Light bundles and diffraction

1. Sep 25, 2010

Thormen

I have a question regarding light bundles and the diffraction of waves. I've been trying to wrap my head around the processes that govern how diffraction works and it all seems to make sense to me regarding water waves and sound. If I just apply Huygens' principle that every point in a wave is to be considered a point source for a similar wave, the behavior in a ripple tank can be explained: an advancing wavefront, which is actually a row of point sources reinforcing each other, reaches a wall with a slit in it; part of the wavefront goes through a short tunnel, where the point sources still reinforce each other because they form a row as wide as the tunnel; then at the end of the tunnel, the wavefront is out in the open again, where the two outer borders of the row can't be reinforced from the side because that's where the row ends, so the wave diffracts in 180 degrees.

If I apply the same logic to light waves I can understand the going-through-the-tunnel part and the emerging-at-the-other-end part, but I don't understand how light behaves BEFORE it goes through the slit. The problem with light is that it moves in bundles, which have borders similar to the ones of the wavefronts that emerge at the other end of a diffracting slit, so Huygens' principle would suggest that light in a bundle would diverge to all possible sides too, which it clearly doesn't. So my question is: what is wrong with my understanding of the concept?

2. Sep 25, 2010

granpa

Where are you getting this?
A plane wave shouldnt have any such borders

3. Sep 25, 2010

Thormen

What I mean is that, when the wavefront emerges from the slit, some points on it are on the outskirt of the wavefront, meaning they passed the sides of the slit narrowly. If the original wave came from a point source, such as in a ripple tank or with sound, all the points on the wavefront would have neighbors all around that reinforced each other, but in a bundle there are still points on the outskirt of it.

4. Sep 25, 2010

granpa

you mean like a plane wave passing through a window?

5. Sep 25, 2010

Thormen

Yes, or laser light, or basically whenever light casts a shadow.

6. Sep 25, 2010

granpa

In any case its the same thing.
It diffracts at the edges.

7. Sep 29, 2010

Thormen

At the edges of the window, yes, but it should also diffract in mid-air.

8. Sep 29, 2010

sophiecentaur

Surely, you only get diffraction where the wavefront is interfered with by some obstruction. Huygen's idea (/construction) shows that a wavefront will just progress as it was, spreading, parallel or focused, because the result of adding all the secondary wavelets over the existing surface will produce a new wave front just a bit further along - the next step in the progress of the wave. If you put any obstacle in the way (aperture or object) the result will be that some of those wavelets aren't there and a diffracted wave pattern will be formed which is not the shape of the original wave but has peaks and dips.
The process of adding wavelets must occur everywhere as the wave progresses but I don't think what happens when it's not obstructed would be called 'diffraction'. Or else its 'zero diffraction', perhaps.
It's interesting to note that the diffraction pattern of a hole has the same shape as that of an object of the same size and shape, except that the peaks are dips and the dips are peaks. Not too surprising, really because, if you add the two together, you will get no diffraction. It can help with the calculation sometimes because you need only integrate over the extent of the object rather than to infinity in every direction.

9. Sep 29, 2010

Thormen

I know, but my problem is that if you put an obstacle in the way, like the edges of a window, you shouldn't just get diffraction immediately after the edge, but in the whole area after it. Just after the window the points of the wavefront that narrowly passed the edge will 'leak' a portion of their wavelets around the corner because of the Huygens-Fresnel principle, but that same principle predicts that a similar process will occur, say, a centimeter beyond the window. When the light is a centimeter farther, there still is this space next to the light bundle where there is no light, so, being point sources of a wave, the points near the edge of the wavefront should be leaking wavelets to the side, which should eventually lead to the light bundle spreading all over the room. This is clearly not what happens.

10. Sep 29, 2010

sophiecentaur

I don't see what you're getting at.
Once you have disturbed the pattern of the wavelets then their neat, regular relationships have changed. Depending on where you 'put your screen' you'll get a different pattern as they combine in different phases - far field / near field are just catch-all descriptions and, because of the approximations you can make about path lengths, the far field pattern is easier to calculate.
Huygen's principle describes what will happen at the 'next step' and, whether you're in the gap, a bit in front of it or 10m away, Huygens will tell you what pattern to expect. You'd need to follow the process step by step all the way, though, to describe, in detail, what happens on the way.
Instead, all you need to do is to start with a set of secondary wavelets (and just for convenience) right across the aperture and then sum their effects at what ever distance you choose. You get the same answer if you look at what you get at your 1cm distance and then do the calculation starting from there. If you did want to do your calculation just after the aperture then, instead of integrating just over the aperture, you would need to integrate over an infinite range (limited by the coherence length of the light source, of course)
I see no reason why, in principle, you couldn't apply Huygen's construction over any surface you might choose. I don't think that it is necessary to choose a constant phase front for the calculation. Will someone correct me on this?

I'm not too happy with the term "light bundles', though; it has connotations of lots of parallel rays, rather than the wavelet idea. The wavelets system gives an adequate and accurate prediction of what you call "leaking" - wherever you observe it.

" When the light is a centimeter farther, there still is this space next to the light bundle where there is no light"
No there isn't. There will be some field there due to light that arrived at a slightly earlier time (/phase) which will add to that which is just creeping through (but I don't like these animated cartoon descriptions as much as the actual Maths 0n which you can rely). There is a predicted 'sideways' component of the diffraction pattern at anything but 90 degrees exactly. It's not only the light which passes near the edges of the slit that contribute to this. All the wavelets are involved. Diffraction is a very simple idea - it's just that the actual calculations can get too meaty for comfort.