Reducing coating thermal noise
with folded cavities
IPAS Institute for Photonics and Advanced Sensing
GWADW
平成26年5月28日
高山市、日本
LIGO-G1400586
Stefan Ballmer
David Ottaway
Outline
IPAS Institute for Photonics and Advanced Sensing
• Coating thermal noise
– Solutions: Material vs. Geometry
• Resonant Delay Lines
– The idea
– Noise reduction potential
– Optimization constraints
– Issues with folding Resonant Delay Lines
• Conclusion
Advanced LIGO Noise
Curve
IPAS Institute for Photonics and Advanced Sensing
• Coating thermal noise is the dominant noise!
Material Improvements to
the Rescue ?
IPAS Institute for Photonics and Advanced Sensing
• Initial LIGO Coatings were SiO2 and Ta2O5
• Advanced LIGO improvement: 31%
(after nearly a decade)
• Significant improvement from crystalline
coatings?
– Scalable to large optics ?
Coating Brownian Noise
• Due to mechanical
coating loss
IPAS Institute for Photonics and Advanced Sensing
4 k BT  c
S xx 

2
 f w Y
• Scales with beam area
Coating Brownian
• Limiting 2nd gen. detectors (i.e. Ta)
Note : O (1) constants dropped (e.g. Poisson raito)
Correlation length
• Coating Brownian noise
gr-qc/0610041v3 (2007)
– Set by elastic Greens function
• But driven on surface only – short range!
– Correlation length, on surface
• Transverse correlation ~coating d (<<w)
– Exponential drop-off (beam profile)
IPAS Institute for Photonics and Advanced Sensing
Thermo-optic noise
IPAS Institute for Photonics and Advanced Sensing

 eff d   eff   k BT

2
• Due to heat diffusion S xx
• Scales w/ beam area
w
2
2
Cf
Thermo-optic
• Key for crystalline
coatings
Note : O (1) constants dropped (e.g. Poisson raito)
Correlation length
• Thermo-optic noise
– Set by (freq. dependent) diffusion length
– Correlation length ~ diffusion length
• O(30u) around 100Hz
• Transverse correlation ~diff. length (<<w)
– Exponential drop-off (beam profile)
Caution: Not true for cryogenic
reference cavities
small spot &
large diffusion length
IPAS Institute for Photonics and Advanced Sensing
Other beams
IPAS Institute for Photonics and Advanced Sensing
• Effective beam area larger - Noise averages
– For LG33: x1.61 (in power noise, =27% ampl.)
• But modes are degenerate
– Contrast defect unacceptable
PRD 84, 102001 (2011)
– Ideas for thermal correction
PRD 87, 082003 (2013)
LG33 beam
• Other shapes have the similar problem
(Flat-top, conical)
Outline
IPAS Institute for Photonics and Advanced Sensing
• Coating thermal noise
– Solutions: Material vs. Geometry
• Resonant Delay Lines
– The idea
– Noise reduction potential
– Optimization constraints
– Issues with folding Resonant Delay Lines
• Conclusion
Multiple beams
• TEM00 is good – use more of them!
• Multiple spots per mirror
– exploit spatial de-correlation
IPAS Institute for Photonics and Advanced Sensing
Spatial correlation (for
TEM00)
IPAS Institute for Photonics and Advanced Sensing
Coherent spots
Amplitude noise increase
Substrate Brownian
Coating Brownian &
Thermo-Optic
2 reflections
Incoherent spots
Beam center separation (w)
Multiple beams
• TEM00 is good – use more of them!
• Multiple spots per mirror
– exploit spatial de-correlation
• How much can we get with this?
– Packing of beams?
– Geometry of mirrors?
• Start with spherical mirrors…
IPAS Institute for Photonics and Advanced Sensing
Herriot Delay Line (1964)
• Only spherical
mirrors
• Elliptical orbits
• Input /output
holes
IPAS Institute for Photonics and Advanced Sensing
Resonant Delay Lines
Negative Branch
IPAS Institute for Photonics and Advanced Sensing
Positive Branch
• Combine Herriot Delay Lines with Fabry-Perots
– Already used on GEO600 (1.5 Bounce)
– Use the robust lowest order TEM00 modes
• Increasing cavity length => Increased Signal
• Increased bounces => Increased thermal noise but
slower than signal => Increased signal to noise
Traveling wave vs standing
wave cavity
Standing Wave
IPAS Institute for Photonics and Advanced Sensing
Traveling Wave
• Traveling wave cavity:
– All reflections incoherent
– Corner interferometer also has to be traveling wave
• Reduced isolation requirement for squeezing injection
• Standing wave cavity:
– Simpler corner interferometer
– Slightly more complicated mirror.
– Thermal noise of folding mirrors needs mitigation
FSR (kHz)
TN Improvement
Traveling Wave vs
Standing Wave
IPAS Institute for Photonics and Advanced Sensing
2.5
2
1.5
1
1
10
2
10
1
10
0
1
1.5
2
2.5
3
3.5
Standing Wave
Traveling Wave
4
4.5
5
Standing Wave
Traveling Wave
1.5
2
2.5
3
3.5
Mirror Bounce Number
4
4.5
Compared to aLIGO, spot size same as
aLIGO
5
Free Spectral Range
IPAS Institute for Photonics and Advanced Sensing
• Lower by # reflections: FSR~37kHz/Nrefl
– getting close to observation band
• There is NO sensitivity at the FSR
– to displacement or strain
– unlike a non-folded Fabry-Perot cavity
• FSR > 3.75 kHz
10 bounce TW and 4.5 bounce SW
 3.2 (TW) and 2.1 (SW) Thermal Noise
Improvement
Outline
IPAS Institute for Photonics and Advanced Sensing
• Coating thermal noise
– Solutions: Material vs. Geometry
• Resonant Delay Lines
– The idea
– Noise reduction potential
– Optimization constraints
– Issues with folding Resonant Delay Lines
• Conclusion
Resonant Delay Lines Closing
• Traveling-wave needs path-closure:
• For aLIGO g-factors: Nb ~7.4
• But we get degeneracy…
IPAS Institute for Photonics and Advanced Sensing
Connection to HOM
IPAS Institute for Photonics and Advanced Sensing
vs.
• Condition for Nb-spot traveling-wave RDL:
gITMgETM = cos2(pi/Nb)
• Implies that transverse mode spacing:
fTM = FSR/Nb
 0th and m*Nbth HOM co-resonant (all m)
 any mode with Nb-fold symmetry co-resonant
• Folded cavity no longer mode-selective
– Need curvature changes at 2 spots
Achievable Spot Size
IPAS Institute for Photonics and Advanced Sensing
Average Spot Size (cm)
7
6
5
4
3
2
4
6
Bounce Number
8
10
Realizing multiple beams
• Delay line with spherical mirrors
IPAS Institute for Photonics and Advanced Sensing
(Herriot, APPLIED OPTICS,
Vol. 4, No. 8 (1965) )
– g-factor determines beam orbit
– Size and ellipticity of orbit unrestricted
– closed as FB cavity by terminating wedges
Example: 4.5-spot standing-wave cavity
Optimization:
Maximize the total spot area
IPAS Institute for Photonics and Advanced Sensing
• Constraints:
– Both individual spot size and # of spots per
orbit directly dependent on g-factor
– Orbit determined by injection angle
– # reflections limited to <10
– Clipping loss ~<1ppm
• Possible solution:
– Optimize g-factor for big beam sport
– Inject beams in an elliptical orbit
– Use less than one full orbit
Spot Patterns on Ring
IPAS Institute for Photonics and Advanced Sensing
Small Test Mass
-0.6
-0.4
-0.2
0
0.2
0.4
4 Bounces
0.6
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1
8 Bounces 8 Bounces Elliptical
• Bounce number determined by mirror parameters ie g-factor
• Spot pattern determined by beam injection angle
• SW Geometry allows patterns that do not close and hence can use
part of an ellipse
• Assuming no loss greater than 1ppm per bounce - Spot spacing limits
NB ≈ 6
A Robust Design
IPAS Institute for Photonics and Advanced Sensing
• Biggest constraint:
– Beam tube aperture: ~1m
• Test mass aspect ratio:
– for 160kg: e.g. diameter 80cm, thickness 15cm
– Use 5 bounce ITM, 4 Bounce ETM design
• Thermal noise improvement
– RDL = 2.1 amplitude
– Compare to max size TM00: ~2.35
Example:
4.5 spot Resonant Delay
Line
IPAS Institute for Photonics and Advanced Sensing
Use Partial Ellipses
Elliptical beam orbits
IPAS Institute for Photonics and Advanced Sensing
4.5 spot Resonant Delay
Line
Rest uniform RoC, no wedge (no clipping!)
IPAS Institute for Photonics and Advanced Sensing
Wedged areas
Input coupler
(>2.5w beam separation,
<1ppm loss)
End spot
(>2.5w beam separation,
<1ppm loss)
Folding issues
IPAS Institute for Photonics and Advanced Sensing
• Standing wave leads
to intensity pattern on
folding mirror
• Affects noise calculation
~23% noise amplitude increase
• Possible Solutions:
Fig from Heinert et. al.
– Use travelling wave
– Wash out pattern (e.g. FSR modulation)
IPAS Institute for Photonics and Advanced Sensing
GEO End Transmission
Further Exploration
IPAS Institute for Photonics and Advanced Sensing
• Detailed Optics Tolerancing
• Thermal compensation and aberration
• Thermal noise calculation because taking
into account test mass resonances and
“folding mirror fringe pattern”
• Radiation Pressure Effects
– Sidles/Sigg Instability
– Parametric Instability
Impact on Other
Systems
IPAS Institute for Photonics and Advanced Sensing
• Coating: None!
• Optics: Large Spherical Optics – Wedge alignment
will be challenging
• Suspension/Seismic:
– Must accommodate large optic
– Large optics are being planned for most third generation
detectors
• Lasers: none!
• Angular control: none
• Thermal aberrations and compensation:
– Less power per spot, but complicated pattern
Conclusion
IPAS Institute for Photonics and Advanced Sensing
• Coating thermal noise remains one of the
biggest challenges for future GW
Detectors
• Resonant Delay Lines look promising for
achieving a significant reduction in coating
thermal noise
• More details: Phys. Rev. D 88, 062004
The End
IPAS Institute for Photonics and Advanced Sensing
Spare Slides
IPAS Institute for Photonics and Advanced Sensing
Alignment Control
IPAS Institute for Photonics and Advanced Sensing
• The need to maintain alignment is
complex interferometers is crucial
• Pushing towards more marginally stable
systems makes alignment control harder
(Possible exception LG33)
• How do resonant delay lines compare ?
Alignment signals / Spot
motion
– aLIGO g-factor
(but ITM=ETM)
– w=57.3mm
– For 3urad ITM
misalignment
m
• Reference:
• Spot move 6.4cm
m
IPAS Institute for Photonics and Advanced Sensing
Alignment signals / Spot
motion
IPAS Institute for Photonics and Advanced Sensing
– w=57.3mm
– For 3urad ITM
misalignment
• Spot move 6.4cm
• (identical)
ITM 2
ITM 4
ETM 4
ETM 1
m
• RDL with 4 ETM
and 5 ITM spots,
all same size as
(symmetric)
aLIGO
ITM 3
ITM 5
ITM 1
ETM 3
ETM 2
m
Easier than traditional
delay lines!
IPAS Institute for Photonics and Advanced Sensing
• N much smaller than traditional delay lines
• Two mirrors define optical mode
– No “threading of the beam”
– Mode-matching identical to regular FB cavity
– As easy to align as a regular FB cavity
• Scatter
– Exists, but cavity is locked, no fringe wrapping
• Alignment sensitivity
– identical to simple 2-mirror FB cavity