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Can two perfect point monochromatic sources be incoherent?

  1. Nov 3, 2015 #1
    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 :)
     
  2. jcsd
  3. Nov 3, 2015 #2
    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.

    --
    lightarrow
     
  4. Nov 3, 2015 #3
    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
     
  5. Nov 3, 2015 #4
    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.
     
  6. Nov 3, 2015 #5
    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. :)
     
  7. Nov 4, 2015 #6
    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.
     
  8. Nov 4, 2015 #7

    ehild

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    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.
     
  9. Nov 4, 2015 #8

    blue_leaf77

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    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.
     
  10. Nov 4, 2015 #9
    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)?

    I don't understand what it means, please tell in some more simplified way.

    Thank you guys, you are all awesome:)

    Regards
     
  11. Nov 4, 2015 #10

    blue_leaf77

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    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)##.
     
  12. Nov 4, 2015 #11

    sophiecentaur

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    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.
     
  13. Nov 4, 2015 #12

    Andy Resnick

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    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.
     
  14. Nov 4, 2015 #13

    ehild

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    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
    youngs-frings-screen.jpg
    In case of two monocromatic sources of the same wavelength it would be a sine function.
     
  15. Nov 4, 2015 #14
    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
    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
     
  16. Nov 4, 2015 #15

    ehild

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    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.
     
    Last edited: Nov 4, 2015
  17. Nov 4, 2015 #16

    sophiecentaur

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    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.
     
  18. Nov 4, 2015 #17
    I think something similar is said blue_leaf77

    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?

     
  19. Nov 5, 2015 #18
    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.
     
  20. Nov 5, 2015 #19

    ehild

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    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.
     
  21. Nov 5, 2015 #20
     
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