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\section{Theory}  In this section a brief theoretical explanation of the operation of a  Mach-Zehnder interferometers interferometer  is given in terms of their gain spectrum response. \subsection{Mach-Zehnder Interferometer basic operation} 
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$I_{0}=\frac{I_{i}}{4}\left|\exp\left(-j\beta_{1}L_{1}-\frac{\alpha_{1}}{2}L_{1}\right)+\exp\left(-j\beta_{2}L_{2}-\frac{\alpha_{2}}{2}L_{2}\right)\right|^{2}$  \end{center}  Assuming no propation propagation  loss along the waveguides, one can simplify the output intensity as: \begin{center}  $I_{0}=\frac{I_{i}}{2}\left\{ 1+\cos\left(\beta_{1}L_{1}-\beta_{2}L_{2}\right)\right\} $ 
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