I rechecked the TF between power fluctuation and frequency noise in beat measurement that I did last year. The estimated result agrees more with the measured result. This can be used to estimate the requirement for ISS for SiO2/Ta2O5 and AlGaAs coatings.
The calculation is taken from Farsi etal 2012 (J. Appl. Phys. 111, 043101), and compared with the measurement from 8" cavities, SiO2/Ta2O5 QWL with SiO2 1/2 wave cap. The code I wrote before has several mistakes, so I fixed them.
**Mistakes in the original code:**
- Beta effective was for 1/4 cap of nL: I changed it to the right one (1/2 cap of nL). This can be done by GWINC or an analytical result.
- Cut off frequency w
_{s}, w_{c} in the paper, I divided by a factor of 2*pi make them in Hz.
- Missing a factor of imaginary in thermoelastic in coatings calculation.
- r0 in the paper is where the power is dropped by 1/e, so r0 = w0/sqrt(2) where w0 is the radius of the beam when the power is dropped by 1/e^2.
Above: Measurement(purple) from SiO2/Ta2O5 coatings and analytical result (cyan) in comparison. Finesse = 7500 (old ACAV), absorbtion = 5ppm. The slope at high frequency seems to be real TO noise. Notice that phases from TE and TR have different sign and cancel one another.
**==for TO optimized AlGaAs coatings== **
Above: Calculation for RIN induced thermo noise for optimized AlGaAs coatings in Hz/Watt unit. The calculation is for 200 ppm transmission,-> Finesse ~14 000. 1.45" cavity. The cancellation in coatings will reduce the noise. The estimated effect is plot against the measurement from 8" cavity, T=300ppm, SiO2,Ta2O5 cavity.
We might have to make sure that RIN is small enough, since this time we will have no common mode rejection like what we had with just a single laser. I'll add the estimated requirement later. |