1. Specifications for OMC telescope in AdVirgo R. Gouaty, E. Tournefier Estimation of carrier HOM power at the dark port Constraints on OMC waist and position of the waist OMC telescope in Virgo

2. 12/05/20102 High Order Mode power at the dark port (1/4) Waist mismatch couples Laguerre-Gauss HOM into TEM 00 (resonant in OMC).  Constraints on OMC waist depends on HOM power at the dark port LMA simulation with differential thermal lensing in input mirror substrates: NDRC cavity (  gouy = 20°) – SRC zero tuning - FP cavities with Finesse = 880 Realistic focal lens: f 1 = 40 km / f 2 = 60 km FP cavities detuning:  L = 10 -11 m  Same power in HOMs and TEM 00 P HOM ≈ P 00 ≈ 0.1 W Simple analytical model: (underestimates total HOM power by a factor 4) HOM power varies with:- power recycling gain G rec for TEM00 - Signal recycling gain G SRC for LG mode - SR transmission

3. 3 High Order Mode power at the dark port (2/4) What do we expect with FP finesse = 450 ?  New mirror transmissions - power recycling gain G rec for TEM00 - Signal recycling gain G SRC for LG mode - SR transmission x 2 (probably conservative in NDRC) x 2 ?

4. 4 High Order Mode power at the dark port (3/4) Gain in SRC cavity with Finesse = 880 Gain in SRC cavity with Finesse = 450 100 10 1 SRC zero tuning (TEM00 anti-resonant) At SRC zero tuning, G SRC (HOM) does not vary with FP finesse Analytical model

5. 5 High Order Mode power at the dark port (4/4) What do we expect with FP finesse = 450 ?  New mirror transmissions - power recycling gain G rec for TEM00 - Signal recycling gain G SRC for LG mode - SR transmission x 2 ≈ cst  HOM power increases by a factor 4 For TEM 00: reduction of finesse compensates increase in G rec and T SR  Power does not change Conclusion (with FP finesse = 450): P HOM ≈ 4 x P 00

6. 04/03/20106 Constraints on OMC waist (1/2) Waist of incident beam: w 0 +  w P HOM ≈ 0.4 W P 00 ≈ 0.1 W OMC waist: w 0 ≈ 236 μm Effect of a waist mismatch Coupling of HOMs to TEM 00 inside OMC  (  w/w 0 )² Contribution to Shot Noise < 1%  (  w/w 0 )² < 0.02 x (P 00 /P HOM ) Requirement on waist size   w < 17 μm

7. 04/03/20107 Constraints on OMC waist (2/2) Effect of an error on the position of the waist:  z Incident beam: P HOM ≈ 0.4 W P 00 ≈ 0.1 W OMC waist: w 0 ≈ 236 μm Coupling of HOMs to TEM 00 inside OMC  (  z/kw 0 ²)² Contribution to Shot Noise < 1%  (  z/kw 0 ²)² < 0.02 x (P 00 /P HOM ) Requirement on waist position   z < 2.3 cm

8. 04/03/20108 Effect of beam astigmatism Waist mismatch induced by astigmatism: VIR-0256A-10 (M. Granata): waists of PRM1 calculated for  gouy = 20°, incidence angle =0.9° w x = 2.0 mm w y = 2.5 mm   w/w 0 ≈ 25% At the entrance of OMC:  w ≈ 59 μm  Waist mismatch due to astigmatism might exceed the specifications! Error on waist position ?  z ≈ L PRM1-PRM2 (1/cos(  i ) – 1) ≈ 1.2 mm  Error on waist position due to beam astigmatism should be negligible.

9. 04/03/20109 OMC Telescope in Virgo

10. 04/03/201010 Virgo OMC bench Incoming beam (w=2 cm) L1, f = 2 m L3, f = 45 cm L2, f = 10 cm OMC (w=140 μm)

11. 04/03/201011 Virgo OMC Telescope L1, f = 2m L2, f = 10cmL3, f = 45cm OMC w=2 cm w=1 mm Distance L1-L2: determines the size of the waist Position of L3: determines the position of the waist Tuning of waist size Tuning of waist position