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Mach-Zehnder interferometers can be built with bulk optic elements, optical fibers with fiber couplers and using integrated optics. In this course we are going to build MZI interferometers using SOI integrated technology.  An MZI interferometer is formed by two couplers (or as in this course with two Y-branch) and two waveguide arms of different lengths, in order to have an optical phase difference. The intensity of the propagating wave at the output of an interferometer can be expressed as: \cite{chrostowski2015silicon}  \begin{center}  $I_{0}=\frac{I_{i}}{4}\left|\exp\left(-j\beta_{1}L_{1}-\frac{\alpha_{1}}{2}L_{1}\right)+\exp\left(-j\beta_{2}L_{2}-\frac{\alpha_{2}}{2}L_{2}\right)\right|^{2}$ 
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