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 Thu Mar 4 17:04:52 2021, Paco, General, Design specs, Silicon TM dichroic coatings for phase I Wed Mar 17 19:51:42 2021, Paco, General, Design specs, Silicon TM dichroic coatings for phase I Wed Mar 17 21:24:27 2021, gautam, General, Design specs, Silicon TM dichroic coatings for phase I Wed Mar 24 17:36:46 2021, Paco, General, Design specs, Least common multiple stacks and varL cost Fri Apr 2 19:59:53 2021, Paco, General, Design specs, Differential evolution strategies Fri Jun 4 11:09:27 2021, Paco, General, Design specs, HR coating tolerance analysis Wed Mar 24 17:42:50 2021, Paco, General, Design specs, Silicon TM dichroic coatings for phase I
Message ID: 15     Entry time: Fri Jun 4 11:09:27 2021     In reply to: 10
 Author: Paco Type: General Category: Design specs Subject: HR coating tolerance analysis

The HR coating specifications are:

 2128.2 nm 5.0 ppm $\pm$ 2 ppm 1418.8 nm 50.0 ppm $\pm$ 2 ppm

 2128.2 nm 2000.0 ppm $\pm$ 200 ppm 1418.8 nm 50.0 ppm $\pm$ 2 ppm

### Analysis

• Main constraint: Relative arm finesses @ 2128.2 nm should not differ by > 1%.
• Secondary constraint: Relative arm finesses @ 1418.8 nm may differ, but the ETM and ITM pair should ensure critically coupled cavity to benefit ALS calibration PD shot noise.

Just took the finesse of a single arm:

$\mathcal{F} = \frac{\pi \sqrt{r_1 r_2}}{1 - r_1 r_2}$

and propagated transmissivities as uncorrelated variables to estimate the maximum relative finesse. Different tolerance combinations give the same finesse tolerance, so multiple solutions are possible. I simply chose to distribute the relative tolerance in T for the test masses homogeneously to simultaneously maximize the individual tolerances and minimize the joint tolerance.

A code snippet with the numerical analysis may be found here.

Tue Jun 8 11:52:44 2021 Update

The arm cavity finesse at 2128 nm will be mostly limited by the T = 2000 ppm of the ITM, so the finesse changes mostly due to this specification. Assuming that the vendor will be able to do the two ETM optics in one run (x and y), we really don't care so much about the mean value achieved in this run as much as the relative one. Therefore, the 200 ppm tolerance (10% level) is allowed at the absolute level, but a 20 ppm tolerance (1% level) is still preferred at the relative level; is this achievable?. Furthermore, for the AUX wavelength, we mostly care about achieving critical coupling but there is no requirement between the arms. Here a 20 ppm tolerance at the absolute level should be ok, but a 2 ppm tolerance between runs is highly desirable (although it seems crazier); is this achievable?

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