types of waves?

Yes, Huygens's principle can be applied to any type of wave, including sound waves and water waves. It is a fundamental principle of wave propagation and helps to explain many phenomena in the physical world.

## 5. How is Huygens's principle related to the wave equation?

Huygens's principle is closely related to the wave equation, which describes the mathematical behavior of waves. The secondary wavelets described in Huygens's principle can be seen as a solution to the wave equation, and the principle itself can be used to derive the wave equation in certain cases.

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