I extended the ringdown data analysis to the reflected beam following Isogai et al.
The idea is that measuring the cavity's reflected light one can use known relationships to extract the transmission of the cavity mirrors and not only the finesse.
The finesse calculated from the transmission ringdown shown in the previous elog is 1520 according to the Zucker model, 1680 according to the first exponential and 1728 according to the second exponential.
Attachment 1 shows the measured reflected light during an IMC ringdown in and out of resonance and the values that are read off it to compute the transmission.
The equations for m1 and m3 are the same as in Isogai's paper because they describe a steady-state that doesn't care about the extinction ratio of the light.
The equation for m2, however, is modified due to the finite extinction present in our zeroth-order ringdown.
Modelling the IMC as a critically coupled 2 mirror cavity one can verify that:
![m_2=P_0KR\left[T-\alpha\left(1-R\right)\right]^2+\alpha^2 P_1](https://latex.codecogs.com/gif.latex?m_2%3DP_0KR%5Cleft%5BT-%5Calpha%5Cleft%281-R%5Cright%29%5Cright%5D%5E2+%5Calpha%5E2%20P_1)
Where  is the coupled light power
 is the power rejected from the cavity (higher-order modes, sidebands)
 is the cavity gain.
 and  are the power reflectivity and transmissivity per mirror, respectively.
 is the power attenuation factor. For perfect extinction, this is 0.
Solving the equations (m1 and m3 + modified m2), using Zucker model's finesse, gives the following information:
Loss per mirror = 84.99 ppm
Transmission per mirror = 1980.77 ppm
Coupling efficiency (to TEM00) = 97.94% |