I changed the power input from 1mW to 2mW for both cavities and measure the beat signal. From the measured results, there is no difference between the beat signal at different power input levels. This means that the current signal is unlikely to be sitting on shot noise or electronic noise that depend on power level.
With the current laser (500mW), we can increase the power to both cavities up to 2mW. With higher input power, shot noise and electronics noise can be brought down. Even though the noise budget suggests that we are not limited by shot noise and electronic noise, I think it is a good idea to verify it . If we are limited by the shot noise due to low input power or electronic noise due to low frequency discriminator gain, we can see the change if we increase the power.
==results and comments==
I plot the beat measurement with 1mW (black) and 2mW(pink) power together to show that there is no apparent improvement. Note that the noise budget is corrected for 2mW input power for both cavities. (I have not include the noise due to power fluctuation yet, I'll add that soon).
The slope around 50 Hz to 200 Hz is strongly go with 1/f^0.5 which is the slope of Brownian noise. However, it is ~ a factor of 1.2 above the upper limit of our estimation. I will check with Peter if he still has some information about the coating or not, and also the parameters in the noise budget calculation (for example, the loss in SiO2 for spacer, substrate to see if the values I use are sensible or not.