I checked the noise budget code psl_refcav_sio2_300K.m on Laser intensity noise.
The value for df/dp, which is intensity dependence of the cavity resonance frequency, from Alnis et al. is 70 Hz/uW (page 6, just before section 3)
for the light coupled into the cavity. I'm not sure where the original value, 25 Hz/uW, in the code came from. I'll ask Rana about this.
df/dp already incorporates both effects from photo elastic and photo refractive noise in the coatings + substrate,
so we don't have to worry about dn/dT, or
thermal expansion coeff of the material.
Their coating materials are SiO2, Ta2O5, 38 layers. Our coating materials are similar, but only 17 layers thick.
So we should be able to rescale their df/dp for our cavity.
| Alnis etal| PSL |
cavity length [mm] | 77.5 | 203.5 |
Finesse | 4e5 | 1e4 |
wavelength [nm] | 972 | 1064 |
If we have dp (the power fluctuation of the coupled power, coupling efficiency * input power * RIN,),df can be calculated.
However, df should depend on the cavity length, and the nominal frequency of the beam.
df ~ f dL / L, where f = nominal frequency, L = cavity length.
And dP should depend on the circulating power inside the cavity which truly tells the value of absorbed power on the coatings.
dp ~ Pcirculating/ Finesse.
Thus, our df/dp should be rescaled to
70e6 * (203.5 / 77.5 ) * (1e4 / 4e5) = 4.6e6 Hz/W.
About Pointing noise. The instability of laser pointing will cause power fluctuation coupled into the cavity.
This power fluctuation will induce frequency noise. If we know
how the beam moves, power coupled into the cavity and fluctuation can be calculated.
I'm thinking about using 2 QPDs to measure the beam position. A beam splitter will split the beam between 2 QPDs, the difference between
two readouts should tell us about angular and tranlational motion, and the power will be
P = Po Exp [ - (dx/w0)2 - (dtheta/ div angle)2]
where dx = translational motion
w0 = beam's waist
dtheta = angular motion
div angle = beam divergence angle.