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Specifications for OMC telescope in AdVirgo

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. High Order Mode power at the dark port (1/4).

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Specifications for OMC telescope in AdVirgo

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  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. 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: f1 = 40 km / f2 = 60 km • FP cavities detuning: L = 10-11 m •  Same power in HOMs and TEM 00 • PHOM ≈ P00 ≈ 0.1 W • Simple analytical model: (underestimates total HOM power by a factor 4) HOM power varies with: - power recycling gain Grec for TEM00 - Signal recycling gain GSRC for LG mode - SR transmission

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

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

  5. High Order Mode power at the dark port (4/4) What do we expect with FP finesse = 450 ?  New mirror transmissions x 2 - power recycling gain Grec for TEM00 - Signal recycling gain GSRC for LG mode - SR transmission ≈ cst x 2 • HOM power increases by a factor 4 • For TEM 00: reduction of finesse compensates increase in Grec and TSR • Power does not change • Conclusion (with FP finesse = 450): PHOM ≈ 4 x P00

  6. Constraints on OMC waist (1/2) • Effect of a waist mismatch Waist of incident beam: w0 + w PHOM ≈ 0.4 W P00 ≈ 0.1 W OMC waist: w0 ≈ 236 μm Coupling of HOMs to TEM00 inside OMC  (w/w0)² Contribution to Shot Noise < 1% (w/w0)² < 0.02 x (P00/PHOM) Requirement on waist size  w < 17 μm

  7. Constraints on OMC waist (2/2) • Effect of an error on the position of the waist: z Incident beam: PHOM ≈ 0.4 W P00 ≈ 0.1 W OMC waist: w0 ≈ 236 μm Coupling of HOMs to TEM00 inside OMC  (z/kw0²)² Contribution to Shot Noise < 1% (z/kw0²)² < 0.02 x (P00/PHOM) Requirement on waist position  z < 2.3 cm

  8. 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° • wx = 2.0 mm • wy = 2.5 mm • w/w0 ≈ 25% • At the entrance of OMC: w ≈ 59 μm • Waist mismatch due to astigmatism might exceed the specifications! • Error on waist position ? • z ≈ LPRM1-PRM2(1/cos(i) – 1) ≈ 1.2 mm •  Error on waist position due to beam astigmatism should be negligible.

  9. OMC Telescope in Virgo

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

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

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