deletions | additions       diff --git a/Filter_based_MZI_Gain_Responses__.tex b/Filter_based_MZI_Gain_Responses__.tex  index 693df05..3ab1a97 100644  --- a/Filter_based_MZI_Gain_Responses__.tex  +++ b/Filter_based_MZI_Gain_Responses__.tex 
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Filter based MZI Gain Responses (MZ8, MZ9)  Here a demonstration of a filter response is shown by cascading two interferometers and considering no loss. Figure \ref{fig:mzi8-9}(a) shows the response when two interferometers with similar path length difference are chain together. The response is a bit similar to MZI6 interferometer. However, figure \ref{fig:mzi8-9}(b) shows an interesting response where clearly the transmission peaks are a bit narrower. If at each stage of interferometers the path difference follows a geometric progression i.e. $\Delta L$, $2\Delta L$, $4\Delta L$, ... then low passband loss occurs and clearly defined peaks are obtained.\cite{madsen1999optical} Another interesting application for these filters is as a channel selector or de-multiplexer. By cascading multiples of these devices, one can narrowly select closely spaced optical channels. \cite{Agrawal_2005}