deletions | additions       diff --git a/section_Theory_subsection_Mach_Zehnder__.tex b/section_Theory_subsection_Mach_Zehnder__.tex  index e7bf713..6b379dc 100644  --- a/section_Theory_subsection_Mach_Zehnder__.tex  +++ b/section_Theory_subsection_Mach_Zehnder__.tex 
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%From Agarwal pp. 293  By putting multiple interferometers in cascade arrangement, a filter can be obtained. If we have M MZI devices connected in a chain as seen in Fig.[], chain,  then the a  transfer function of the overall filter can be extracted following the sum of $2^M$ paths. An expression for the transfer function in frequency domain is: \cite{Agrawal_2005}  \begin{center}  $\left|H\left(\omega\right)\right|^{2}=\overset{M}{\underset{m=1}{\prod}}\cos^{2}\left(\frac{\omega\tau_{m}}{2}\right)$ 
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Applying the previous variable conversion, the transfer function of two cascaded MZI with two unequal path length difference i.e. $\Delta L$ and $2\Delta L$ become as:  \begin{center}  $\left|H\left(\lambda\right)\right|^{2}=\frac{1}{4}\left[1+\cos\left(\beta\Delta L\right)+\cos\left(2\beta\Delta L\right)+\frac{1}{2}\cos\left(\beta\Delta L\right)+\frac{1}{2}\cos\left(3\beta\Delta L\right)\right]$ $\left|H\left(\lambda\right)\right|^{2}= \left[ \cos\left(\beta\Delta L\right)^2 \times \cos\left(2\beta\Delta L\right)^2 \right]$  \end{center}