Threshold for OPOs (Cont.)
We have already seem that the gain coefficient is given by
g2=k1k2|Ep|2 = Ip(2w1w2deff2)/(n1n2n3e0c3)
For a singly resonant device we have
g2l2=2as=2(1-Rs)= Ipl2(2w1w2deff2)/(n1n2n3e0c3)
Solving for Ip we have the threshold for a singly resonant device given by
(Ip)SROthreshold=(1-Rs)(n1n2n3e0c3)/l2(w1w2deff2)
For a doubly resonant device we have
g2l2=aias=(1-Ri)(1-Rs)= Ipl2(2w1w2deff2)/(n1n2n3e0c3)
(Ip)DROthreshold=(1-Ri)(1-Rs)(n1n2n3e0c3)/l2(2w1w2deff2)
If we assume that Ri=99%we have 2/(Ri-1)=50 and the threshold for the doubly resonant device would be 50 times less than the singly resonant device