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Message ID: 14058     Entry time: Thu Jul 12 15:15:47 2018
Author: Sandrine 
Type: Update 
Subject: Beat Note Measurements for Cavity Scans 

(Gautam, Sandrine)

We calculated the expected power of the beat note for Annalisa's Y arm cavity scans. 

Beat Note Measurement

We began by calculating the transmitted power of the PSL and AUX. We assumed that the input power of the PSL was 25 mW and the input power of the AUX was 250 uW. We also assumed a loss of 25 ppm for the ITM and ETM. We used T1 = 0.0138 and T2 = 25 x 10-6. 

P_{t} = \frac{t _{1}^{2}t_{2}^{2}}{1+r_{1}^{2}r_{2}^{2}-2r_{1}r_{2}}

t = \sqrt{T}          

r = \sqrt{1-T-L} = {\sqrt{R}}

The transmitted power of the PSL is approximately 100 uW, and the transmitted power of the AUX is approximately 0.974 uW. 

P_{t}^{PSL} = 100 uW                          P_{t}^{AUX} = 0.974 uW

The beat note was calculated with the following:

P_{beat} = 2\sqrt{P_{PSL}P_{AUX}} = 20 uW

The  expected beat note should be approximately 20 uW. 

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