Transcript Laguerre-Gauss Mode Research at Birmingham

LG MODES FOR THERMAL NOISE
REDUCTION
Paul Fulda, Charlotte Bond
for
University of Birmingham and University of Glasgow
LIGO-G1100578
GWADW
ELBA
26.05.2011
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,
2Fulda,
S. et al, ‘Prospects of LG modes in GWDs’, Phys Rev D, 79, 122002, June 2009, LIGO-P0900006
P. et al, ‘Experimental demonstration of higher-order LG mode interferometry’, Phys Rev D, 82, 012002, July
2010, LIGO-P1000040.
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Paul Fulda GWADW Elba
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LG33 mode in the Glasgow 10m
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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
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Paul Fulda GWADW Elba
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LG33 mode in the Glasgow 10m (2)
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LG33 mode in the Glasgow 10m (3)
 LG33 mode path installed
on laser bench
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 LG33 Beam transmitted
through PMC
Paul Fulda GWADW Elba
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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
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Paul Fulda GWADW Elba
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Towards mirror specs for LG modes
 Mirror surfaces well described as a sum of Znm terms
y(cm)
surface height (nm)
y(cm)
surface height (nm)
Zernike version (C. Bond)
‘Bad’ JIF input mirror R=95%
x(cm)
x(cm)
 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…)
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Paul Fulda GWADW Elba
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Simple example of Zernike advantage
MIRROR
BEST
Relative
Relative
Z2±2 content Z20 content
(astigmatism) (curvature)
Circulating
beam
LG33 mode
content [%]
0.494
0.506
78.54
“AVERAGE”
0.758
0.224
64.5
WORST
0.856
0.144
See poster/talk at Amaldi
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Paul Fulda GWADW Elba
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Credit: C. Bond
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Thanks for listening!
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Mirror map simulations with Zernike
polynomials
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With astigmatism removed…
Z2±2 polynomials held at zero
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Paul Fulda GWADW Elba
92.6% LG33 mode content
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Coupling of tilt to phase in FP
cavity
Cavity tuning ( )
 We investigated the tilt to phase coupling in a
3km cavity
Alignment analysis of an arm
cavity
 A detailed and realistic simulation of the arm
cavity alignment sensing was performed
PDH error signal for a LG33 mode
Measuring coating thermal noise in the
LIGO band
G. Ciani, J. Eichholz, M. Hartman, G. Mueller, J.
Sanjuan
LIGO/LISA groups @University of Florida
Summary
• Motivation
• Experimental concept
• A few design details
• Experimental plan
May 2011
GWDAW 2011 – Isola d’Elba, Italy
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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: 10-16 Hz-1/2
@ 1 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
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Experiment concept
Laser 1
PD1
PD2
Laser 2
PD3
The beat signal at PD3
is used to control the
NCO and keep Laser2
resonant in the
thermal noise cavity
X
X
NCO
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.
May 2011
PM1
PM2
PM2
The beat signal at PD2 is
used to lock Laser1 to the
reference cavity. Residual
error is measured by PM2.
GWDAW 2011 – Isola d’Elba, Italy
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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…
May 2011
GWDAW 2011 – Isola d’Elba, Italy
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Mechanical and optical layout
• Reference cavities and beam splitters
(except the first) installed on a single
Viewport
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-ofvacuum photodiodes through
viewports
• Two orthogonal reference cavities to
avoid common mode rejection of
acceleration
May 2011
GWDAW 2011 – Isola d’Elba, Italy
Viewport
Optical fiber from
outside vacuum
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Reference cavity noise budget (preliminary)
Relative displacement noise [Hz-1/2]
10 14
L = 25 cm
CLEARCERAM-Z HS
Fused silica substrates
Tantala-Silica coating
Spacer Thermal
Spacer Temperature
Spacer acceleration
Substrate Thermal
10 15
Coating Thermal
Total
Out[178]=
10 16
10 17
5
10
50
100
500
1000
Frequency [Hz]
May 2011
GWDAW 2011 – Isola d’Elba, Italy
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Relative displacement noise [Hz-1/2]
Test cavity noise budget (preliminary)
L = 1 cm
CLEARCERAM-Z HS
Fused silica substrates
Tantala-Silica coating
10 15
10 16
10 17
10 18
Spacer Thermal
Spacer Temperature
Spacer acceleration
Substrate Thermal
Coating Thermal
Total
5
May 2011
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Frequency 50[Hz]
GWDAW 2011 – Isola d’Elba, Italy
100
500
1000
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Can we measure it?
Reference cavity
Displacement noise [m Hz-1/2]
10 16
Test cavity, 80 micron
Test cavity, 180 micron
10 17
10 18
10 19
5
10
50
100
500
1000
Frequency [Hz]
May 2011
GWDAW 2011 – Isola d’Elba, Italy
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Phase Meter
Equivalent displacement noise [m/Hz1/2]
10
10
10
10
10
10
-12
-14
-16
-18
-20
10
May 2011
Measured phase
Difference
Clock timing Jitter
-10
-1
10
0
10
1
2
10
Frequency (Hz)
GWDAW 2011 – Isola d’Elba, Italy
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3
10
4
10
5
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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
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AEI 10m Prototype Interferometer
Benefits and drawbacks of Khalili cavities
The
Tobias Westphal for the AEI 10 m Prototype team
http://10m-prototype.aei.uni-hannover.de
GWADW Elba, May 2011
SQL interferometer layout
8 W @ 1064 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
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Where does coating noise appear?
Coating noise
Reflectivity
N
N
High reflective coatings have lots of coating layers
(1) Few layers  medium R, low CTN
(2) Many layers  high R, high CTN
The Idea: mechanical separation of reflectivity and losses
F. Ya. Khalili, Physics Letters A 334 (2005) 67-72
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Khalili cavity and etalon
• Length actuation problem
(thermal expansion?)
• Thermal gradients
destroy homogenity
• Mechanical coupling
(thicker substrate!)
• perfectly
decoupled
• longer cavity
(about 1m)
to fit sidebands
• 2 more DOF
to sense
ETM
EETM
IETM
(2n+1) l/2
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Optimize rIETM for thermal noise
NIETM = 2
rIETM ≈ 0.7
NEETM = 15
tEETM ≈ 30ppm
RETM = 1-(T )(T +a)/4
= 99.9993%
IETM
EETM
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Optimize rIETM for rad. press.
NIETM
rIETM
rEETM
meff
≈ ½?
= 30%
≈ 100%
= 0.5mIETM
• Effective mass
can be doubled
• opt. thermal noise:
NIETM = 2
meff ≈ 0.7mIETM
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“Abyss of instability”
ITM
IETM
EETM
gkhal
gii, gei
Problem: Big spots to reduce coating noise
• 10 mm @ 5 m distance
• large g factors, close to instability
• extremely sensitive to deviation from specification
garm = 0.9982
gkhal = 0.999988
gaLIGO = 0.83
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Sensitivity w/o Khalili cavities
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Sensitivity with Khalili cavities
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Sensitivity with doped coatings
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Sensitivity with doping & Khalili
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