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We have a Mach-Zehnder interferometer with two non-polarizing beam splitters. The polarisation state of the input beam is a superposition of +45˚ and -45˚ polarizations. In the upper arm of the interferometer there is a polarizer oriented at 0˚. In the lower arm there is a polarizer oriented at 90˚. Both output beams are passed through polarizers oriented at 90˚. The upper output beam is detected by detector D1 and the lower output beam by D2. Will the interference fringes, observed at D1 be in phase with the fringes observed at D2 or shifted by π rad and why?

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  • $\begingroup$ if input beam is a combination of $\pm 45$deg polarization, isn't simply horizontal or vertical polarization? or are you assuming unequal strength? $\endgroup$
    – wcc
    Aug 4, 2018 at 7:47
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    $\begingroup$ actually, according to your setup, neither detector will see light from path 1, since the polarizations are orthogonal. So the detectors only see light from path 2 and there is no fringe. $\endgroup$
    – wcc
    Aug 4, 2018 at 7:52
  • $\begingroup$ @IamAStudent When the polarizations in the two paths are orthogonal, light from both paths will strike both of the detectors and no interference will be observed when the phase of any of the beams is changed. Now if the input light is H or V or superposition of both when you place a polarizer at ±45˚ at any of the output beams there will be interference at the detectors. If the input light is a superposition of ±45˚then an output polarizer at ±45˚ will not restore interference. Only a V or H oriented output polarizer should restore the interference. $\endgroup$ Aug 4, 2018 at 10:46

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The output will depend on the phase relationship between the two input beams. If they are mutually coherent and their phase difference is 0 degrees, they will combine to form a beam with vertical polarization. If they are 180 degrees out of phase, they will combine to form a beam with horizontal polarization. Various other phase relationships will give right-circular, left-circular, or elliptical polarization.

If the phase relationship is constant, you will get a stable interference pattern at the output of the interferometer. Whatever gets past the polarization filters will form the interference pattern. If, for example, the input beams are in phase so that they amount to a vertically polarized beam with polarization oriented at 0 degrees, nothing will get past the polarizing filters at the output. Rotate the filters to 0 degrees and you will get a bright interference pattern.

You did not specify what the light source(s) is(are). Assuming they aremonochromatic but not mutually coherent, the portion of the beam from each source will form its own interference pattern at the output, and the two interference patterns will overlap. Their intensities will add, but their amplitudes will not. That is, the light from the two sources will not interfere unless the sources are mutually coherent.

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