Owing to the orthogonality relations of , we get
For Gaussian beams, we substitute the ’s in the preceding formulas. For the parameters
corresponding to Virgo input mirrors (
, w = 2 cm) we find
In the case of the flat beam, one should note the peaks at the location of the sharp edges of the intensity distribution. This was the cause of the divergence of the infinite mirror approach. However, the estimation for the flat and mesa beams are not very different.
The components of the gradient of the trace of the strain tensor on the reflecting surface can be obtained
from the model developed for the Brownian thermal noise. We consider a new solution of the
Navier–Cauchy equations, matched to the bulk solution at , and depending on specific parameters
and
. The components of the gradient are as follows, with the notation already introduced.
With the coating parameters already given, we get the following results for the coating noise. For the
mode with w = 2 cm waist:
http://www.livingreviews.org/lrr-2009-5 | ![]() This work is licensed under a Creative Commons License. Problems/comments to |