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1Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
“Colliding Black Holes”, National Center for Supercomputing Applications
Support: NSF
LIGO – Optical Science and Engineering In Search of Black Holes
David ReitzePhysics DepartmentUniversity of Florida
Gainesville, FL 32611
For the LIGO Science Collaboration
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2Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Outline
Overview of gravitational waves» GWs, GW sources and why they’re interesting
Laser interferometry to detect gravitational waves» LIGO Laser Interferometer Gravitational Wave Observatory
» Fundamentals of Interferometry– Noises
» Lasers and Optics in LIGO
Second generation ground-based gravitational wave interferometers» Advanced LIGO
» Challenges in Advanced LIGO
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3Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Gravitational Waves
Gravitational Waves: “Odd man out” in general relativity; predicted, but never directly observed.
ds2 = gdxdxghh(r,t) = h+.x exp[i(k.r - t)]
Weak Field Limit: h is a strain: L/L
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4Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Gravitational Waves & Electromagnetic Waves: A Comparison
Electromagnetic Waves Time-dependent dipole moment
arising from charge motion
Traveling wave solutions of Maxwell wave equation
Two polarizations: +, -
Spin 1 fields ‘photons’
Gravitational Waves Time-dependent quadrapole
moment arising from mass motion
Traveling wave solutions of Einstein’s equation
Two polarizations: h+, hx
Spin 2 fields ’gravitons’
prrr
trE ˆˆ
4~, 0
),(
2,
4tI
cr
Gth
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5Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
One Possible Source: Binary Neutron Star Inspiral and Merger
measure masses
and spins of binary system
detect normal modes of
ringdown to identify final NS or BH.
observe strong-field spacetime dynamics, spin
flips and couplings…
Sketch:Kip Thorne
Credit: Jillian Bornak
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6Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Other Sources Lurking in the Dark
BANG!
Binary systems» Neutron star – Neutron star» Black hole – Neutron star» Black hole – Black hole
Periodic Sources» Rotating pulsars
“Burst” Sources » Supernovae
– Gamma ray bursts
Residual Gravitational Radiation from the Big Bang
» Cosmic Strings
?????
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7Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
LIGO Sites
LIGO Livingston Observatory• 1 interferometers
• 4 km arms
• 2 interferometers• 4 km, 2 km arms
LIGO Hanford ObservatoryLIGO Observatories: Caltech and MIT
4 km
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8Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Interferometer Network
LIGO
To be six or seven detectors worldwide by 2010-2020.
• Redundancy
• Confidence
• Source location
GEO VirgoTAMA
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9Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Fundamentals of LIGO Interferometry
…causing the interference pattern
to change at the photodiode
As a wave passes, the arm lengths change in different ways….
Arms in LIGO are 4 km long Measure difference in
length to one part in 1021 or 10-18 meters
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10Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Interferometry: the basics
Simple Michelson
» Phase: = 4 (Lx – Ly) / L
» Power: PPD = PBS sin2– dP/d ~ PBS sin cos
» Strain: h = 2L/L– Phase sensitivity:
d/dh L Lx
Ly
L
PPD X
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11Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Beefed-up Interferometry:Fabry-Perot Arm Cavities
Fabry-Perot cavity» Increases power in arms
– Overcoupled cavity gain: GFP ~ 4 / Tinput
» Enhances storage time of light in cavity– Phase shift on resonance– Effectively ‘lengthens’ arms
df/dh GFP x L
Lx
Ly
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12Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Advanced Interferometry II:Power Recycling
‘Recycle’ light coming back from beamsplitter» Add a mirror which forms a resonant
cavity with the rest of the interferometer
PBS
= GRC
Pinput
df/dh GFP x L
+
= Enhanced Phase Sensitivity! GRC ~ 50, GFP ~ 80
Lx
Ly
‘Complex Mirror’
5 W
~ 10000 W
250 W
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13Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Keeping the Interferometer Together
• All length degrees of freedom must be held on resonance (ie, locked)• heterodyne detection
• reference field provided by electro-optic modulator
• LIGO Interferometers are very complex: 4 length + 10 alignment degrees of freedom• Absolute position must be held to 10-13 m
E = Ein ei 2 cos(mt) E
in [1 + i ei mt + i e-i mt]
m
E
cESB
LaserModulator
LO
Mixer
PDServo electronics
Error Signal
Cavity Length
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14Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
The LIGO Length Control Scheme
Length Degrees of freedom
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15Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Locking the Interferometer•Multiple Input / Multiple Output.
•Four tightly coupled cavities.
•Ill-conditioned (off-diagonal) plant matrix.
•Highly nonlinear response over most of phase space.
•Transition to stable, linear regime takes plant through singularity.
•Employs adaptive control system that evaluates plant evolution and reconfigures feedback paths and gains during lock acquisition. MICH
GO
GO
QPOB
QREFL
SSpob
SSref
glmPob
glmRef
_
_
DARM
CARM
PRC
GOGO
GOGOGO
GOGOGO
QAS
IPOB
IREFL
CasyCasy
CpobCpobSSpob
CrefCrefSSref
gLAsy gLAsy 0
gLPob gLPob glpPob
gLRef gLRef glpRef
_
_
_
1.
2.
POB
REFL AS
GW Signal is measured from DARM Control
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16Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Alignment Sensing and Control
Need to also control angular fluctuations x, y of the mirrors x, y for 5 of the 6 interferometer mirrors
Spatially-resolved PDH locking…
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17Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Alignment Sensing and Control
Cavity modes U decompose into HG0 and HG1 modes:
» Displacement: U(x) = HG0(x-) HG0(x) + (/wo) HG1(x)
» Tilt: U(x) = HG0(x’) / cos x HG0(x) + i xwo/) HG1(x)
x
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18Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
The earth is a noisy place
Thermal (Brownian)
Noise
LASER
test mass (mirror)
beamsplitter
Residual gas scattering
Wavelength & amplitude fluctuations
Seismic Noise
Quantum Noise
"Shot" noise
Radiation pressure
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19Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
‘Noises’ in LIGO
Noise Sources:
• Displacement noise
• Seismic noise
• Radiation Pressure
• Thermal noise
• Suspensions
• Optics
• Sensing Noise
• Shot Noise
• Residual Gas
• Electronic Noise
h(f) = 3 x 10-23 / rHz
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20Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Frequency Stabilization in LIGO
Nested control loops» Stage 1 – thermally-20 cm long
stabilized reference cavity» Stage 2 – in vacuum
suspended 12 or 15 m long “mode cleaner’ cavity
» Stage 3 – Fabry Perot arm cavities
f/f ~ 3 x 10-22 @ 100 Hz
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21Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
LIGO Pre-stabilized Laser
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22Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Seismic Noise
Tubular coil springs with internal damping, layered between steel reaction masses
Isolation Performance
Need 10-19 m/rHz @100 Hz
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23Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
More Seismic isolation
• pendulum design
• provide 102 suppression above 1 Hz
• provide ultraprecise control of optics displacement (< 1 pm)
Mirror Suspensions
Wire standoff & magnet
“OSEM”
LOS
SOS
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24Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Thermal NoiseThermal Noise
Dissipative Thermal Noise: the fluctuation-dissipation theorem
tells us that random thermal fluctuations are converted to mechanical motion mirror surfaces, optical coatings, and suspension wires
Extrinsic Thermal Noise: external coupled energy drives thermal motion
» laser power (which fluctuates) couples into mirrors, driving thermal expansion fluctuations in mirrors and optical coatings
therm
diss22
B2diss F
)f(x~f2i)f(Y)}f(YRe{
f
Tk)f(x~
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25Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Suspension Thermal Noise
G. Gonzalez, Class. Quantum Grav. 17, 4409-4435 (2000)
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26Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Thermal Effects in LIGO Core Optics
Absorption in the mirror substrates and coatings leads to thermal aberrations in the mirrors» Temperature couples to index of
refraction n, thermal expansion T, and photo-elastic stress
E2(r,z)(Reflected from R1)
z
x
wo
R(z)R1
OPL(r)
E1(r,z)(Incident)
E2(r,z)(Transmitted through the substrate)
e
wo
R(z)R1
OPL(r)
E1(r,z)(Incident)
(b)
Mirror
Mirror
(a)
-0.03 -0.02 -0.01 0 0.01 0.02 0.03-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0x 10
-5
Radial Distance (m)
The
rmal
Abe
rrat
ion
(m)
Thermal Aberration
12 th Degree Fit
Optimal Solution
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27Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Thermal Effects in LIGO Core Optics
High quality low absorption fused silica substrates
» ~ 2 -10 ppm/cm bulk absorption
» ~ 1-5 ppm coating absorption
– Different for different mirrors
– Can change with time
» All mirrors are different» Unstable recycling cavity
Requires adaptive control of optical wavefronts
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28Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Thermal Compensation
CO2
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29Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
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30Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
LIGO IS Doing Astrophysics!
~2x10-25
~2x10-25
Upper Limits on the ellipticity of galactic pulsars
Lowest ellipticity limit to date: 4.0x10-7 for PSR J2124-3358 (fgw= 405.6Hz, distance = 0.25 kpc)
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31Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Advanced LIGO
At current sensitivity, LIGO detectors are rate-limited
» 0.01 – 1 event per year
Advanced LIGO will increase sensitivity, hence range, by 10X over initial LIGO
» AdvLIGO rate ~ 500X current LIGO
– At least a few EVENTS per year
Anticipate funding to start in 2008, construction to begin in 2011
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32Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Enhancements to Advanced LIGO
PRM Power Recycling MirrorBS Beam SplitterITM Input Test MassETM End Test MassSRM Signal Recycling MirrorPD Photodiode
SILICA
40 kg
180 W
830 kW
830 kWQuad Noise Prototype
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33Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Advanced LIGO Pre-stabilized Laser
180 W amplitude and frequency stabilized Nd:YAG laser Two stage amplification
» First stage: either MOPA (NPRO + single pass amplifier) or ring cavity (not shown)
» Second stage: injection-locked ring cavity
Developed by Laser Zentrum Hannover (and MPI at Hannover)
front-end output
PZT
BP
high-power laser
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34Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Advanced LIGO PSL performance Requirements
» Good spatial mode quality» Intensity stabilization < 3 x 10-9 /rHz» Frequency noise ~ (20 Hz/ f) Hz/rHz
To date» 183 W obtained in good spatial
mode profile (no spatial filtering)» RIN of oscillator @ 3 x 10-9 /rHz
70 80 90 100 110 120 130 140 150 1600,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
M2 < 1.2
wa
ist s
ize
[mm
]
rel. position [mm]
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35Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
High Power Faraday Isolatorsfor Advanced LIGO
Faraday Isolator designed to handle high average power
» Increased immunity from thermal birefringence
In excess of 40 dB at 100 W loading
» thermal lensing /10 thermal distortions demonstrated /20 possible
0 20 40 60 80 100-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Fo
cal P
ow
er (
m-1)
Incident Power (W)
Rotator only Compensator only Rotator and Compensator
0 20 40 60 80 10015
20
25
30
35
40
45
50
Op
tical Is
ola
tio
n
Incident Laser Power
Current EOT Isolator Compensated Isolator
Isolation versus power
Focal power vs power
Khazanov, et al., J. Opt. Soc. Am B. 17, 99-102 (2000).Mueller, et al., Class. Quantum Grav. 19 1793–1801 (2002).Khazanov, et. al., IEEE J. Quant. Electron. 40, 1500-1510 (2004).
Lens Compensation
FaradayTGG Crystals
TFP TFP/2QR
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36Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Interesting physical effects in Advanced LIGO
Stored arm cavity power: 830 kW on resonance» Radiation pressure on resonance:
Frad = 2Pcav/c ~ 6 mN» Leads to (uncontrolled) L = 150 m
3 types of potential instabilities» Optical ‘spring’ effect
– From dynamic force as mirrors go through resonance
» Angular ‘tilt’ Instabilities – From misaligned cavities
» Parametric Instabilities– From excitation of acoustic mirror modes from
higher order cavity modes and
Frad40 kg
L
mg
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37Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Optical Spring Effect
For small displacements off resonance, Frad depends linearly on L
Total spring constant felt by mirror is
if ktot < 0, cavity is unstable
Sheard, et al., Phys. Rev. A69 051801 (2004)
Solution for AdvLIGO: higher length servo gain
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38Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Angular Instabilities
If cavity beam is displaced, Frad exerts torques on mirrors:
Mirrors act as torsional pendulum
» Solving equations of motions leads to one unstable mode
c
xP2 cav
Solution for AdvLIGO: higher alignment servo gain
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39Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Parametric Instabilities
Solution for AdvLIGO: acoustic damping, thermal ROC tuning
Coupling of intracavity photon-acoustic modes
» High intracavity powers excite acoustic modes in the mirrors (Stokes mode)
» Instability depends on– Intracavity power – Substrate material
Speed of sound, mechanical Q – Cavity parameters
Length, mirror RoC
Parametric Gain; R> 1 leads to instability
V. B. Braginsky, et al., Phys. Lett. A, 305, 111, (2002);C. Zhao, et al, Phys. Rev. Lett. 94, 121102 (2005).
TM acoustic mode TEM 10 mode
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40Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
The LIGO Science Collaboration
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41Optical Science and Engineering Seminar, University of Colorado 30 Oct 2006
Conclusions
Acknowledgments
• Members of the LIGO Laboratory, members of the LIGO Science Collaboration, National Science Foundation
More Information
• http://www.ligo.caltech.edu; www.ligo.org
• LIGO is operational and taking data as we speak
• ½ way through S5 Science Run
• Gravitational wave detection pushes state-of-the art in CW
solid state laser technology, optical fabrication and metrology,
and control systems
• Advanced LIGO design is well underway