deletions | additions       diff --git a/section_Theory_subsection_Mach_Zehnder__.tex b/section_Theory_subsection_Mach_Zehnder__.tex  index 88c3f83..78ae14d 100644  --- a/section_Theory_subsection_Mach_Zehnder__.tex  +++ b/section_Theory_subsection_Mach_Zehnder__.tex 
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The transfer function can be rewritten as a function of wavelength, by noticing two important definitions: the propagation constant $\beta = \frac{n_{eff}\omega}{c}$ and the relative delay is related to the path difference of the MZI as $\tau = \frac{n_{eff}\Delta L}{c}$. Therefore $\omega \tau = \frac{\omega n_{eff}}{c}\Delta L = \beta \Delta L$. Therefore the Transfer function of the filter with two MZI with equal path difference is:  \begin{center}  $\left|H\left(\lambda)\right|^{2}=\frac{1}{4}[\frac{3}{2} + 2 \cos(\beta \Delta L) + \frac{1}{2}\cos(\beta \Delta L)] $ $\left|H\left(\lambda\right)\right|^{2}=\frac{1}{4}\left[\frac{3}{2}+2\cos\left(\beta\Delta L\right)+\frac{1}{2}\cos\left(2\beta\Delta L\right)\right]$  \end{center}