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$I_{0}=\frac{I_{i}}{2}\left\{ 1+\cos\left(\Delta\beta L\right)\right\} $  \end{center}  Another way to control the optical phase is by changing the path length difference of the two arms of the interforemeter. This is the method used here in interferometer. In  this course, this is the preferred method,  because we deal are dealing  only with passive silicon photonics photonic  designs. The path difference is denoted as by  $\Delta L$ and it should be no less than $21 \mu m$. The intensity at the output of the MZI is: \begin{center}  $I_{0}=\frac{I_{i}}{2}\left\{ 1+\cos\left(\beta\Delta L\right)\right\} $ 
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