Can two perfect point monochromatic sources be incoherent?

I know none of the source can perfectly be monochromatic. All that we can talk about is the degree of coherence.

What I wanted to know is that suppose magically some how I get two independent perfect point sources of monochromatic light, then will then two independent sources be act
as coherent or incoherent source of light.

Thanks :)

Answers and Replies

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I think they can't be incoherent to each-other if they are *perfectly* monochromatic: the difference of the phases cannot vary suddenly or in a random way without disturbing the sources' monochromaticity.

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lightarrow

Thanks lightarrow,

I an my exam notes it is written,

"Two independent "monochromatic" sources, emit wave of same wavelength. But the waves are not in phase. So they are I'm coherent. This is because, atoms cannot emit light waves in same phase and these sources(independent monochromatic sources which give same wavelength) are said to be incoherent. "

So the notes are trying to say that even if the two independent sources are producing same wavelength only they can't maintain constant phase and hance are incoherent. Kindly guide me on this.

Regards

Chandra Prayaga
Science Advisor
When they say two monochromatic sources, they are automatically coherent. Coherent does not mean "in phase". Depending on path difference, the phase of the wave from one source will be different from that of the other. Two waves being coherent means that they maintain the same phase difference at a given point in space.

Yup, that I know that light wave from coherent sources need not to be in phase their should only be a constant phase difference.

I am concerned with authenticity of the statement that is given in my exam notes that I posted in earlier post, where it claims that even if the two sources are monochromatic(producing single unique wavelength) they will not act as a coherent(they mean only by using single point source and dividing it into two could produce coherent source as was done by Thomas Young in double slit experiment.

The statement is however quiet shaggy when it says the waves are not in phase(when it appears to say the waves could not have constant phase difference) hence incoherent.

Well I think it is wrong as you all seem to agree that if the sources are perfectly(magically) monochromatic they will certainly coherent.

Thank you all. :)

Oh I need to hold on this.
lightarrow pointed out that any abrupt phase change can't occur without disturbing the monocromacity of source.

It means whenever the phase of emitting wave from the source change abruptly it's wavelength changes and such a source where this happen can't produce wave of single wavelength. (No practical source is source of single unique wave wavelength).

Now the problem that I am facing with to comprehend this is a paragraph given in my text book, where it discuss the famous experiment of Thomas Young for double slit.

The text says, Young used sodium lamp and an ordinary source like sodium lamp undergoes abrupt phase changes in time of order of 10^-10 seconds. (This make me think that wavelength must change in sodium lamp as pointed out by lightarrow.

The text says thus using two independent sodium light lamp will not have a fixed phase relationship. Young however brilliantly solve the problem constant phase difference.

He made two pin holes S1 and S2 receiving light from a common source ,and the text goes on two explain that how S1and S2 as source will always have the same phase because any phase change from the main source(sodium lamp) will manifest in exactly similar phase changes in the light coming from S1 and S2.

This clearly no doubt solves the problem of phase change but as the phase of each of waves from the two surface changes) though by equal amount) it would definitely as pointed out by light arrow change the wavelength of light with time(thought at any time wavelength from the two sources will be same).

Now my doubt arises by thinking if wavelength is changing(due abrupt change in phase) how could Young got a sustained interference. Because as the position of maxima and minima(λD/d) depends on wavelength.

ehild
Homework Helper
Now my doubt arises by thinking if wavelength is changing(due abrupt change in phase) how could Young got a sustained interference. Because as the position of maxima and minima(λD/d) depends on wavelength.
Completely monochromatic source does not exit. Even the best lasers emit a finite bandwidth of light. The change of wavelength makes the interference peaks to have some width.

blue_leaf77
Science Advisor
Homework Helper
When a phase jump occurs, it's actually not that the wavelength suddenly changes. The non-monochromaticity of a light, which in this case is manifested as a phase jump, implies that the light's spectrum is not an exact line standing on top of a single wavelength. Non-monochromatic light always has certain non-zero spectrum bandwidth. The wavelength components within this bandwidth exist all the time (hence called "stationary component") and they interfere so as to produce a resultant wave which has a phase jump that we were talking about. The non-zero-ness of the bandwidth of a source translates into widened interference fringes, where around the central part, the widening is not so significant, but it gets more and more vivid as you go further from the center such that the fringes far from the center will be completely blurred.

Completely monochromatic source does not exit. Even the best lasers emit a finite bandwidth of light. The change of wavelength makes the interference peaks to have some width.
Wow that's really make sense:)

So should I think that if we some how have perfectly monochromatic source than the bright and dark fringe would only be a very thin line(straight or otherwise)?

When a phase jump occurs, it's actually not that the wavelength suddenly changes. The non-monochromaticity of a light, which in this case is manifested as a phase jump, implies that the light's spectrum is not an exact line standing on top of a single wavelength.
I don't understand what it means, please tell in some more simplified way.

Thank you guys, you are all awesome:)

Regards

blue_leaf77
Science Advisor
Homework Helper
I don't understand what it means, please tell in some more simplified way.
One says a light to be monochromatic if it has only one single frequency or wavelength. Mathematically, a single frequency spectrum is represented by a delta function centered at the light's frequency, ##F(\omega) = \delta(\omega-\omega_0)## with ##\omega_0## being the light's frequency. In time coordinate, a monochromatic light is pictured as a sinusoidal oscillation of electric field extending way out toward both minus and plus infinities, ##f(t) = E_0 e^{-i\omega_0 t}##. It can be shown that ##f(t)## and ##F(\omega)## defined before are related through Fourier transform relation.
However, when the light is polychromatic, its ##f(t)## cannot have a simple form as a mere sinusoidal oscillation like before, one example being the case where there is phase jump as you discussed. The corresponding frequency coordinate representation of this polychromatic light will not be a delta function anymore, instead it will have some shape with certain width. In other words, the spectrum spans certain frequency region, say from ##\omega_1## to ##\omega_2## and all frequencies inside this range will interfere so as to constitute its time representation ##f(t)##.

sophiecentaur
Science Advisor
Gold Member
One way to look at a 'nearly monochromatic' light source is to take a single frequency and then introduce some phase modulation to it. The RF approach could make this a more acceptable way of thinking.
The interesting thing about very high stability oscillators is that they tend to lock together, even when they are sited apart. The very high Q circuit (which is what it is) makes a very selective receiver with oodles of gain at the tuned frequency. This involves the two oscillators in a massive phase lock loop. At RF, this effect can easily happen within an equipment bay but I don't know how it could apply with optical lasers(?) as the wavelengths are a bit different.

Andy Resnick
Science Advisor
Education Advisor
What I wanted to know is that suppose magically some how I get two independent perfect point sources of monochromatic light, then will then two independent sources be act as coherent or incoherent source of light.
Just calculate the mutual coherence function, even though it's easy only for scalar fields (no polarization). You've already set up the problem to have a simple solution- 2 ideal monochromatic point sources, presumably with fixed positions. Clearly, the mutual coherence is 1, since you can unambiguously calculate the complex-valued field at any observer position at any time.

ehild
Homework Helper
Wow that's really make sense:)

So should I think that if we some how have perfectly monochromatic source than the bright and dark fringe would only be a very thin line(straight or otherwise)?
No, in the Young experiment the intensity of the interference pattern varies about sinusoidally with the distance from the centre. See
http://www.a-levelphysicstutor.com/images/waves/youngs-frings-screen.jpg

In case of two monocromatic sources of the same wavelength it would be a sine function.

The change of wavelength makes the interference peaks to have some width.
No, in the Young experiment the intensity of the interference pattern varies about sinusoidally with the distance from the centre.
In case of two monocromatic sources of the same wavelength it would be a sine function.
True! This is what I just pointed out and opened PF to discuss you about this.
As their not just constructive and destructive interference(not just maxima and minima) their could be intermediate intensities for even a particular unique wavelength.

So sadly this reminder stand me back on my previous question-

That is, if their are sudden abrupt phase changes in sodium lamp used by Young, which would mean(according to you and lightarrow) would mean disturbance in the monocromocity of the light source meaning source undergoes change in wavelength as its phase is changing abruptly, so as wavelength is changing the position of maxima and minima(λD/d) should change and Young should not be able to get a sustained interference.

And this contradicts the fact because Young got a sustained interference where the position of maxima and minima do not change with time.

As this can only happen if wavelength do not change. As I mentioned that my text book says sodium lamp undergoes abrupt phase change and it explains how Young brilliantly managed to keep the two sources in constant phase by illuminating two slits S1 and S2 from same source S1. So even though their is abrupt phase shift in S(shift in phase means change in frequency according to previous discussion) phase difference between S1 and S2 doesn't vary. But the question here is that there wavelength is changing(though at any time it is same for S1 and S2) how then this arrangement is able to give sustained interference?

I mean sustained interference in this arrangement is indicating that wavelength is not changing. Or completely sustained interference is telling that the sodium lamp is giving only one unique wavelength (this is violating the well know fact that sources never produce single unique wavelength).

It also voilates what light mare said
the difference of the phases cannot vary suddenly or in a random way without disturbing the sources' monochromaticity.

--
lightarrow
Because we note text book says their is abrupt phase change the light wave from in sodium lamp and lightarrow posted out such a phase change disturbs monocromocity but disturbance in monocromocity(inability to produce single wavelength) would mean unsustained interference pattern. But sustained interference pattern was observed by Young.

Regards

ehild
Homework Helper
It is not true that a light source suddenly changes its wavelength, At some time interval, a lot of photons are emitted. They can have slightly different frequencies. There is a finite bandwidth for the frequencies/wavelengths around the central frequency of the photons, which does not change. The finite bandwidth causes that the intensity distribution of the interference pattern is not quite sinusoidal, but dos not alter the position of the maxima.

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sophiecentaur
Science Advisor
Gold Member
And this contradicts the fact because Young got a sustained interference where the position of maxima and minima do not change with time
Geometry of the Young's Slits experiment is not enough to reveal the effect of a small amount of spread in the wavelength of the light source. (No numbers here, I realise)
You can get the first few fringes even when you use the light from a very crude coloured filter (i.e. wide bandwidth). Young's experiments do not actually produce any significant disagreement with the earlier statement. The depth of the minima can be limited by failure to get really good destructive interference. The position of the minima is determined by the mean frequency.

It is not true that a light source suddenly changes its wavelength, At some time interval, a lot of photons are emitted. They can have slightly different frequencies. There is a finite bandwidth for the frequencies/wavelengths around the central frequency of the photons, which does not change.
I think something similar is said blue_leaf77

When a phase jump occurs, it's actually not that the wavelength suddenly changes. The non-monochromaticity of a light, which in this case is manifested as a phase jump, implies that the light's spectrum is not an exact line standing on top of a single wavelength.
So in this regard one of the question that raised to my mind is that, it was told to me by lightarrow and others; whenever their is sudden phase change their comes disturbance in the monochromocity of source, and here blue_leaf77 Saying when a phase jump occurs(in sodium lamp) it's actually not the wavelength changes...

Isn't disturbance of monoctomocity mean change in wavelength? Otherwise want did lightarrow mean when he said, the difference of a phases can't vary suddenly or randomly without disturbing source's monoctomocity?

At some time interval, a lot of photons are emitted. They can have slightly different frequencies. There is a finite bandwidth for the frequencies/wavelengths around the central frequency of the photons, which does not change
So here comes a different reason for (sodium lamp) emitting varying wavelength(reason = not abrupt phase change but not all photons of same frequency instead a bandwidth of frequency around its central frequency).

In this regard I have two questions:

1) As blue_leaf77 said, when a phase jump occurs it's not the wavelength that suddenly changes, what then is the effect of sudden phase change or phase jump, about which my text book is talking about, in the discussion of Young's experiment?

2) Let's forget about what is causing the change in wavelength or non-single(non-monochromatic) wavelength from (phase jump or number of photons at a time emitting with a band of frequencies), well whatever be the reason you all agree that wavelength is changing, how could light with wavelength havingnot unique value, is able to give sustained interference.

I must be missing something, I think.

The finite bandwidth causes that the intensity distribution of the interference pattern is not quite sinusoidal, but dos not alter the position of the maxima.
Also I do not understand this.

Geometry of the Young's Slits experiment is not enough to reveal the effect of a small amount of spread in the wavelength of the light source. (No numbers here, I realise)
Effect of small amount of spread in wavelength(the above two questions are about the cause of this spread) while here in this paragraph I am more concerned to ask you how the spreading in wavelength is providing sustained interference.

Say if I have a bandwidth of wavelength not just unique wavelength(that is wavelength is some how spread) how will then I have position of maxima and minima unique because position of maxima and minima will no more be unique as each of the wavelength is ready to form it's maxima(and minima too) in some position other then the other wavelength so no maxima and talking about position of maxima and minima in such a band of wavelength should have no meaning.

The change of wavelength makes the interference peaks to have some width.
I think the change of wavelength(if it changes with time) rather rather changes the position of maximas (nλD/d) and minimas should change and Young should not have sustained interference.

And if instead the wavelength change means their is a band of wavelengths then I think as you said we have peaks to have a band.

Not sure if the abrupt phase jump not causing change in wavelength with time and why not giving unjustified interference when it was said phase jump is sure to affect monoctomocity of source.

ehild
Homework Helper
Monochromacy means that wave of infinite length and time of duration is emitted. In the photon picture it means that the source emits lot of identical photons with infinite coherence length. If such sources existed and two sources were of the same frequency, you would get a static interference pattern.
But the photons have some finite lifetime and finite coherence length.
Imagine that the source emits sinusoidal signal of duration d in every T second. The Fourier series of that signal contains components around the frequency of the sine function. That means, the emitted photons have a distribution of frequency around the main frequency of the sine function - because of the finite lifetime.
There is no abrupt phase change. It only happens that a photon emitted some time ago ceases to exit.

Monochromacy means that wave of infinite length and time of duration is emitted. In the photon picture it means that the source emits lot of identical photons with infinite coherence length.[QUOTE/]

Ok, you mean by wave of "infinite length and time of duration" you mean wave remain continues or unbroken till infinite length and time no that it's wavelength is infinite. Right?

If such sources existed and two sources were of the same frequency, you would get a static interference pattern.
But the photons have some finite lifetime and finite coherence length.[QUOTE/]

OK understood

Imagine that the source emits sinusoidal signal of duration d in every T second. The Fourier series of that signal contains components around the frequency of the sine function. That means, the emitted photons have a distribution of frequency around the main frequency of the sine function - because of the finite lifetime.[QUOTE/]

But here for not understand how the finite life time of photon result in a distribution of frequency around the "main" frequency?

There is no abrupt phase change. It only happens that a photon emitted some time ago ceases to exit.
If an emitted photon after some time ceases to exit it should simply be understood as reduction in the number of photons of a particular frequency, why we are making it(ceasing of an emmted photon) responsible for distribution of frequency when you already told that from source photons if different frequency do emit.
... At some time interval, a lot of photons are emitted. They can have slightly different frequencies.[QUOTE/]

There is a finite bandwidth for the frequencies/wavelengths around the central frequency of the photons, which does not change. The finite bandwidth causes that the intensity distribution of the interference pattern is not quite sinusoidal, but dos not alter the position of the maxima.
So the band of intensity in interference pattern is not strictly due to finite band of frequency band.
That's great I understand, but I still doubt full of the role of photons being cease in the middle of path or abrupt phase shift as written in text. When already the photons from sources have a distribution of frequency.

Regards

sophiecentaur
Science Advisor
Gold Member
But the photons have some finite lifetime and finite coherence length.
That is a very controversial statement that implies properties of a photon that are not established. How can you define the wavelength of a photon which has no defined position or extent? Does the introduction of photons help in this discussion at all?

This discussion has ranged all over the place and it has become more and more divergent. Anything that one says about the 'nature' of light waves must also apply to RF waves. The only difference is the energy of the quanta (photons) involved. If you are considering a specified phase change then the resulting spectrum is given by the Fourier Transform. There will be a carrier wave with sidebands for a period of time that relates to the time for the transition (very basic signal theory). The fringes will not shift or change in width but the nulls will be 'filled in' for a short while.

ehild
Homework Helper
Ok, you mean by wave of "infinite length and time of duration" you mean wave remain continues or unbroken till infinite length and time no that it's wavelength is infinite. Right?
Yes.
Assume a monochromatic source. A photon arises from a transition between two quantum levels. The transition takes some time, during that time the photon travels some distance, it is its coherence length. In a light source, lot of such transitions happen again and again. There is some phase difference among the emitted photons.
The electric field produced by the light source is the resultant of the fields represented by the individual photons. If all photons have the same frequency, the resultant is a wave with the same frequency, and an amplitude and phase constant which depend on the phases of the constituent elementary waves. As the photon emission is random, they change with time, but due to the lot of elementary waves, this change is not abrupt.
Watching the time dependence of the electric field at some place you observe a sinusoidal function with amplitude and phase "constant" slightly changing with time.
In the frequency domain, the Fourier transform of this time dependent signal produces a band of frequencies.
You can explain Young experiment with photons or with the light of finite bandwidth of frequencies.

In the Young experiment, normally the photons interfere with themselves. The wave represented by a photon is diffracted by the slits and produces an interfence pattern, maxima and minima at places where the path difference between the diffracted waves is less than the coherence length of the photon. An other photon with different phase constant produces the same pattern.

If you think in frequencies, you can imagine that you have waves of infnite coherence lengths, but slightly different frequencies. The different frequencies mean different wavelengths, and different positions of maxima and minima, so a blurred interference pattern.

sophiecentaur
Science Advisor
Gold Member
Assume a monochromatic source. A photon arises from a transition between two quantum levels. The transition takes some time, during that time the photon travels some distance, it is its coherence length.
@ehild: the following is not particularly arguing against your particular post; it's just a general objection to the very popular views that it contains.
I have a big problem with this sort of explanation. It implies that photons are somehow distinguishable from one another - i.e that there has to be another 'number' associated with a photon, in addition to hf (the energy). It implies that a photon detector, that detects single photons and then shuts down (something in the nature of a photomultiplier) would or should be able to 'know' something more about the source than just the photon energy - based on its 'coherence length'. Is this realistic?
None of these problems arise if the wave phenomena are dealt with in terms of waves. The way that stimulated emission occurs can reasonably be described in terms of wave / atom interaction. It wouldn't be hard to make an electronic circuit that works in the equivalent way, dumping the energy stored in the C of an LC a resonant circuit when an external wave is detected. This would not involve any quantum model at all.
In the Young experiment, normally the photons interfere with themselves.
And even with this statement, which is very frequently made, there is a problem. An EM beam with high coherence can produce interference effects with massive path length differences which, using that description, can imply that a single photon can 'exist' or extend over a huge interval of time / space. That's fair enough but when does a particular photon take on the nature of long or short coherence? Using an interferometer with a huge baseline, it is possible to detect / resolve images of non-coherent sources (that is all astronomical objects). What does that say about the 'coherence length' of a photon'?
Whilst it's quite possible that explanations exist that could resolve my problem, the sort of explanations that are generally used (like the ones in this thread) don't really hold water. Someone may contribute the term "Fock State" to this thread and the explanation may well lie in that direction. The problem is that it requires a massive leap in understanding, to relate the term to a straightforward thing like interference and coherence length. Straightforward, if you approach it in terms of waves and modulated sources with finite bandwidth.