deletions | additions       diff --git a/subsection_Coupled_Parametric_Oscillators_A__1.tex b/subsection_Coupled_Parametric_Oscillators_A__1.tex  index ce3e111..aabfee2 100644  --- a/subsection_Coupled_Parametric_Oscillators_A__1.tex  +++ b/subsection_Coupled_Parametric_Oscillators_A__1.tex 
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-R & T  \end{pmatrix}\]  The eigen-states being,  \[\lambda_\pm \[ \begin{matrix}  \lambda_\pm  = T \pm iR; iR &  V_\pm = \frac{1}{\sqrt{2}} \begin{pmatrix} \begin{matrix}  1 \\ \pm i \end{pmatrix}\] \end{pmatrix}  \end{matrix}  \]  Demostration of the effect in optical resonators is difficult due to losses - some gain mechanism must be added to the system for the effect to be noticeable, but since different modes experience different gain, one mode will always dominate and the beats won't be noticeable.  Parametric gain offers a way to avoid this problem altogether, since it can only amplify frequency pairs that satisfy the conditions above. 
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