Mach-Zehnder interferometer
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The Mach-Zehnder interferometer is used to determine the phase shift caused by a small sample which is to be placed into one of the two beams D and U, respectively, from a coherent light source.
There are - in contrast to the Michelson interferometer - two detectors: 1 and 2.
Mach-zender-interferometer.gif
Function:
A coherent beam is split up by a beamsplitter and each one is reflected by a mirror. The two beams pass a second beamsplitter and enter detector 1 and 2, respectively.
There are some simple rules for phase shifts due to material (i.e. non-vacuum, which has a refractive index of exactly n = 1):
- reflection or refraction at a surface with lower n causes NO phase shift
- reflection or refraction at a surface with higher n there is a shift of half a wavelength
- the speed of light is slower in material with n > 1. This means that in a slab of material the wavelength is decreased by its n :
<math>\lambda_{mat} = \frac{\lambda_{vac}}{n}<math>
This effect can be measured with this setup as every slab of material will change the initial situation: Without a sample there is no phase difference for the two beams in detector 1, thus yielding constructive interference: both have passed three transitions from lower to higher n. On the other hand, at detector 2 there is complete destructive interference: beam D has experienced three phase changes whereas beam U has gone through four, thus yielding a phase difference of half a wavelength. If a sample is now placed into a beam, there will be a variation in the intensities for 1 and 2, which allows the calculation of the phase shift.