galimberti - gwadw 2010 - kyotogw.icrr.u-tokyo.ac.jp/gwadw2010/program/2010_gwadw... · m....

Mirror requirementsMirror requirementsfor 3for 3rdrd generation GW detectors generation GW detectors

Massimo Galimberti, Raffaele FlaminioLMA/CNRS, Lyon

[email protected]

GWADW

Kyoto, May 21, 2010

M. Galimberti - GWADW, Kyoto May 21, 2010 2

GoalGoal

Mirror requirements: are they realistic? Can we make them?

Real mirror defects:☹ flatness defects (long-scale, low freq) – include aberrations☹ roughness (microscopic scale, high freq)


Why should we care?Why should we care?1) defects losses

2) other modes resonating (degeneracy)


OutlineOutline

✔ Goals & motivations

● Mirror surface characterization & simulation▶ analysis of real surfaces▶ surface simulation

● ET arm cavity simulation


Real mirror surfacesReal mirror surfaces

Surface (deviation from ideal shape) of Virgo+ NI mirror

rms flatness = 4.1 nmon Ø 150 mm

How to characterize it?


Power spectral densityPower spectral densityE.L. Church, Appl. Opt. 27:1518 (1988)

V. Loriette, VIR-NOT-PCI-1380-127 (1995)

F. Bondu, VIR-027-1A-10 (2009)

F. Bondu, MirrorShape software2-D power spectral density:

1-D power spectral density:


Virgo mirrors PSDVirgo mirrors PSD

Computation:

1) take the map

2) apply 2-D Hann window

3) 2-D FFT

4) 2-D PSD = |FFT|2

5) 1-D PSD = sum over annuli



Computation:

1) take the map

2) apply 2-D Hann window

3) 2-D FFT

4) 2-D PSD = |FFT|2

5) 1-D PSD = sum over annuli

approximated with

n ≈ 2.3


Simulation of mirror surfaces (1)Simulation of mirror surfaces (1)

1) create a map in the

frequency plane

→ modulus of the FT of the

surface

2) add a random phase

3) iFFT → random surface

4) scale surface to the

required rms



1) create a map in the

frequency plane

→ modulus of the FT of the

surface

2) add a random phase

3) iFFT → random surface

4) scale surface to the

required rms

rms flatness = 4.1 nm on Ø 150 mm(as Virgo+ NI mirror)


A word of cautionA word of caution

This seems all right, but...

• simulations for ET are done with n = 2.3 as in Virgo and Virgo+:we do not know what n will be for ET mirrors (or even AdV or AdLIGO)

• corrective coating will modify the spectrum – still to be characterized

• approximation with is already a bit crude, will it still hold for ET mirrors?

• we assumed surface defects to be homogeneous and isotropic,which is likely to be wrong (how much?)


OutlineOutline

✔ Goals & motivations

✔ Mirror surface characterization & simulation

● ET arm cavity simulation▶ configurations & methods▶ results▶ discussion


ConfigurationConfigurationsee e.g. Hild et al., arXiv:0906.2655v2

• Cavity length L = 10 km

• Test masses diameter: 620 mm

• Finesse = 893.8 (as AdV)

• Two wavelengths: 1064 and 1550 nm

• Two modes: TEM00 and LG33

• Spotsize on ETM: 120 mm TEM0072.5 mm LG33

• Same ratios L/R as in AdV → same stability and degeneracy

1.6 ppm clipping losses

R2 = 5490 m

L = 10 000 m

4 600 m 5 400 m

R1 = 4706 m

TEM00 @ 1064nm


What has been computedWhat has been computed

➢ For every configuration (1064/1550 nm, TEM00/LG33, mirror flatness):

1) circulating power (input mode)

2) round-trip losses (input mode) r.t. losses=P inj−P trans−Prefl

Pcirc

➢ For every rms flatness:

10 simulations (10 pairs of generated surfaces, always the same ones)

➢ Four values of rms flatness: 0 nm (perfect mirrors)0.5 nm1.0 nm2.0 nm

➢ FFT simulations – SIESTA


ResultsResults

(Theoretical value: Pcirc

= 568.2 W/W)

1064 nm 1550 nm

TEM00 LG33 TEM00

0 nm 568 2 568 3 568 3

0.5 nm

1.0 nm

2.0 nm

rms flatness Pcirc

input mode(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)


1064 nm 1550 nm

TEM00 LG33 TEM00

0 nm 568 2

0.5 nm

1.0 nm

2.0 nm

rms flatness Pcirc

input mode(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

563 ± 2 35 ± 12

548 ± 7 134 ± 47

520 ± 34 329 ± 242

ResultsResults

1.0 nm rms over Ø 620 mm 0.4 - 0.8 nm rms over Ø 150 mm

(AdV and AdLIGO requirements)


1064 nm 1550 nm

TEM00 LG33 TEM00

0 nm 568 2 568 3

0.5 nm

1.0 nm

2.0 nm

rms flatness Pcirc

input mode(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

563 ± 2 35 ± 12 566 ± 1 19 ± 5

548 ± 7 134 ± 47 558 ± 3 66 ± 21

520 ± 34 329 ± 242 532 ± 16 241 ± 105

ResultsResults




1064 nm 1550 nm

TEM00 LG33 TEM00

0 nm 568 2 568 3 568 3

0.5 nm

1.0 nm

2.0 nm

rms flatness Pcirc

input mode(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

Pcircinput mode

(W/W)

r.t. losses(ppm)

563 ± 2 35 ± 12 558 ± 2 64 ± 15 566 ± 1 19 ± 5

548 ± 7 134 ± 47 531 ± 9 248 ± 61 558 ± 3 66 ± 21

520 ± 34 329 ± 242 446 ± 24 (*) 911 ± 216 (*) 532 ± 16 241 ± 105

ResultsResults




When LG33 goes bad (1)When LG33 goes bad (1)

Results of the 10 simulations with 2.0 nm rms

good

419 418 1168

424 423 1120

467 458 799

470 468 717

465 464 750

bad

165 53 15235

59 7 55602

88 14 37892

217 85 11094

75 10 44871

Pcircall modes

(W/W)

Pcircinput mode

(W/W)

r.t. losses(ppm)


When LG33 goes bad (2)When LG33 goes bad (2)See Rana Adhikari's talk - May 172.0 nm rms


When LG33 goes wellWhen LG33 goes well

1.0 nm rms


What about contrast?What about contrast?

dark fringe: all possible cavity pairs with 1.0 nm rms (“Ad-detectors-like”)

contrast = (1.9 ± 0.6) · 10-3

LG33


What about contrast?What about contrast?

LG33 TEM00

dark fringe: all possible cavity pairs with 1.0 nm rms (“Ad-detectors-like”)

contrast = (1.9 ± 0.6) · 10-3 contrast = (1.1 ± 0.5) · 10-3


What about alignment?What about alignment?

perfect mirrors, ETM tilted at an angle

See Massimo Granata's talk - May 18


ConclusionsConclusions

losses are reasonable for flatness up to 1 nm rms (approx. equivalent to requirements for AdV and AdLIGO)

TEM00: λ = 1550 nm gives slightly better performances

LG33: ok on average but more sensitive to defects and alignment

➔ take into account corrective coating (see F. Bondu's work)

➔ expand to recycling cavities

To do nextTo do next


SparesSpares


Virgo+ mirrors PSDVirgo+ mirrors PSD


Virgo and Virgo+ ITMsVirgo and Virgo+ ITMs


Virgo and Virgo+ ETMsVirgo and Virgo+ ETMs


Simulation parametersSimulation parameters

1064 nm 1550 nm

TEM00 LG33 TEM00

w0 (mm) 15.4 27.2 22.6

w1 (mm) 103 63.4 103

w2 (mm) 120 72.5 120

l1 (m) 4600 4600 4600

l2 (m) 5400 5400 5400

R1 (m) 4706 5640 4833

R2 (m) 5490 6286 5599

g1 = 1 – L/R1 -1.1251 -0.77308 -1.07

g2 = 1 – L/R2 -0.82148 -0.59088 -0.786

g1*g2 0.924 0.457 0.840


Fancy LG33Fancy LG33


RMS histogramRMS histogram

flatness RMS (nm)


RMS histogramRMS histogram

galimberti - gwadw 2010 - kyotogw.icrr.u-tokyo.ac.jp/gwadw2010/program/2010_gwadw... · m....

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