deletions | additions       diff --git a/subsection_Coupled_Parametric_Oscillators_A__1.tex b/subsection_Coupled_Parametric_Oscillators_A__1.tex  index 1587d13..6ada6c1 100644  --- a/subsection_Coupled_Parametric_Oscillators_A__1.tex  +++ b/subsection_Coupled_Parametric_Oscillators_A__1.tex 
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\[ \varphi = \theta N\]  By substituting $N = t/\tau$, where $\tau$ is the round trip time in the cavity, and taking the time derivative we get,  \[ \Omega_\pm = \pm \theta/\tau \equiv \pm \Omega\]  The system will beat with this frequency, that depends on the coupling strength.  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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