Current setup in ADV-GWINC

Up to now (April 2009) in the Advanced Virgo GWINC we did not take any signal losses into account which originate from:

• imperfect thermal compensation.
• potential astigmatism inside the signal recycling cavity.

As we know that we will encounter signal losses from these two effects, what will consequently reduce the Advanced Virgo sensitivity, we have start caring about the implementation of these effects into our GWINC model. Eventhough, we don't have numbers for these two types of losses at the current stage of the design, it is a good time to start understanding the principle implementation of the losses into the ADV GWINC.

Status and Goal:

The main parameter we have to properly implement is:

     ifo.TCS.SRCloss=0.0;

This value needs to be specified inside the ADV configuration file. So far we used 0.0 which correponds to perfect TCS (NO thermal distorsions!) and NO astigmatism inside the SRC.
The Goal for the next weeks is to put a realistic number on ifo.TCS.SRCloss.

How does ifo.TCS.SRCloss plug into the GWINC code?

This the corresponding extract from the ADV configuration file:

     %% Parameter describing thermal lensing --------------------------------------
     % The presumably dominant effect of a thermal lens in the ITMs is an increased
     % mode mismatch into the SRC, and thus an increased effective loss of the SRC.
     % This increase is estimated by calculating the round-trip loss S in the SRC as
     % 1-S = |<Psi|exp(i*phi)|Psi>|^2, where
     % |Psi> is the beam hitting the ITM and
     % phi = P_coat*phi_coat + P_subs*phi_subs
     % with phi_coat & phi__subs the specific lensing profiles
     % and P_coat & P_subst the power absorbed in coating and substrate
     %
     % This expression can be expanded to 2nd order and is given by
     % S= s_cc P_coat^2 + 2*s_cs*P_coat*P_subst + s_ss*P_subst^2
     % s_cc, s_cs and s_ss where calculated analytically by Phil Wilems (4/2007)

     %TBC
     ifo.TCS.s_cc=7.024; % Watt^-2
     ifo.TCS.s_cs=7.321; % Watt^-2
     ifo.TCS.s_ss=7.631; % Watt^-2

     % The hardest part to model is how efficient the TCS system is in
     % compensating this loss. Thus as a simple Ansatz we define the
     % TCS efficiency TCSeff as the reduction in effective power that produces
     % a phase distortion. E.g. TCSeff=0.99 means that the compensated distortion
     % of 1 Watt absorbed is eqivalent to the uncompensated distortion of 10mWatt.
     % The above formula thus becomes:
     % S= s_cc P_coat^2 + 2*s_cs*P_coat*P_subst + s_ss*P_subst^2 * (1-TCSeff)^2
     %
     % To avoid iterative calculation we define TCS.SCRloss = S as an input
     % and calculate TCSeff as a bench output.
     % TCS.SRCloss is incorporated as an additional loss in the SRC

     ifo.TCS.SRCloss=0.0;

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ifo.TCS.SRCloss is then used in two gwinc functions:

• the main file 'gwinc.m'
• and in the quantum noise routine 'shotrad.m'

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ifo.TCS.SRCloss in 'gwinc.m'

In the 'gwinc.m' the ifo.TCS.SRCloss is used to calculate the required efficiency of the TCS, TCSeff :

         gwinc.m:  TCSeff=1-sqrt(ifo.TCS.SRCloss/S_uncorr);

where S_uncorr  is given by the following lines from 'gwinc.m':

        PowAbsITM = [finesse*2/pi*ifo.Optics.ITM.CoatingAbsorption/2;...
                           ifo.Materials.MassThickness*ifo.Optics.SubstrateAbsorption/2 ]*pbs;

        M=[ifo.TCS.s_cc,ifo.TCS.s_cs;ifo.TCS.s_cs,ifo.TCS.s_ss];
        S_uncorr=transpose(PowAbsITM)*M*PowAbsITM;

Here pbs is the power on the beam splitter.

ifo.TCS.SRCloss in 'shotrad.m'

This is the section where ifo.TCS.SRCloss shows up in 'shotrad.m':

         % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
         bsloss  = ifo.Optics.BSLoss;                  % BS Loss [Power]
         mismatch = 1 - ifo.Optics.coupling;           % Mismatch
        mismatch = mismatch + ifo.TCS.SRCloss;        % Mismatch

        % BSloss + mismatch has been incorporated into a SRC Loss
        lambda_SR = mismatch + bsloss;                % SR cavity loss [Power].m'

Here ifo.Optics.BSLoss is the sum of losses accumulated around the beamspliter, i.e. BS-AR coating, CP-AR coatings etc. Currently the standard value in the configuration file is somehwat too high for my felling (probaly a fact 10 smaller is more realistic...):

         ifo.Optics.BSLoss  = 2e-3;                   % power loss near beamsplitter

ifo.Optics.coupling gives the losses from the modes between the arm cavities and the signal recycling cavity. So this is the variable we should use to introduce losses from astigmatism inside the SRC. Currently this value is set to 0.997 in the configuration file,  representing rather small astigmatism in the SRC, i.e. a signal loss of only 0.3%:

         ifo.Optics.coupling = 0.997;                   % mismatch btwn arms & SRC modes; used to

Finally we have to follow lambda_SR through the computation inside 'shotrad.m'. First lambda_SR is directly used as signal loss for the computation of the quadrature densities of the quantum noise. Second lambda_SR is also used to calculate rho, which is the effective amplitude reflectivity of the signal recycling mirror:

         tau     = sqrt(ifo.Optics.SRM.Transmittance); % SRM Transmittance [amplitude]
         rho     = sqrt(1 - tau^2 - lambda_SR);        % SRM Reflectivity [amplitude]

rho is then used for the quantum noise calculation, too.