1. Lasers and Optics of Gravitational Wave Detectors
Rick Savage
LIGO Hanford Observatory

2. GW detector – laser and optics
end test mass
4 km (2 km) Fabry-Perot arm cavity
recycling
mirror
input test mass
beam splitter
Power Recycled
Michelson
Interferometer
with Fabry-Perot
Arm Cavities
signal

3. Closer look - more lasers and optics

4. Pre-Stabilized Laser System
Laser source
Frequency pre-stabilization and actuator for further stab.
Compensation for Earth tides
Power stab. in GW band
Power stab. at modulation freq. (~ 25 MHz)

5. Initial LIGO 10-W laser
Master Oscillator Power Amplifier configuration (vs. injection-locked oscillator)
Lightwave Model 126 non-planar ring oscillator (Innolight)
Double-pass, four-stage amplifier
Four rods watts of laser diode pump power
10 watts in TEM00 mode

6. LIGO I PSL performance
Running continuously since Dec on Hanford 2k interferometer
Maximum output power has dropped to ~ 6 watts
Replacement of amplifier pump diode bars had restored performance in other units
Servo systems maintain lock indefinitely (weeks - months)

7. Frequency stabilization
Three nested control loops
20-cm fixed reference cavity
12-m suspended modecleaner
4-km suspended arm cavity
Ultimate goal: Df/f ~ 3 x 10-22

8. Power stabilization 3e-8/rtHz In-band (40 Hz – 7 kHz) RIN
Sensors located before and after suspended modecleaner
Current shunt actuator - amp. pump diode current
RIN at 25 MHz mod. freq.
Passive filtering in 3-mirror triangular ring cavity (PMC)
Bandwidth (FWHM) ~ 3.2 MHz
3e-8/rtHz

9. Earth Tide Compensation
Up to 200 mm over 4 km
Prediction applied to ref. cav. temp. (open loop)
End test mass stack fine actuators relieve uncompensated residual
100mm
prediction
residual

10. Concept for Advanced LIGO laser
Being developed by GEO/LZH
Injection-locked, end-pumped slave lasers
180 W output with 1200 W of pump light

11. Brassboard Performance
LZH/MPI Hannover
Integrated front end based on GEO 600 laser – watts
High-power slave – 195 watts M2 < 1.15

12. Concept for Advanced LIGO PSL

13. Core Optics – Test Masses
Low-absorption fused silica substrates
25 cm dia. x 10 cm thick, 10 kg
Low-loss ion beam coatings
Suspended from single loop of music wire (0.3 mm)
Rare-earth magnets glued to face and side for orientation actuation
Internal mode Qs > 2e6

14. LIGO I core optics Caltech data
RITM ~ 14 km (sagitta ~ 0.6 l) ; RETM ~ 8 km
Surface uniformity ~ l/100 over 20 cm. dia. (~ 1 nm rms)
“Super-polished” – micro-roughness < 1 Angstrom
Scatter (diffuse and aperture diffraction) < 30 ppm
Substrate absorption < 4 ppm/cm
Coating absorption < 0.5 ppm

15. Adv. LIGO Core Optics fused silica sapphire
LIGO recently chose fused silica over sapphire
Familiarity and experience with polishing, coating, suspending, thermally compensating, etc. – less perceived risk
Other projects (e.g. LCGT) still pursuing sapphire test masses
Thermal noise in coatings expected to be greatest challenge
fused silica
sapphire
38 cm dia., 15.4 cm thick, 38 kg

16. Processing, Installation and Alignment
Experience indicates that processing and handling may be source of optical loss
gluing vacuum baking
wet cleaning
suspending balancing
transporting

17. Thermal Issues Surface absorption depth radius Bulk absorption
Circulating power in arm cavities
~ 25 kW for initial LIGO
~ 600 kW for adv. LIGO
Substrate bulk absorption
~ 4 ppm/cm for initial LIGO
~ 0.5 ppm/cm ($) for adv. LIGO
Coating absorption
~ 0.5 ppm for initial & adv. LIGO
Thermo-optic coefficient
dn/dT ~ 8.7 ppm/degK
Thermal expansion coefficient
0.55 ppm/degK
“Cold” radius of curvature of optics adjusted for expected “hot” state
depth
radius
Bulk absorption

18. Thermal compensation system
CO2 Laser ?
ZnSe Viewport
ITM
PRM
SRM
ITM
Compensation Plates
Over-heat Correction
Under-heat Correction
Inhomogeneous Correction
Adv. LIGO concept

19. Coating vs. substrate absorption
Optical path difference
Surface distortion
substrate
coating
coating
substrate
OPD almost same for same amount of power absorbed in coating or substrate
Power absorbed in coating causes ~ 3 times more surface distortion than same power absorbed in bulk

20. Summary LIGO utilizes 10-W solid state lasers
Relative frequency stability ~ 10-21/rtHz
Relative power stability ~ 10-8/rtHz
Advanced LIGO lasers: similar requirements at 200 watt power level
LIGO test masses (mirrors) 25 cm dia., 10 cm thick fused silica
Surface uniformity ~ l/100 p-v (1 nm rms) over 20 cm diameter
Coating absorption < 1 ppm, bulk absorption ~ few ppm/cm
Active thermal compensation required to match curvatures of optics
Non-invasive measurement techniques required for characterizing performance of optics

21. Anomalous absorption in H1 ifo.
ITMY
ITMX
Negative values imply annulus heating
Significantly more absorption in BS/ITMX than in ITMY
How to identify absorption site?
TCS power is absorbed in HR coatings of ITMs

22. Need for remote diagnostics
Water absorption in viton spring seats makes vacuum incursions very costly.
Even with dry air purge, experience indicates that 1-2 weeks pumping required per 8 hours vented before beam tubes can be exposed to chambers
Development of remote diagnostics to determine which optics responsible of excess absorption

23. Spot size measurements
ITMX
BeamView CCD cameras in ghost beams from AR coatings
Lock ifo. w/o TCS heating
Measure spot size changes as ifo. cools from full lock state
Curvature change in ITMX path about twice that in ITMY path
ITMY

24. Arm cavity g factor changes
Again, lock full ifo. w/o TCS heating, break lock, lock single arm and measure arm cavity g factor at precise intervals after breaking lock
g factor change in Xarm larger than Yarm by factor of ~ 1.6
Calibrate with TCS (ITM-only surface absorption)

25. Results and options Beamsplitter not significant absorber
ITMX is a significant absorber ~ 25 mW/watt incident
ITMY absorption also high ~ 10 mW/watt incident
Factor of ~5 greater than absorption in H2 or L1 ITMs
Options
Try to clean ITMX in situ
Replace ITMX
Higher power TCS system
30-watt TCS laser was tested
Eventually ITMX was replaced and ITMY was cleaned in-situ
ETM surface
ITM surface
ITM bulk
From analysis by K. Kawabe

26. Origin of G-factor measurement technique
Simple question: “For a resonant optical cavity, can the Pound-Drever-Hall locking signal distinguish between frequency and length variations?”
i.e. does
Of course! Or does it?

27. High-frequency response of optical cavities
Dynamic resonance of light in Fabry-Perot cavities (Rakhmanov, Savage, Reitze, Tanner 2002 Phys. Lett. A, ).

28. High frequency length response
1FSR
2FSR
LIGO band
Peaks in length response at multiples of FSR suggest searches for GWs at high frequencies.
HF response to GWs different than length response
Different antenna pattern, but still enhancement in sensitivity

29. High frequency response to GWs
Long wavelength approximation not valid in this regime
Antenna pattern becomes a function of source frequency as well as sky location and polarization
All-sky-averaged response about a factor of 5 lower than at low freq.
Significant sensitivity near multiples of 37.5 kHz (arm cavity FSR)
Movie (by H. Elliott): Antenna pattern for one source polarization as source frequency sweeps from 22 to 36 kHz

30. G-factor Measurement Technique
Dynamic resonance of light in Fabry-Perot cavities (Rakhmanov, Savage, Reitze, Tanner 2002 Phys. Lett. A, ).
Laser frequency to PDH signal transfer function, Hw(s), has cusps at multiples of FSR and features at freqs. related to the phase modulation sidebands.

31. Misaligned cavity
Features appear at frequencies related to higher-order transverse modes.
Transverse mode spacing: ftm = f01- f00 = (ffsr/p) acos (g1g2)1/2
g1,2 = 1 - L/R1,2
Infer mirror curvature changes from transverse mode spacing freq. changes.
This technique proposed by F. Bondu, Aug Rakhmanov, Debieu, Bondu, Savage, Class. Quantum Grav. 21 (2004) S487-S492.

32. H1 data – Sept. 23, 2003 2ffsr- ftm Lock a single arm
Mis-align input beam (MMT3) in yaw
Drive VCO test input (laser freq.)
Measure TF to ASPD Qmon or Imon signal
Focus on phase of feature near 63 kHz
2ffsr- ftm

33. Data and (lsqcurvefit) fits.
ITMx TCS annulus heating  decrease in ROC (increase in curvature)
R = m
R = m
Assume metrology value for RETMx = 7260 m
Metrology value for ITMx = m