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Want to understand how a diffraction grating works?

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19 replies to this topic

#1
jsandse

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Hi all,
Was just updating a presentation on spectroscopy I am going to give shortly when I realised to my embarrassment that I couldn't explain to my own satisfaction how diffraction gratings work. So I had a hunt around and found out that Quantum Electrodynamics (QED) was the part of physics that answers this question along with reflection, refraction and many other things.

Anyway I read some books on QED which were to say the least a bit technical :)

And then I came across a beautiful book by Richard Feynmann that explains it all in a non-technical manner.

QED - The Strange Theory of Light and Matter Penguin Press Science: Amazon.co.uk: Richard P Feynman: Books

This book has no equations in it (not even the grating equation!) - just a beautiful description of the theory.

Well worth a read.

cheers

John
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#2
andrew s

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Yes it is a fun read John, but you don't need QED to explain the diffraction grating as I am sure you know. Classical optics using Maxwell's equations will do the job just fine including detailed diffraction efficiencies. It is the most rigorous approach I know of. You can also derive the diffraction equation from just normal wave theory or even Heisenberg's uncertainty principle. This last approach might be good for your lecture.

Andrew

Edited by andrew s, 16 April 2012 - 07:47 AM.


#3
jsandse

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Well that depends on what you mean by "explain".... I am sure Feynman would not have bothered with QED had he thought classical electromagnetism adequately "explained" reflection, refraction, diffraction of light....

I personally would prefer to understand the more accurate description.
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#4
andrew s

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Hi John - I am sure Feynman would have had considerable respect for Maxwell's equations.

While I fully accept QED is the most, accurate descriptions of the interaction of light and matter at the quantum level the formalism does not allow one to calculate in some typical real world situations as the equations can't be solved even by renormalization, perturbation theory or numerical methods.

Similarly, Maxwell's equations can't predict quantum effects but can and do predict many of the effects normally ascribed to them for example frustrated total internal reflection.

In these matters I am generally a logical positivist and take the view that our physical theories are models of the real world and not the real world itself - which would be the Platonist stance.

I would like to see your derivation of the grating equation using QED or reference to the source you used as I am keen to learn.


Regards Andrew

#5
jsandse

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Of course Feynman would have respected Maxwell and his equations... well probably more respect than the university I went to (Aberdeen) who made him lose his chair when two of the colleges were amalgamated.

In fact to quote from Feynmans lectures on physics (vol 2):
"From a long view of the history of mankind - seen from,say, ten thousand years from now - there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics".

In terms of the grating equation the following optics paper is available for free and derives the grating equation - no problems with renormalization, perturbation theory or numerical methods I can see here. The paper also gives references to the works of Dirac and Feynman you can refer to:

http://www.opticsjou...-640 (1997).pdf

Also I thought logical positivism as a philosophy died a long time ago - even Wikipedia says it is dead - so it must be true :D and its final supporter A J Ayer admitted that most of it was wrong.
Though I agree with the conclusion of your argument that our physicals theories are models of the real world. (but we don't need to be logical positivists for that to be the case!)

In my opinion Wittgenstein's later philosophy has a lot more going for it than logical positivism...
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#6
andrew s

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John - Glad we have a similar view on the nature of physical theories. Also thank you for the paper which I have glanced at and will read more carefully and follow up the references.

I probably should have been more explicit by what I intended as real world situations. What I had in mind was a derivation which included both the gratings optical properties (coatings, substrate, grove spacing & profile etc.) and the radiation field fully under the same theory i.e. classical, classical quantum or full blown QED.

Anyway, I wish you luck with you talk and hope you bring more into the fold.

Best regards Andrew

#7
andrew s

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Hi John - Think I must have misunderstood you

Well that depends on what you mean by "explain".... I am sure Feynman would not have bothered with QED had he thought classical electromagnetism adequately "explained" reflection, refraction, diffraction of light....

I personally would prefer to understand the more accurate description.



I took this to mean you had used QED to derive the grating equation. If you based it on the paper you provided in the link to then it is certainly not QED based. As it states equations 1 through 3 use the Dirac formalism i.e. classical quantum mechanics not QED.

From equation 4 on the derivation is exactly as any wave based (classical or quantum) derivation would be using just the phase of the waves & the geometry to explain the interference.

Indeed in deriving the grating equation his equation 11 is from the classical optics text by Born & Wolf!

There may be more in reference 17 which gives figure 2 but it would cost me $30+ to get it and it is based on classical quantum mechanics not QED.

I had made my comments on the difficulties in doing the sums based on using QED not this hybrid approach.

Nevertheless, I did find it interesting though where he shows that for a very fine grating compared to the wave length the light effectively no longer sees the groves and only the zero order remains giving the Snell’s law.

Regards Andrew

#8
jsandse

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Hi Andrew,
Yes I knew this was a bit of a hybrid approach...but it is still doing QED as far as I am concerned as it is applying quantum effects to light.... Maybe my understanding of what QED is wider in scope than what yours is but I am just following what Feynmans own definitions is and that is applying quantum effects to electromagnetism/light.

Further interesting links I have found are:
The actual videos Feynman's lectures are based on:
The Vega Science Trust - Richard Feynman - Science Videos
An application which demonstrates diffraction gratings using the QED theory from Feynman's book:
The Strange Theory of Light

cheers

John
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#9
andrew s

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John We will just have to agree to differ on what is and is not QED. Thanks for the links I will follow them up. One positive thing for me is I got Feynman's lectures on physics vIII. I have had the others since 1972 when I went to university but never had this one.

Even though it is a very long time since I formally studied physics I still try to keep up.

I imagine you have already read it but Roger Penrose's book The Road to Reality is an interesting read even if it is a little bulky for a holiday book!

Regards Andrew

Edited by andrew s, 25 April 2012 - 08:33 AM.


#10
jsandse

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Hi Andrew,
I have read Road to Reality which is a very interesting read. If you want to see what Penrose is up to now - Conformal Cyclic Cosmology - it's worth looking at the perimeter website:
PIRSA - Perimeter Institute Recorded Seminar Archive
Very interesting how he tries to deal with the second law of thermodynamics!

Coming back to QED - the original eqns set out by Feynman, Schwinger and Tomonaga really only deal with small numbers of particles. Otherwise they would not be able to get the huge accuracy in their theory (of the order of 10 parts in 1 billion!!!!)
So asking to use these equations directly to derive the grating equation - is a very tall order :). Its analogous to taking Newtons equations directly and trying to solve problems in fluid dynamics! - it just won't work.

You have to build some sort of statistical model and make gross assumptions about the system you are modeling. In Classical Physics you use Kinetic theory.... and from Boltzmans transport equation you derive the equations for fluid/hydrodynamics.

So you could do something similar for QED. In fact some physicists have recently combined QED with Kinetic Theory for hot plasmas. ScienceDirect.com - Nuclear Physics B - Kinetic theory and quantum electrodynamics at high temperature

Easier though is to build QED models based on even more gross assumptions - as the examples I hae already given - the application written by Ladislav Szántó does this The Strange Theory of Light as well as the paper I referred to above.

However just because you are not using the original QED equations for small numbers of particles does not mean you are not doing QED - that would be then like saying you are not doing classical physics when you are doing hydrodynamics

Cheers

John
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#11
Merlin66

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Whoooo!
John/ Andrew - I think you've left me and the other 167 viewers waaaaay waaaaay behind!!
Here am I thinking in terms of pebble being thrown in the pool etc.....
Sometimes it's easier to just think - KISS
A mystery in life...just like belly button fluff.
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#12
andrew s

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John - I don't want to prolong this but I was responding to your comment about wanting to "I personally would prefer to understand the more accurate description."

I am not sure your wider use of “QED” and the approximations involved is any more accurate in this case (the diffraction equation) than Maxwell's as they give the same answer but don’t answer this for fear of boring the rest of the world.

Ken - on a lighter note I think I have discovered macroscopic fermions, namely my socks, as no two indistinguishable socks ever seem to be in the same place at the same time!

Regards Andrew

Edited by andrew s, 25 April 2012 - 11:09 AM.


#13
Merlin66

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Andrew,
Yes!
I think I've also found the source of the Unified Force - it's not gravity or nuclear bonding etc. but the ability for washing machines to make a pair of sox into a single entity!
(John, sorry to hijack your thread! ;-) )
"Astronomical Spectroscopy-The Final Frontier" -to boldly go where few amateurs have gone before.

C11, NEQ6pro, DMK41AF04, ATik314L+, 1000D modded, SM60DS/BF15, 102mmPST, Spectra-L200 and other Spectroscope(s).
"Astronomical Spectroscopy for Amateurs", "Grating Spectroscopes -How to use them" - Springer
http://tech.groups.y...l_spectroscopy/

#14
jsandse

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Guys,
I am an optimist and am sure the rest of the world are probably not bored by our discussions :)

Ken - a polite tip for you - if you want to move towards unification and try to get towards the theory of quantum gravity that everyone is trying to find then perhaps you should be looking at the outputs from the Quiet project which is trying to detect E and B mode polarisation in the Cosmic Microwave Radiation (QUIET: Science) and not what you find in your washing machine!!!!:)

And Andrew lets call our argument a no score draw - unfortunately Mr Feynam is not around to adjudicate (and give one or both of us the knock out blow!)

cheers

John

cheers

John
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#15
Merlin66

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John,
I stand corrected! as usual
I'll get back to my 1800 l/mm grating trials and practise on SPCaudAce..... ;-)
"Astronomical Spectroscopy-The Final Frontier" -to boldly go where few amateurs have gone before.

C11, NEQ6pro, DMK41AF04, ATik314L+, 1000D modded, SM60DS/BF15, 102mmPST, Spectra-L200 and other Spectroscope(s).
"Astronomical Spectroscopy for Amateurs", "Grating Spectroscopes -How to use them" - Springer
http://tech.groups.y...l_spectroscopy/

#16
andrew s

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Agreed John and amen. I just noticed you have a place in Villeveyrac we have a place in Saint-Pargoire just up the road - small world.

Ken stop wasting time on the 1800 l/mm grating and get on with a cost effective echelle!

Andrew

Edited by andrew s, 25 April 2012 - 01:13 PM.


#17
jsandse

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Wow thats close Andrew. I passed through Saint-Pargoire last week when I was in France.
Next time you are down we should meet up. Observing in the summer there is very nice.

cheers

John
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#18
Merlin66

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Andrew...Yes, Dear!!
"Astronomical Spectroscopy-The Final Frontier" -to boldly go where few amateurs have gone before.

C11, NEQ6pro, DMK41AF04, ATik314L+, 1000D modded, SM60DS/BF15, 102mmPST, Spectra-L200 and other Spectroscope(s).
"Astronomical Spectroscopy for Amateurs", "Grating Spectroscopes -How to use them" - Springer
http://tech.groups.y...l_spectroscopy/

#19
Merlin66

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Andrew,
What if I said I've found a source for F2 prisms?
Any angle, up to 60mm square - that would be a nice echelle cross disperser......
"Astronomical Spectroscopy-The Final Frontier" -to boldly go where few amateurs have gone before.

C11, NEQ6pro, DMK41AF04, ATik314L+, 1000D modded, SM60DS/BF15, 102mmPST, Spectra-L200 and other Spectroscope(s).
"Astronomical Spectroscopy for Amateurs", "Grating Spectroscopes -How to use them" - Springer
http://tech.groups.y...l_spectroscopy/

#20
andrew s

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Yes Ken, it would but we had better start another thread if we want to dicuss it more.

John, should be down again in the summer will send a PM nearer the time

Regards Andrew




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