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Transparency via destructive interferance.

  1. Jul 3, 2013 #1
    Suppose I have 2 lasers. 1 emits light of exactly 500 THz and the second emits light of a frequency exactly 1 hertz higher. A semitransparent mirror is used to superimpose the 2 beams and create a composite beam. The beam is directed to a detector which detects the intensity of the beam fluctuating in 1 second cycles as the 2 sources come in and out of phase with each other.

    Now here's the part I'm not sure about. During the time that the 2 sources are out of phase both light beams still exist and still travel together without effecting one another. They become undetectable when they are out of phase because when they encounter a charged particle they try to push it in opposite directions, and therefore have no effect on it. Therefore the light cannot interact with matter when it is out of phase. The out-of-phase beams go straight through the detector without interfering with it. If I place a long glass rod on the far side of the detector the glass will slow the propagation of the shorter wavelength more then that of the longer wavelength. Eventually the 2 waves should be in phase again and therefore detectable to a second detector.

    If all this reasoning is true then it is possible to cause coherent light to go through an otherwise opaque object by introducing a second coherent source that interferes destructively with the first. Is this correct or is there an error in my reasoning?
  2. jcsd
  3. Jul 4, 2013 #2
    I think if you fire two in phase lasers at a half-silvered mirror then the combined beam will go one way, and if they are out of phase the combined beam will go the other way. The beam won't pass through the detector because the beam didn't go that way.
  4. Jul 5, 2013 #3
    That doesn't really make sense to me but it's beside the point. I'm sure there IS a way to get 2 out-of-phase laser beams superimposed, direct them to an opaque object, and then if they still exist bring them back in phase. The question is will they be absorbed by the object despite being out-of-phase? Why or why not?
  5. Jul 5, 2013 #4


    Staff: Mentor

    This is a very interesting idea.

    To make it more concrete. Suppose you have one coherent point source and an absorber, then the absorber will cast a shadow. Now suppose you have the same absorber and a different coherent point source of the same wavelength, then the absorber will cast a different shadow. Your question seems to be if the net shadow from the two sources will be the sum of the two shadows or if, by locating the object at a region of destructive interference if there will be no shadow at all.

    Since Maxwell's equations are linear we know that the resultant shadow is indeed the sum of the two shadows. But your reasoning makes sense and I don't see where it is wrong.
  6. Jul 5, 2013 #5
    The point of my post above is that the lasers conserve energy. The side with constructive interference will carry all of the power of the beam, and the side with destructive interference won't carry any power. There's no way for power from the beam to pass through the opaque barrier if there isn't any power in the beam to begin with.

    The reasoning is flawed because there's no way to bring them back in phase on the other side of the barrier. You just said that the beam does not interact with matter (because there's no power in the beam), and then you say it interacts with a glass rod, which is matter.

    So what happens if you pass the no-power beam into a diffraction grating? Geometric optics will fail because the diffraction effects of the beam are large compared with the angle difference between the two diffracted angles.
  7. Jul 7, 2013 #6
    A classical analysis:

    Adding waves with frequencies 500 THz and 500 THz +1 Hz is equivalent to amplitude modulating a 500 THz wave with a 1 Hz signal. When the amplitude is low then a detector detects a low amplitude.

    A quantum mechanical analysis:

    If one wave has frequency exacly 500 THz and other wave has frequency exactly 500 THz + 1 Hz, then these waves do not collide in Hilbert space, so there is no quantum interference.
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