1. 30-03-07ILIAS - Geneve1 Input mirrors thermal lensing effect in Virgo J. Marque

2. 30-03-07ILIAS - Geneve2 Overview o Thermal lensing model for Finesse o Degenerated flat-flat cavity o The 2 “resonances” in Virgo o Transient and demodulation phase change

3. 30-03-07ILIAS - Geneve3 Thermal lensing model for Finesse

4. 30-03-07ILIAS - Geneve4 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).

5. 30-03-07ILIAS - Geneve5 PRCL and MICH vs PR and BS PRCL plan MICH plan 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

6. 30-03-07ILIAS - Geneve6 Degenerated flat-flat cavity: the power recycling cavity example

7. 30-03-07ILIAS - Geneve7 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 >0 2 resonances are are well visible ROC(ni)< 0  f <0  Power absorbed by ni <0 3 resonances are are well visible

8. 30-03-07ILIAS - Geneve8 Analysis of the resonances for ROC>0 1 5 4 3 2 13 54 The main resonance looks like a gaussian beam with decreasing waist. The second resonance looks to converge roughly towards a LG10 shape. 2

9. 30-03-07ILIAS - Geneve9 The 2 “resonances” in Virgo o Carrier and sidebands recycling gain o Locking error signals

10. 30-03-07ILIAS - Geneve10 The recycling gains 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 mirrors d = lambda/2 * (Schnupp asymmetry / PRCL length) = 39nm MICH dof PRCL dof d d

11. 30-03-07ILIAS - Geneve11 The locking error signals B2_3f_ACp = PRCL error signal B5_ACq = MICH error signal The 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. PRCL dof MICH dof

12. 30-03-07ILIAS - Geneve12 MICH error signal respect to PRCL lenght PRCL lenght = 12.053m PRCL lenght = 12.093m

13. 30-03-07ILIAS - Geneve13 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!!!!

14. 30-03-07ILIAS - Geneve14 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!!!!

15. 30-03-07ILIAS - Geneve15 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

16. 30-03-07ILIAS - Geneve16 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.

17. 30-03-07ILIAS - Geneve17 EVOLUTION with thermal lensing (dark fringe)

18. 30-03-07ILIAS - Geneve18 What would see a phase camera? (no thermal lensing) 1 3 2 132 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).

19. 30-03-07ILIAS - Geneve19 What would see a phase camera? (carrier, power abs by NI=35mW) 1 2 1 2 Both resonances have a nice gaussian shape for the carrier. The FP cavities behave as a filter for the carrier.

20. 30-03-07ILIAS - Geneve20 What would see a phase camera? (sb, power abs by NI=35mW) 1 23 4 2 3 4 All sidebands look as expected by the analysis of the degenerated fla-flat cavity 1

21. 30-03-07ILIAS - Geneve21 Transient and demodulation phase change

22. 30-03-07ILIAS - Geneve22 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.

23. 30-03-07ILIAS - Geneve23 1

24. 30-03-07ILIAS - Geneve24 2

25. 30-03-07ILIAS - Geneve25 3

26. 30-03-07ILIAS - Geneve26 5

27. 30-03-07ILIAS - Geneve27 6

28. 30-03-07ILIAS - Geneve28 7

29. 30-03-07ILIAS - Geneve29 8

30. 30-03-07ILIAS - Geneve30 9

31. 30-03-07ILIAS - Geneve31 10

32. 30-03-07ILIAS - Geneve32 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”

33. 30-03-07ILIAS - Geneve33 12

34. 30-03-07ILIAS - Geneve34 13

35. 30-03-07ILIAS - Geneve35 14

36. 30-03-07ILIAS - Geneve36 15

37. 30-03-07ILIAS - Geneve37 16

38. 30-03-07ILIAS - Geneve38 17

39. 30-03-07ILIAS - Geneve39 18

40. 30-03-07ILIAS - Geneve40 19

41. 30-03-07ILIAS - Geneve41 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”

42. 30-03-07ILIAS - Geneve42 Transient and final state depends on many parameters… o Frequency modulation / PRCL length detuning o Mode matching detuning o Higher finesse for the FP cavities => difficult analysis…

43. 30-03-07ILIAS - Geneve43 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 FP LMA absorption characterisation: 0.7ppm/cm + 1.2 ppm => 8mW absorbed Mirror temperature measurement (drum mode frequency shift => 4 to 6 times more Finesse simulation => at least 2 to 3 times more Thermal lensing compensation system is mandatory for higher input power.