I have been thinking that the TF measurement (coupling from RIN to frequency noise) we plotted before has unusable unit [Frequency noise /RIN]. We have to correct it by converting it to [frequency noise/ watt]. With that we can compare the result to other experiment/ calculation or use it in the noise budget. As an example, I plot the result calculated by Cerdonio etal 2003 here as well.
==we use wrong unit==
I am editing my noise budget code to incorporate the effect from RIN induced noise and find out that, the unit we have in Fnoise/RIN is not making sense. In order to get the noise due to RIN I have to multiply measured RIN to the measured TF, that is Freq noise due to RIN = [measured TF] x [measured RIN behind CAV] = [Hz/RIN] x [RIN] = Hz. As we can see, it does not change with the input power level. In reality, it should depend on the power level as well. That is why I think Hz/RIN unit is unusable.
==result from Cerdonio==
Braginsky etal calculated the noise from thermal expansion due to heat absorbed from shot noise. The result was later corrected for all frequency span by Cerdoniot etal in 2003. The result tells us the displacement noise due to shot noise. With some modification, we can apply the result to get the displacement noise due to RIN. This will be compared with the measurement later. [add calculation]
fig1: calculation for TF using Cerdonio etal's result.
fig2: calculated TF in unit of [Hz/Watt] (I convert the result from m/watt to Hz/watt). Frequency noise can be calculated by multipling the TF with RIN x Pin. [fig file, code]
==some thing about the measurement setup==
The nice thing from the measurement is that we can see the Cerdonio effect when the thermal diffusion length is comparable to the spot size (around 3Hz) nicely. However, the asymptotic behavior of our measurement does not agree well with the prediction. It has a slope of 1/f0.75 , while we expect 1/f. I'll find out what's wrong with the setup (bad alignment on EAOM, PDH signal, etc) or other mechanism that might cause this effect. |