deletions | additions       diff --git a/subsection_Parametric_Oscillator_An_optical__.tex b/subsection_Parametric_Oscillator_An_optical__.tex  index 0af2b08..7064219 100644  --- a/subsection_Parametric_Oscillator_An_optical__.tex  +++ b/subsection_Parametric_Oscillator_An_optical__.tex 
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\[\omega_p = \omega_s + \omega_i\]  \[\varphi_p = \varphi_s + \varphi_i\]  The optical resonator resonates in at least one of the generated frequencies, the non-linear interaction in the crystal leads to amplitude gain for the signal and idler waves and attenuation of the pump wave (parametric amplification), if the amplification is enough to overcome the losses, the resonator will resonate in one of the generated frequencies (singly-resonant) or both (doubly-resonant).   A special case is when the idler and signal frequencies arethe  degenerate. \[\omega_s = \omega_i = \omega_p/2\]  The generated frequency can be tuned by changing the phase-matching conditions of the OPO, thus making the OPO a source of tunable radiation, also, as explained in the next section, the light produced is "squeezed" and useful for various purposes. 
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