deletions | additions       diff --git a/subsection_Coupled_Parametric_Oscillators_A__1.tex b/subsection_Coupled_Parametric_Oscillators_A__1.tex  index e2554c4..dce8707 100644  --- a/subsection_Coupled_Parametric_Oscillators_A__1.tex  +++ b/subsection_Coupled_Parametric_Oscillators_A__1.tex 
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As the system evolves, the eigen-states only accumulate phase.  \[\varphi = \theta N_\pm\]  Substituting $N_\pm = \frac{t}{\tau}$, where $\tau$ is the round-trip time inside the cavity, we get the angular frequency,  \[\Omega_\pm = \pm  \frac{\theta}{\tau}\] 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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