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\subsection{Parametric Oscillator}  An optical parametric oscillator consists of an optical resonator and a non-linear crystal, medium,  a pump wave is inserted into the resonator, the resonator is noisy and thus many frequencies are present, through non-linear interaction the pump wave amplifies resonant frequency pairs that satisfy the conditions. \[\omega_p = \omega_s + \omega_i\]  \[\varphi_p = \varphi_s + \varphi_i\]  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).  
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