Mach-Zehnder interferometer

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.

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/refraction at a surface with lower n causes NO phase shift
• 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.