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

12/05/2010 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 = 880Realistic focal lens: f1 = 40 km / f2 = 60 kmFP 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

- power recycling gain Grec for TEM00- Signal recycling gain GSRC for LG mode- SR transmission

x 2 (probably conservative in NDRC)

x 2?

4

High Order Mode power at the dark port (3/4)

Gain in SRC cavity with Finesse = 880

Gain in SRC cavity with Finesse = 450100

10

1

SRC zero tuning (TEM00 anti-resonant) • At SRC zero tuning, GSRC (HOM) does not vary with FP finesse

Analytical model

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 Grec for TEM00- Signal recycling gain GSRC for LG mode- SR transmission

x 2

x 2≈ cst

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

04/03/2010 6

Constraints on OMC waist (1/2)

Waist of incident beam: w0 + wPHOM ≈ 0.4 WP00 ≈ 0.1 W

OMC waist: w0 ≈ 236 μm

• Effect of a waist mismatch

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

04/03/2010 7

Constraints on OMC waist (2/2)

• Effect of an error on the position of the waist: z

Incident beam:PHOM ≈ 0.4 WP00 ≈ 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

04/03/2010 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 mmwy = 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.

04/03/2010 9

OMC Telescope in Virgo

04/03/2010 10

Virgo OMC bench

Incoming beam (w=2 cm)

L1, f = 2 m

L3, f = 45 cm

L2, f = 10 cm

OMC (w=140 μm)

04/03/2010 11

Virgo OMC Telescope

L1, f = 2m

L2, f = 10cm L3, f = 45cmOMC

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 sizeTuning of waist position