1. LG MODES FOR THERMAL NOISE REDUCTION
Paul Fulda, Charlotte Bond
for
University of Birmingham and University of Glasgow
LIGO-G
GWADW ELBA

2. Previous LG mode research
Simulations of control signals for main IFO components1: positive results for LG33
LG33 Sensitivity improvements for AdVirgo1
First demonstration of LG33 mode cleaning to 99% purity using a PDH locked linear cavity2
1Chelkowski, S. et al, ‘Prospects of LG modes in GWDs’, Phys Rev D, 79, , June 2009, LIGO-P
2Fulda, P. et al, ‘Experimental demonstration of higher-order LG mode interferometry’, Phys Rev D, 82, , July 2010, LIGO-P
26/05/11
Paul Fulda GWADW Elba

3. LG33 mode in the Glasgow 10m
Collaboration between Birmingham and Glasgow
Advancing from the table top to prototype system
Suspended optics and full control
Larger beam sizes on the mirrors
Could (should?) encounter LG mode degeneracy
Compare resonating beam to simulations
26/05/11
Paul Fulda GWADW Elba

4. LG33 mode in the Glasgow 10m (2)
26/05/11
Paul Fulda GWADW Elba

5. LG33 mode in the Glasgow 10m (3)
LG33 mode path installed on laser bench
LG33 Beam transmitted through PMC
26/05/11
Paul Fulda GWADW Elba

6. Aims of the prototype experiment
Find out where the LG33 mode becomes unusable
Compare simulations with actual experimental results over a wide parameter range:
Different finesses (between about 100 and 8000)
Different mirror surfaces, i.e. ‘good’ mirrors, but also have some particularly ‘bad’ ones
Systematic study (rather than single point comparison) to increase the reliability of the simulations and to learn which are the most import influences
26/05/11
Paul Fulda GWADW Elba

7. Towards mirror specs for LG modes
Mirror surfaces well described as a sum of Znm terms
Analytical formula derived for estimating coupling between degenerate LG modes due to specific Znm terms
Next: compute limits on Znm orders (astigmatism, coma…) based on optical requirements (loss, contrast…)
‘Bad’ JIF input mirror R=95%
Zernike version (C. Bond)
y(cm)
y(cm)
surface height (nm)
surface height (nm)
x(cm)
x(cm)
26/05/11
Paul Fulda GWADW Elba

8. Simple example of Zernike advantage
Relative
Z2±2 content
(astigmatism)
Relative
Z20 content
(curvature)
MIRROR
Circulating beam
LG33 mode content [%]
SAME SPATIAL FFT
FOR THE MIRRORS
BEST
0.494
0.506
78.54
“AVERAGE”
0.758
0.224
64.5
WORST
0.856
0.144
52.35
See poster/talk at Amaldi
Credit: C. Bond
26/05/11
Paul Fulda GWADW Elba

9. Thanks for listening!
26/05/11
Paul Fulda GWADW Elba

10. Mirror map simulations with Zernike polynomials
26/05/11
Paul Fulda GWADW Elba

11. With astigmatism removed…
Z2±2 polynomials held at zero
92.6% LG33 mode content
26/05/11
Paul Fulda GWADW Elba

12. Coupling of tilt to phase in FP cavity
We investigated the tilt to phase coupling in a 3km cavity
Cavity tuning ( )

13. Alignment analysis of an arm cavity
A detailed and realistic simulation of the arm cavity alignment sensing was performed

14. PDH error signal for a LG33 mode

15. Measuring coating thermal noise in the LIGO band
G. Ciani, J. Eichholz, M. Hartman, G. Mueller, J. Sanjuan
LIGO/LISA of Florida
Should I add LIGO/UF logs?

16. GWDAW 2011 – Isola d’Elba, Italy
Summary
Motivation
Experimental concept
A few design details
Experimental plan
May 2011
GWDAW 2011 – Isola d’Elba, Italy

17. GWDAW 2011 – Isola d’Elba, Italy
What and why?
Current coating thermal noise data:
Suspended cavities: above ~ 500 Hz (TNI)
Fixed spacer cavities: around or below 1 Hz
Coating thermal noise as one of the limiting source of noise, not the aim of the measurement.
Our idea:
Use a fixed spacer, ~ 25 cm long cavity as a reference
State of the art frequency stabilization with compact cavities: Hz
Measure coating thermal noise in short (1 cm), small beam size (~10-4 m) fixed spacer cavities
May 2011
GWDAW 2011 – Isola d’Elba, Italy

18. GWDAW 2011 – Isola d’Elba, Italy
Experiment concept X
PM2
PD2
PM1
Laser 1
Laser 2
NCO X
PD1
PM2
PD3
The beat signal at PD3 is used to control the NCO and keep Laser2 resonant in the thermal noise cavity
Could add formulas for the PDs signals, or put them in an extra slide. Think about it.
The beat signal at PD1 is used to phase lock Laser1 to Laser2 with a frequency offset set by the NCO (Numerically Controlled Oscillator). Residual phase error is measured by PhaseMeter1. -
The beat signal at PD2 is used to lock Laser1 to the reference cavity. Residual error is measured by PM2.
May 2011
GWDAW 2011 – Isola d’Elba, Italy

19. GWDAW 2011 – Isola d’Elba, Italy
Our noisy enemies
Identified noise sources (so far…):
Spacer thermal noise
No need to fight…
Substrate thermal noise
Fought with low loss substrate materials (fused silica)
Coating thermal noise (in reference cavity)
Fought with long cavity
Acceleration noise
Fought with stiff material, seismic isolation and wise cavity suspension
Temperature noise:
Fought with active temperature stabilization and low CTE material
Readout noise:
Some help from the Space…
Laser intensity noise (coupling via thermal effect in the substrate):
Waiting on the battlefield…
Not sure I want to put this in
May 2011
GWDAW 2011 – Isola d’Elba, Italy

20. Mechanical and optical layout
Viewport
Optical fiber from
outside vacuum
Reference cavities and beam splitters (except the first) installed on a single breadboard
Breadboard suspended in both horizontal (pendulum) and vertical (blades) directions
Suspended assembly enclosed in temperature stabilized vacuum tank
Input signal to the platform delivered by optical fiber
Beat signals delivered to out-of-vacuum photodiodes through viewports
Two orthogonal reference cavities to avoid common mode rejection of acceleration
Add schematic of suspension with blades
May 2011
GWDAW 2011 – Isola d’Elba, Italy

21. Reference cavity noise budget (preliminary)
L = 25 cm
CLEARCERAM-Z HS
Fused silica substrates
Tantala-Silica coating
Relative displacement noise [Hz-1/2]
Frequency [Hz]
May 2011
GWDAW 2011 – Isola d’Elba, Italy

22. Test cavity noise budget (preliminary)
L = 1 cm
CLEARCERAM-Z HS
Fused silica substrates
Tantala-Silica coating
Relative displacement noise [Hz-1/2]
Frequency [Hz]
May 2011
GWDAW 2011 – Isola d’Elba, Italy

23. GWDAW 2011 – Isola d’Elba, Italy
Can we measure it?
Displacement noise [m Hz-1/2]
Frequency [Hz]
May 2011
GWDAW 2011 – Isola d’Elba, Italy

24. GWDAW 2011 – Isola d’Elba, Italy
Phase Meter
May 2011
GWDAW 2011 – Isola d’Elba, Italy

25. GWDAW 2011 – Isola d’Elba, Italy
Experimental plan
Preliminary:
Create two almost identical reference cavities and characterize one against the other
Coating thermal noise measurement:
Measure coating thermal noise in short cavity and indentify it via its frequency dependence
Vary beam size in short cavities to check coating thermal noise scaling
Future work:
Measure substrate thermal noise using higher-loss materials
Measure thermal noise from different coatings
May 2011
GWDAW 2011 – Isola d’Elba, Italy

26. The AEI 10m Prototype Interferometer
Benefits and drawbacks of Khalili cavities
Tobias Westphal for the AEI 10 m Prototype team
GWADW Elba, May 2011

27. SQL interferometer layout
nm fiber coupled
Tap off
130 mW
10 m Fabry-Perot arm cavity
Finesse ca. 700
100 g Mirrors
Monolithic silica suspensions
Anti-resonant
Fabry-Perot cavities
as compound end mirrors
Frequency
reference cavity
Length: 12 m
Finesse: ca. 7500
Triple pendulum suspension
Mirror mass: 860 g

28. Where does coating noise appear?
Reflectivity N N
High reflective coatings have lots of coating layers
Few layers  medium R, low CTN
Many layers  high R, high CTN
The Idea: mechanical separation of reflectivity and losses
F. Ya. Khalili, Physics Letters A 334 (2005) 67-72

29. Khalili cavity and etalon
Length actuation problem
(thermal expansion?)
Thermal gradients
destroy homogenity
Mechanical coupling
(thicker substrate!)
ETM
perfectly
decoupled
longer cavity
(about 1m)
to fit sidebands
2 more DOF
to sense
IETM
EETM
(2n+1) l/2

30. Optimize rIETM for thermal noise
NIETM = 2
rIETM ≈ 0.7
NEETM = 15
tEETM ≈ 30ppm
RETM = 1-(TIETM)(TEETM+a)/4
= %

31. Optimize rIETM for rad. press.
NIETM ≈ ½?
rIETM = 30%
rEETM ≈ 100%
meff = 0.5mIETM
Effective mass
can be doubled
opt. thermal noise:
NIETM = 2
meff ≈ 0.7mIETM

32. “Abyss of instability”
ITM
IETM
EETM
gkhal
gii, gei
Problem: Big spots to reduce coating noise
10 5 m distance
large g factors, close to instability
extremely sensitive to deviation from specification
garm =
gkhal =
gaLIGO = 0.83

33. Sensitivity w/o Khalili cavities

34. Sensitivity with Khalili cavities

35. Sensitivity with doped coatings
Titania

36. Sensitivity with doping & Khalili
Titania