Anti-Reflection Coating

[Karnuvap]

When I was being taught about anti-reflection coatings on lenses the explanation given was that the thickness of the coating equalled n+1/4 λ so any light reflected off the surface of the lens, via the coating would be destructively interfered with light reflecting off the surface of the coating thus cancelled out. (2*[n+1/4] λ=2n+1/2 λ=destructive interference)

 

Now the bit that confused me came next. The explanation given was that instead of being reflected (whereupon it would destructively interfere) the light goes through the lens or whatever. This achieves the desired effect of reducing reflections and maximising transmission.

 

What confused me was that this explanation sort of assumes that the light 'knows' that it would be destructively interfered with if it is reflected and so it 'doesn't bother trying' and just goes on through instead. Almost like it gives up on the whole reflection idea and decides to pass on through instead.

Or it passes a message back in time to itself along the lines of "I wouldn't bother reflecting from there if I were you , you'll only get destroyed. Better go thru the lens instead - much safer".

 

My question is therefore, do any of you recall your optics lessons and does any of this remind you of the explanations you were given about anti-reflection coatings? If so, what's the real explanation?

[modest]

I imagine (but don't know) that this is very much like interference by way of a classic double slit experiment. The interference is not so much a real physical thing that happens between 2 photons, as wikipedia's Double Slit page says:

 

The Copenhagen interpretation is similar to the path integral formulation of quantum mechanics provided by Feynman. (Feynman stresses that his formulation is merely a mathematical description, not an attempt to describe some "real" process that we cannot see.) In the path integral formulation, a particle such as a photon takes every possible path through space-time to get from point A to point B. In the double-slit experiment, point A might be the emitter, and point B the screen upon which the interference pattern appears, and a particle takes every possible path, including paths through both slits at once, to get from A to B.

 

The Copenhagen interpretation should similarly explain why the photon chooses the path of non-interference in the case of an interference coating on a lens. In fact, I bet the refractive index of the coated lens would be measured the same even if it were detected one photon at a time - just like the double slit.

 

I find it incredibly difficult to imagine "probability waves" interfering with themselves or considering every possible path through space before deciding on the best possible path - but this is only one of several things quantum that I find very counterintuitive.

 

~modest

[Qfwfq]

Actually Modest, this phenomenon is much less counterintuitive than others.

 

Karnuvap, what I think you aren't considering is that the photon (if we imagine it makes sense to follow its corpuscular trajectory) doesn't really have to "decide" or "know" at all when it reaches the inner boundary. If we imagine it being reflected "the first time" it will return to the outer boundary and, at that point, there isn't the same issue of local causality in the fact that it must be reflected. You could imagine that it may go back and forth an arbitrary number of times, with the "maybe" being only at each time it reaches the inner boundary. There would be a decreasing probability for increasing number of reflections.

 

Strictly, though, if things are analysed properly, what modest says is correct except that the non-locality issue is in time rather than in space; indeed a non-constant amplitude bungles things up a little bit, according to how much the amplitude varies over the time to traverse the coating. However, at least one can imagine it in a less disturbing way by considering that, as a "traditional" corpuscle, it needn't go forward the very first time.

[Pyrotex]

...My question is therefore, do any of you recall your optics lessons and does any of this remind you of the explanations you were given about anti-reflection coatings? If so, what's the real explanation?

I learned about anti-reflection coatings in high school when I was building telescopes. And then again in college getting a BS in Physics. I don't remember it being that difficult or complicated to understand. Let's look at the attached drawing.

 

We see the light coming in from the top. Some portion reflects off each surface it hits.

 

Point 1: The smaller the difference between the two Indexes of Refraction (Ir) at each surface, the smaller the amount of light will be reflected at that surface.

 

Since the AR-coating is in-between the Ir of air and the Ir of glass, both surfaces now reflect less light than an air/glass surface.

 

Point 2: The thickness of the AR-coating is 1/4 wave. This effectively means (A) destructive interference at the top surface and (:evil: constructive interference at the AR-coating/glass surface.

 

(A) effectively means that no light comes OUT of the air/AR-coating surface. Some is absorbed. Most is reflected back down.

 

(:doh: effectively means means that at the AR-coating/glass surface, a higher % of light gets through.

 

Point 3: Internal reflections in the AR-coating means that most of the light that did NOT get into the glass on its first pass, has a another chance to get into the glass.

 

The overall effect of this point is much (if not most) of the light that originally reflected off the glass, now gets into the glass, even if it takes 1, 2, 3, 4, 5, or more internal reflections.

 

Of the original amount of light that would have reflected off an unprotected glass surface, we now have the case that WITH the AR-coating, almost NONE of that light is reflected (thus the name "anti-reflection"); a small portion (<50%) is aborbed by the AR-coating; and most of that light now makes it into the glass. So, AR-coatings not only reduce reflections, they actually increase the amount of light that gets through.

 

At no time did I have a double-slit up either sleeve. :hihi:

[Karnuvap]

Point 1: The smaller the difference between the two Indexes of Refraction (Ir) at each surface, the smaller the amount of light will be reflected at that surface.

 

Since the AR-coating is in-between the Ir of air and the Ir of glass, both surfaces now reflect less light than an air/glass surface.

 

Point 2: The thickness of the AR-coating is 1/4 wave. This effectively means (A) destructive interference at the top surface and ( constructive interference at the AR-coating/glass surface.

 

(A) effectively means that no light comes OUT of the air/AR-coating surface. Some is absorbed. Most is reflected back down.

 

 

Thanks - I really get the bit about the multiple internal reflections and more and more of the light having a chance at penetrating the lens. Especially the bit about the refractive index being between that of air and lens - its all good.

 

But I was still concerned about the "1/4-wave meaning destructive interference at the top surface". The light that is attempting to exit destructively interferes with some of the incident light - OK with this but where does the energy go? Ans: It goes through the coating and into the lens instead. But how does it get from the top surface to the bottom and thus penetrate the lens? Ans: It "knows that it will be destructively interfered and so doesn't bother heading up towards the outer surface"

 

I thought.

 

But Pyrotex has helped me understand that the point of "pre-cognition" is the outer surface of the coating. It doesn't need to communicate with light at the bottom surface of the coating. OK, all it needs to do now is somehow "know" that it will be destructively interfered with should it venture "outside" and so it decides to be internally reflected instead. I am happier with this explanation but, you can see, it is still a little mysterious.

 

Thanks guys for the explanations. I am much happier now.

 

The Vap.