NAOJ GW Elog Logbook 3.2
estimation of birefringence
By combining the several polarization measurements of AZTEC #3, it is possible to compute its birefringence parameters (delta n and theta) as shown in figure 1.
I modified also a bit this analysis as follow :
Because we are only sensitive to the modulus of the birefringence parameters, when theta is negative I take its opposite to only have positive theta.
Also, because delta n is proportional to arcsin( I_po * sin(2 * theta) ^2 ) where I_po is the p polarization when injecting s polarization, there could be points on the mirror where the arcsin is not defined (eg its parameters larger than 1).
In that case, I express delta n as pi/2 + arcsin( I_po * sin(2 * theta) ^2 mod(1) ).
I also show in figures 2 and 3 the stress coefficients.
Interestingly, the folding/discontinuity in theta happens for large stress area.
estimation of losses
From the birefringence parameters, it is possible to compute the s to p polarization losses as sin(2*theta)^2 * sin(pi*d*delta n / lambda) with d = 0.155 m the mirror thickness and lambda the wavelength.
This losses should actually corresponds exactly to the p polarization power when injecting s polarization.
These 2 measurements are shown in the top row of figure 4 (the black circle show the beam area when installed in KAGRA). They match really well except in the area with theta folding/discontinuity. We are currently investigating how to combine these 2 measurements to smoothen theta.
Also, we computed the mean losses as follow :
| from direct Ip measurement | from birefringence measurement | |
| accross all mirror | 0.79 % | 0.95% |
| weighted by the beam power distribution | 0.76 % | 0.96% |
| inside ITM beam diameter | 0.52 % | 0.72 % |
There is a little discrepancy between the 2 ways we compute the s to p polarization losses.
One possible explanation could be that we were using the mean of theta and delta n from 7 measurements during about 5 days.
It is quite probable that alignment condition or translation stage position slightly drifted between each measurements making this mean value a bit different with some sharp features.
I attach to this entry the comparison between the direct estimation of losses and the delta n and theta computed for each input polarization angle.
There is no sharp feature anymore and we have better agreement between the 2 estimations !