I consider a Mach-Zehnder interferometer. It is said that this setup cannot be phase stabilized properly because it has light travelling in two arms, whereas it is more stable in the case of Sagnac interferometer. Please let me know the cause for the variation of phase difference with time and a way to measure it.
Concerning the stabilization there are different options. You could use a Hänsch-Couillaud detector to generate an error signal as in the attached publication and employ a piezo driven mirror as a phase shifter in one of the interferometer arms.
Article Coherent addition of fiber-amplified ultrashort laser pulses
Here is a publication by M. U. Wehner et al. , which may be helpful.
http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-22-19-1455
If you have glass component in an interferometer you have anisotropy of refractive indices in the glass components caused by the photoelastic effect that converts mechanical stress into optical anisotropy. Without antireflection coating you have an anisotropic resonator that is very sensitive to temperature. To calculated this effect you must have the four anisotropic quantities of the glass components (Delta, Phi, Phi, and Rho)
Delta : relative retardation
Phi: orientation of anisotropy (stress)
Psi: relative loss
Rho: Pseudoactivity angle (caused by stress rotation in beam direction)
For getting high stability be following is required:
1. Use a Zerodur basis
2. Use beamsplitters with low stress anisotropy
3. Use an antireflection coating for the beam splitters
4. Use low anisotropy surface mirrors
5. Make a temperatur stabilizaton for the whole set up
In the Sagnac interferometer, both optical paths traverse the same physical space (e.g. an optical fibre), so the only imbalances are due to localised changes in phase length during the time the light traverses the paths. The other factor is that the path lengths in the Sagnac are intrinsically very tightly matched (being the counter propagating beam lengths), so it is easy to be in the zero order fringe. The detected phase noise increases with differential path length, so other interferometers display more phase npise unless carefully balanced.
In MZ the two optical paths are physically different and thus subject to all effects (physical length, temperature, pressure, etc) that changes the optical phase.
In Sagnac interferometer the two optical paths are identical as long as the system is time-invariant and reciprocity is not broken. In reverse actually we can break these conditions to shift the interference fringe in Sagnac interferometer. These tricks include a phase modulator asymmetrically placed in the Sagnac interferometer (the system is now time variant), a polarization controller (including polarization, we actually have two CW paths and two CCW paths), and rotating the Sagnac loop (the fringe shift is proportional to the rotational speed, a basis for fiber optics gyroscope!).
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