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Entry  Fri Dec 27 16:26:11 2019, Yehonathan, Update, PSL, PMC Linewidth measurement PMCTransmissionSpectra.pdf
    Reply  Wed Jan 1 14:14:00 2020, Yehonathan, Update, PSL, PMC Linewidth measurement 150MHzSideBandCreation.pdfLinewidthMeasurment.pdf
       Reply  Wed Jan 15 15:04:31 2020, gautam, Update, PSL, PMC Linewidth measurement 
          Reply  Fri Jan 17 22:11:19 2020, Yehonathan, Update, PSL, Ringdown measurements 20200117_192455.jpg20200117_192448.jpg
             Reply  Sat Jan 25 11:54:42 2020, Yehonathan, Update, PSL, Ringdown measurements Input_beam_path.jpgReflected_Beam_Path.jpgTransmitted_Beam_Path.jpgPMCRingdownNormalizedRawdata.pdfTransPDFits.pdf
                Reply  Mon Jan 27 21:35:06 2020, Yehonathan, Update, PSL, Ringdown measurements IMC_REFL_Beam_Path.jpg
                   Reply  Mon Jan 27 21:48:49 2020, gautam, Update, PSL, Ringdown measurements elevatedSeis.pdf
                      Reply  Tue Jan 28 16:01:17 2020, gautam, Update, IOO, IMC WFS servos stable again QPD_recenter.png
                         Reply  Tue Jan 28 20:51:37 2020, Yehonathan, Update, IOO, IMC WFS servos stable again 
                            Reply  Wed Jan 29 12:40:24 2020, Yehonathan, Update, IOO, IMC Ringdowns preliminary data analysis IMCRingdownNormalizedRawdata.pdfIMCTransPDFits.pdf
                               Reply  Mon Feb 3 13:54:10 2020, Yehonathan, Update, IOO, IMC Ringdowns extended data analysis IMCTransReflAnalysis_anotated.pdf
                                  Reply  Wed Feb 5 21:13:17 2020, Yehonathan, Update, IOO, IMC Ringdowns extended data analysis 
                                     Reply  Sat Feb 15 12:56:24 2020, Yehonathan, Update, IOO, IMC Transfer function measurement IMCFrequencyResponse.pdfIMCRingdownNormalizedRawdata.pdfIMCREFLPDFits.pdf
Message ID: 15183     Entry time: Mon Feb 3 13:54:10 2020     In reply to: 15175     Reply to this: 15190
Author: Yehonathan 
Type: Update 
Category: IOO 
Subject: IMC Ringdowns extended data analysis 

I extended the ringdown data analysis to the reflected beam following Isogai et al.

The idea is that measuring the cavity's reflected light one can use known relationships to extract the transmission of the cavity mirrors and not only the finesse.

The finesse calculated from the transmission ringdown shown in the previous elog is 1520 according to the Zucker model, 1680 according to the first exponential and 1728 according to the second exponential.

Attachment 1 shows the measured reflected light during an IMC ringdown in and out of resonance and the values that are read off it to compute the transmission.

The equations for m1 and m3 are the same as in Isogai's paper because they describe a steady-state that doesn't care about the extinction ratio of the light.

The equation for m2, however, is modified due to the finite extinction present in our zeroth-order ringdown.

Modelling the IMC as a critically coupled 2 mirror cavity one can verify that:

m_2=P_0KR\left[T-\alpha\left(1-R\right)\right]^2+\alpha^2 P_1

Where P_0 is the coupled light power 

P_1 is the power rejected from the cavity (higher-order modes, sidebands)

K=\left(\mathcal{F} /\pi \right )^2 is the cavity gain.

R and T are the power reflectivity and transmissivity per mirror, respectively.

\alpha^2 is the power attenuation factor. For perfect extinction, this is 0.

Solving the equations (m1 and m3 + modified m2), using Zucker model's finesse, gives the following information:

Loss per mirror = 84.99 ppm
Transmission per mirror = 1980.77 ppm
Coupling efficiency (to TEM00) = 97.94%
Attachment 1: IMCTransReflAnalysis_anotated.pdf  658 kB  | Show | Show all
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