# The Naked Scientists Forum

### Author Topic: How does a laser work?  (Read 19654 times)

#### lightarrow

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##### How does a laser work?
« Reply #25 on: 25/03/2009 20:45:03 »
You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.
if you simply make a spot check the frequency could be varying wildly.

I think I have only repeated what Vern said!
That's correct syhprum.

#### lyner

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##### How does a laser work?
« Reply #26 on: 25/03/2009 22:27:26 »
The Fourier transform is, as I said before, not a statistical thing.
It would be better for you to look it up on Wikkers  http://en.wikipedia.org/wiki/Fourier_transform, Vern.

What it says is that, for instance, a single pulse of finite duration can be looked upon as an infinite set of sinewaves of infinite duration and of different amplitudes and phase. They will interfere with each other at all other times to produce a zero value but, for the duration of the pulse, they add together to follow the pulse shape.  If you want to produce your particular shape of pulse then it must involve a vast number of frequency components which stretch over a very wide bandwidth. That is the pulse described in frequency domain. In the case of your single sinusiod, extending for one period, the FT would consist of a component with a maximum at the f (of hf) with a continuum of sidebands which would extend on either side of f.

This is very basic stuff and is not really open to question but it means that, to produce short pulses, you need a big bandwidth. If the only frequencies produced by a transition are in a very narrow band (a line spectrum), this means that the wavetrain must be extremely long.

It means that, if one actually insists on the photon's length being important, then, depending upon the system which produced it (a discrete energy state transition or a transition within a band energy structure) the photon would have a different length. Furthermore, for a photon to  be absorbed by a system with a particular energy structure, it would also have to be the right length. So laser light couldn't be absorbed by an atom in a solid, for instance.

The only thing one can say about a photon is that it has a particular energy associated with it, which corresponds to a particular frequency. There is nothing about its 'length' in its specification. SO, I say that assigning a length to a photon must be meaningless.

I think that it is very optimistic to assume that the photon can be characterised by something so concrete and familiar as a short 'squiggle', bearing in mind what a sophisticated concept it entails.

#### lyner

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##### How does a laser work?
« Reply #27 on: 25/03/2009 22:40:38 »
techmind
You're talking my kinda language.
At least one person seems to be appreciating something of what I am saying.

The problem goes back to the Corpuscular theory of light, which was a very tangible idea. After the idea of light as a wave and then the reconciliation between the two ideas when duality was introduced, people went back to the corpuscle idea because it was / is so attractive and concrete.
Einstein's photoelectric effect experiments confirmed that em waves occur in energy dollops - nothing more. Teaching in School has prolonged what I think is a myth about the little bullet model and the statements by the great and good in the Science world have also been interpreted as confirming it. Whether or not they really have confirmed it, explicitly, is another matter.

#### techmind

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##### How does a laser work?
« Reply #28 on: 26/03/2009 02:00:28 »
The stimulated emission concept is quite interesting.

Now we know that inherently the energy "gap" in the excited-state atom is perfectly matched to the rest of the laser-radiation in the cavity.
We also know that the excited state has to be relatively "long lived" (metastable or whatever) to as to "hang around" long enough to be taken to the ground state predominantly by stimulated emission rather than random emission (sorry I can't think of the proper word).
The fact that it "hangs around" could be interpreted/considered as some kind of energy potential-barrier.
So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state.

Buuuut... I said before the energy gap is "perfectly matched", which might imply a concept a bit like a high-Q resonant system has some relevance? ... something that would couple to an EM wave of the precisely correct frequency...? And if this was the case you might expect the stimulated "photon" to be phase-matched and polarisation-aligned to the stimulating "photon"?

A bit handwavy I'm afraid - tis late at night, plus a decade or more since I studies undergrad photonics.

What do you think? sophiecentaur?

#### swansont

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##### How does a laser work?
« Reply #29 on: 26/03/2009 17:48:14 »
The stimulated emission concept is quite interesting.

Now we know that inherently the energy "gap" in the excited-state atom is perfectly matched to the rest of the laser-radiation in the cavity.
We also know that the excited state has to be relatively "long lived" (metastable or whatever) to as to "hang around" long enough to be taken to the ground state predominantly by stimulated emission rather than random emission (sorry I can't think of the proper word).
The fact that it "hangs around" could be interpreted/considered as some kind of energy potential-barrier.
So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state.

Buuuut... I said before the energy gap is "perfectly matched", which might imply a concept a bit like a high-Q resonant system has some relevance? ... something that would couple to an EM wave of the precisely correct frequency...? And if this was the case you might expect the stimulated "photon" to be phase-matched and polarisation-aligned to the stimulating "photon"?

A bit handwavy I'm afraid - tis late at night, plus a decade or more since I studies undergrad photonics.

What do you think? sophiecentaur?

You've got it right.  The concept of cavity Q and phase matching is very relevant to laser operation.  Though because of the high frequencies involved, and therefore really large Q's, the "free spectral range" is sometimes introduced
http://en.wikipedia.org/wiki/Free_spectral_range

#### Bored chemist

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##### How does a laser work?
« Reply #30 on: 26/03/2009 19:52:59 »
You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.
if you simply make a spot check the frequency could be varying wildly.

I think I have only repeated what Vern said!
That's correct syhprum.
No it's not.
Th FT is a mathematical operation like reciprocal.
You can apply it to  a data set and get an answer. That answer is correct, no matter what happened at some other tme.
If the peaks were 20 msec apart then the frequency at that time was 50Hz.

#### lightarrow

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##### How does a laser work?
« Reply #31 on: 26/03/2009 23:36:02 »
You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.
if you simply make a spot check the frequency could be varying wildly.

I think I have only repeated what Vern said!
That's correct syhprum.
No it's not.
Th FT is a mathematical operation like reciprocal.
You can apply it to  a data set and get an answer. That answer is correct, no matter what happened at some other tme.
If the peaks were 20 msec apart then the frequency at that time was 50Hz.
Can you please find the FT of this function:
(hint: 1<x<15 is not a choice of visualization of the x, it's *the domain* of the function).
« Last Edit: 26/03/2009 23:47:09 by lightarrow »

#### lyner

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##### How does a laser work?
« Reply #32 on: 27/03/2009 00:24:55 »
BC
What you say about the FT is not correct. The FT involves integrals over all time / frequency (depending on which way you are going. You can frigg things to get a sort of answer by 'windowing' to reduce the integration span.
Only a continuous infinite sinewave has a single 'frequency'- . Any other function has an Frequency domain function which is not single valued but extends around the central frequency peak. Just looking at a row of maxes, mins or zero crossings does not define a frequency fully.
« Last Edit: 27/03/2009 00:32:50 by sophiecentaur »

#### lyner

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##### How does a laser work?
« Reply #33 on: 27/03/2009 00:30:09 »
lightarrow
As far as I remember, the FT of your function (I assume that it has zero value above and below the x values given) will be that of a single, top hat function modulated sinewave. That will be, basically a sinx/x  spectrum extending on either side of the 'carrier' frequency - the sinewave you have drawn. The sidebands cover an infinite range.

#### lyner

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##### How does a laser work?
« Reply #34 on: 27/03/2009 12:43:19 »
It struck me that people may be confused between the FT and the DFT (discrete FT) which assumes a repeated waveform.

#### lightarrow

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##### How does a laser work?
« Reply #35 on: 27/03/2009 14:00:30 »
As far as I remember, the FT of your function (I assume that it has zero value above and below the x values given) will be that of a single, top hat function modulated sinewave. That will be, basically a sinx/x  spectrum extending on either side of the 'carrier' frequency - the sinewave you have drawn. The sidebands cover an infinite range.
More precisely (if I computed correctly):
f(ω) = [1/(ω2-1)]*[e-i15ω(sin15+ωcos15) - e-iω(sin1+ωcos1)].

#### lyner

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##### How does a laser work?
« Reply #36 on: 27/03/2009 14:46:53 »
What does that look like when you  plot it?

#### lightarrow

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##### How does a laser work?
« Reply #37 on: 27/03/2009 16:34:38 »
What does that look like when you  plot it?
This is the real part:

#### lyner

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##### How does a laser work?
« Reply #38 on: 27/03/2009 17:58:36 »
OH!
Well, the left hand bit looks like a sinx/x function shape to me but the right hand bit is very strange.
Does the picture differ a lot if you choose a different actual length for the 'burst' of cycles? Does the the x axis zero  correspond to zero frequency?
btw, your use of degrees rather than radians in the sums could be the source of a 'scale' problem. Is it ok?

If you had a very wide window, with many cycles in it, I think you'd expect to see two very sharp peaks (+/- the basic frequency of the squiggle). Is it easy to confirm that / apply the test of your maths?
« Last Edit: 27/03/2009 18:00:40 by sophiecentaur »

#### lightarrow

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##### How does a laser work?
« Reply #39 on: 28/03/2009 00:06:30 »
Ok, you have decided to make me work this evening

It's simpler (for me, at least) to study the function f(x) = cos(ω0x) in the interval (-a,a). Its Fourier transform is real and it is:

f~(ω) = [1/(ω0-ω)]*sin[a(ω0-ω)] + [1/(ω0+ω)]*sin[a(ω0+ω)]

Choosing ω0 = 1 and a = 10 (first case), a = 100 (second case), the resulting plots are, respectively:
« Last Edit: 28/03/2009 00:09:23 by lightarrow »

#### lightarrow

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##### How does a laser work?
« Reply #40 on: 28/03/2009 00:15:35 »
To precise: yes, the x axis zero means zero frequency; you notice that when the "window" goes from 20 to 200 you have two much sharper peaks (as you say).
« Last Edit: 28/03/2009 00:18:30 by lightarrow »

#### lyner

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##### How does a laser work?
« Reply #41 on: 28/03/2009 15:29:33 »
Your second graph looks like a pretty good sinx/x curve which is what one (I) would expect.
The difference between a long burst and a short burst is very significant, when you're talking about the form of spectra from a substance emitting light.

#### lightarrow

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##### How does a laser work?
« Reply #42 on: 28/03/2009 20:24:57 »
Your second graph looks like a pretty good sinx/x curve which is what one (I) would expect.
The difference between a long burst and a short burst is very significant, when you're talking about the form of spectra from a substance emitting light.

Sinx/x actually is the FT of the rectangular impulse of unit height:

f(x) =  1  if  -1< x <1

=  0  if    |x|>1

f~(ω) = 2sin(ω)/ω

#### lyner

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##### How does a laser work?
« Reply #43 on: 28/03/2009 21:52:21 »
That's right. And when you modulate a sinusoid with it, you get sinx/x sidebands (convolving one with the other, i seem to remember - which is the equivalent of modulation only in the f domain). We ex broadcast engineers used to do that stuff for breakfast (but sometimes the theory may be a bit rusty).

#### Bored chemist

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##### How does a laser work?
« Reply #44 on: 29/03/2009 11:51:48 »
If I record that sound of next door's cat and FT the amplitude vs time trace I get an amplitude vs frequecy trace. If I look at the trace and find the lowest frequency peak in it (apart from any DC component) it's reasonable to call that the frequency of the cat's howl.
I think that if I take a 50Hz sine wave like the mains and crop a 20msec part of it then FT it, I will get the convolution of the sinx/x from the cropping functiion and a spike at 50Hz for the sinewave.
The lowest frequency peak in that will be at 50Hz. I can therefore conclude that the mains frequency is 50Hz.

#### lyner

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##### How does a laser work?
« Reply #45 on: 29/03/2009 13:01:01 »
BC
In practical terms you could often say just that.
BUT, if you were half way across the Atlantic and you looked at the 'mains hum' on your amplifier, you would still get a low frequency wave which went up and down. It would also be 'beating' at 10Hz. If you froze the signal and looked at zero crossings, what would your simple analysis tell you?
1. If you took a very long sample and did a DFT on it, then you would get two peaks (50 and 60 Hz).
2. If you took a short burst, you might find that there was  a predominance of 50Hz or 60Hz, depending on when you actually took your sampled waveform and how long it actually was, before you made an endless loop of it. The DFT would have lost some information about the signal.

In the context of the photon, you mustn't do a DFT on it (which is what your treatment is implying) because it really is a 'one off'.

#### yor_on

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##### How does a laser work?
« Reply #46 on: 29/03/2009 14:04:10 »
Techmind, how do you think when you write "So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state."? Can one see a photon as something you can 'borrow' energy from? And still be a 'photon'. Also what are we talking about here, how does it lend that energy, by what 'mechanism' do you see it. The only way I see that happen is by HUP, and then one still have the problem of defining what 'energy' has been 'loaned' as it then will have the same 'energy' after the 'loan' as it had before? Wouldn't this be a violation of the idea of 'conservation' laws?
---

Maybe you are looking at as SC wrote? "a single pulse of finite duration can be looked upon as an infinite set of sinewaves of infinite duration and of different amplitudes and phase. They will interfere with each other at all other times to produce a zero value but, for the duration of the pulse, they add together to follow the pulse shape"?

But this still seem to be a result of HUP?
« Last Edit: 29/03/2009 14:10:33 by yor_on »

#### lyner

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##### How does a laser work?
« Reply #47 on: 31/03/2009 00:11:24 »
I think HUP is consistent with this. The precision of the energy measurement (frequency / momentum /spectral width ) and the precision with which the pulse can be said to be passing (length of pulse) are mutually limiting. I imagine 'h' is in there somewhere.

#### techmind

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##### How does a laser work?
« Reply #48 on: 31/03/2009 10:50:20 »
Techmind, how do you think when you write "So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state."? Can one see a photon as something you can 'borrow' energy from? And still be a 'photon'. Also what are we talking about here, how does it lend that energy, by what 'mechanism' do you see it. The only way I see that happen is by HUP, and then one still have the problem of defining what 'energy' has been 'loaned' as it then will have the same 'energy' after the 'loan' as it had before? Wouldn't this be a violation of the idea of 'conservation' laws?

But this still seem to be a result of HUP?

Indeed I was thinking HUP (in a vague sort of way). There's no violation of conservation of energy as you're just overcoming a potential barrier (or tunneling through it).  You still come down the other side, so no net energy transfer.

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##### How does a laser work?
« Reply #48 on: 31/03/2009 10:50:20 »