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Input mirrors thermal lensing effect in Virgo J. Marque

Input mirrors thermal lensing effect in Virgo J. Marque. Overview. o Thermal lensing model for Finesse o Degenerated flat-flat cavity o The 2 “resonances” in Virgo o Transient and demodulation phase change. Thermal lensing model for Finesse. The Finesse simulation parameters.

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Input mirrors thermal lensing effect in Virgo J. Marque

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  1. Input mirrors thermal lensing effectin VirgoJ. Marque ILIAS - Geneve

  2. Overview o Thermal lensing model for Finesse o Degenerated flat-flat cavity o The 2 “resonances” in Virgo o Transient and demodulation phase change ILIAS - Geneve

  3. Thermal lensing model for Finesse ILIAS - Geneve

  4. The Finesse simulation parameters Next results assume:o CARM and DARM dof are locked with usual error signals B5_ACp and B1_ACp.o Computation is done with TEM06.o MICH and PRCL dof are not locked.o BS and PR are moved around the operating point by a few nm.o Demodulation phases are tuned as in real conditions. Thermal lensing model: The model has been deduced from the fit of the mirrors’ maps from darkF.Beta is the ratio of power absorbed by the NI mirror respect to the WI mirror (deduced from Michele last mirror temperature measurement). ILIAS - Geneve

  5. PRCL and MICH vs PR and BS There are 3 dof in the CITF: lrec, ln and lw.We are sensitive and we want to control 2 dof: MICH and PRCL. We are actually controlling: BS = (lrec-ln+lw)cos45 PR = lrec In Finesse, the control of the BS is a bit different: BS = (lrec+lw)cos45 MICHplan PRCL plan ILIAS - Geneve

  6. Degenerated flat-flat cavity:the power recycling cavity example ILIAS - Geneve

  7. Degenerated flat-flat cavity The thermal lensing effect makes the power recycling cavity (flat-flat at the origin) degenerate.Higher order modes are building up and steal energy from the fondamental mode.Nevertheless, one can distinguish different kinds of “resonances” for a degenerated flat-flat cavity. ROC(ni)> 0  f >0  Power absorbed by ni >02 resonances are are well visibleROC(ni)< 0  f <0  Power absorbed by ni <03 resonances are are well visible ILIAS - Geneve

  8. Analysis of the resonances for ROC>0 1 2 3 3 5 4 2 4 5 1 The main resonance looks like a gaussian beam with decreasing waist. The second resonance looks to converge roughly towards a LG10 shape. ILIAS - Geneve

  9. The 2 “resonances” in Virgo o Carrier and sidebands recycling gaino Locking error signals ILIAS - Geneve

  10. The recycling gains d o CARM and DARM dof are locked with usual error signals B5_ACp and B1_ACp.o Max higher order mode = 6.o MICH and PRCL dof are not locked.o BS and PR are moved around the operating point by a few nm.o Decrease focal length of input mirror  change thermal lensing  Increase power absorbed by input mirrorsd = lambda/2 * (Schnupp asymmetry / PRCL length) = 39nm d MICH dof PRCL dof ILIAS - Geneve

  11. The locking error signals MICH dof PRCL dof B2_3f_ACp= PRCL error signalB5_ACq= MICH error signalThe addition of the absolute values of the 2 signals show that they drive the mirrors towards the coordinates (0,0) = the nominal operating point of Virgo. ILIAS - Geneve

  12. MICH error signal respect to PRCL lenght PRCL lenght = 12.053m PRCL lenght = 12.093m ILIAS - Geneve

  13. Dark fringe signals (before OMC) The power of the carrier/USB/LSB on the dark fringe is around 100-150mW.The best contrast of the ITF does not correspond to the operating point!!!! ILIAS - Geneve

  14. How the dark fringe depends on the end mirrors ROC? The carrier on the dark fringe (the ITF contrast) depends mainly on the asymmetry of the end mirrors ROC: power changes by of a factor 100 between 1m and 100m asymmetry. The best contrast is achieved for different positions of PR and BS depending on end mirrors ROC asymmetry.=> key point for a good ITF contrast!!!! ILIAS - Geneve

  15. Carrier & SB evolution during lock acquisition To understand the variations of the optical paramaters during the lock acquisition, I have repeated the simulations shown in the last slides changing the thermal lensing effect in the input mirrors  power absorbed by the input mirrors ILIAS - Geneve

  16. EVOLUTION with thermal lensing Between 5 and 10mW absorption, transition from one to two zones of resonances for 2 different values of PRCL.Similar to the 2 “resonances” identified for a degenerated flat-flat cavity.Error signals are good for both resonances. ILIAS - Geneve

  17. EVOLUTION with thermal lensing(dark fringe) ILIAS - Geneve

  18. What would see a phase camera?(no thermal lensing) 3 1 2 1 2 3 Note that the size of the gaussian shapes of the sidebands is slightly different from the carrier.Even without thermal lensing, the input mirrors are not perfectly flat in the simulation (ROC have been characterized by LMA). ILIAS - Geneve

  19. What would see a phase camera?(carrier, power abs by NI=35mW) Both resonances have a nice gaussian shape for the carrier. The FP cavities behave as a filter for the carrier. 2 1 1 2 ILIAS - Geneve

  20. What would see a phase camera?(sb, power abs by NI=35mW) 4 2 3 1 1 2 4 3 All sidebands look as expected by the analysis of the degenerated fla-flat cavity ILIAS - Geneve

  21. Transient and demodulation phase change ILIAS - Geneve

  22. 0 No thermal lensing.PRCL error signal is unsensitive to a mistuning of the demodulation phase. CARM, DARM and MICH are always controlled in this simulation. ILIAS - Geneve

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  32. 11 Second zone of resonance appeared.A change by 50 degrees of the demodulation phase of B2_3f allows to jump to the “second resonance”.Critical: time window to operate this change is not well defined… “first resonance” “second resonance” ILIAS - Geneve

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  41. 20 “second resonance”: operating point depends slightly on demodulation phase tuning => offset on error signal to be tuned (see ILIAS talk of Gabriele in Hannover)“first resonance”:error signal sign has flipped!Looks very difficult to keep the lock on this operating point… “first resonance” “second resonance” ILIAS - Geneve

  42. Transient and final state depends on many parameters… o Frequency modulation / PRCL length detuning o Mode matching detuningo Higher finesse for the FP cavities=> difficult analysis… ILIAS - Geneve

  43. Conclusion The recycling cavity is degenerated in 2 “resonances” with the input mirrors thermal lensing effect.These 2 “resonances” are kind of equally resonant in the full Virgo configuration (this has been cross-checked with DarkF = FFT propagation code) => difficult transition in the locking acquisition, jumps, decrease of the recycling gains => demodulation phase change method to keep the lock…And some numbers:150W in input mirror substrate (10cm long), 5kW in FPLMA absorption characterisation: 0.7ppm/cm + 1.2 ppm => 8mW absorbedMirror temperature measurement (drum mode frequency shift => 4 to 6 times moreFinesse simulation => at least 2 to 3 times more Thermal lensing compensation system is mandatory for higher input power. ILIAS - Geneve

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