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24 August 2008 LSC-Virgo Meeting, Amsterdam 1
Thermal compensation simulation
Richard Day
EGO optics group
B. Swinkels
M. Pichot
Based on work by:
M. Punturo
A. Rocchi
V. Fafone
J-Y Vinet
24 August 2008 LSC-Virgo Meeting, Amsterdam 2
Outline
� Thermal Effects – Problem, Solution
� Simulation chain
� Optical Simulation (Zemax)
� Thermal simulation (Matlab) – Validation & preliminary results
� Interferometer simulation (Darkf) – Preliminary results
� Conclusions and further work.
24 August 2008 LSC-Virgo Meeting, Amsterdam 3
Problem
A lot of power in the recycling cavity
A huge amount in the arm cavities
North arm
West arm
~150 W
~5000 W
~5000 W
Power recycling
Beamsplitter
Input mirror
End mirror
Input mirrorEnd mirror
Sidebands resonant in recycling
cavity give locking signals
Current virgo configuration
with 7W input laser power
Sidebands resonant
Carrier resonant
Recycling cavity
~150 W
24 August 2008 LSC-Virgo Meeting, Amsterdam 4
Problem
~150 W~5000 W
Input mirror
Substrate losses in
Fused silica → 0.7 ppm/cm
→ ~2 mW absorbed
Coating losses:
~2.3 ppm for NI
→ ~12 mW absorbed
~7.7 ppm for WI
→ ~39 mW absorbed
10cm
Determined experimentally.
See presentation by A. Rocchihttp://wwwcascina.virgo.infn.it/collmeetings/presentations/2007/2007-05/DetectorMeeting/Alessio%20Rocchi_Rocchi%20LSC-Virgo%20TCS.ppt
24 August 2008 LSC-Virgo Meeting, Amsterdam 5
Problem
~150 W~5000 W
Input mirror
Substrate losses in
Fused silica → 0.7 ppm/cm
→ ~2 mW absorbed
Coating losses:
~2.3 ppm for NI
→ ~12 mW absorbed
~7.7 ppm for WI
→ ~39 mW absorbed
Effect on carrier in arm cavities small… For now!
10cm
Thermal lensing
Inside substrate
Curving of surface
Due to thermal expansion
However situation is critical for sidebands in recycling cavity
Determined experimentally.
See presentation by A. Rocchihttp://wwwcascina.virgo.infn.it/collmeetings/presentations/2007/2007-05/DetectorMeeting/Alessio%20Rocchi_Rocchi%20LSC-Virgo%20TCS.ppt
24 August 2008 LSC-Virgo Meeting, Amsterdam 6
Problem
LSB (dark fringe)
USB (dark fringe)
Power recycled
SB recycled
·One hour of thermal transient can be seen in the signals
·Sideband signals become perilously low making locking extremely difficult
24 August 2008 LSC-Virgo Meeting, Amsterdam 7
Solution
Input mirror
~5000 W ~150 W
CO2Axicon
Project a CO2 laser ring onto the mirror
to create the “opposite” thermal effect
However, not as easy as it sounds.
·First attempts on full interferometer have shown that optimization not easy
·Many Ring parameters to adjust:
Power, Alignment, Thickness, Diameter, Symmetry…
·Transient effects not well understood
24 August 2008 LSC-Virgo Meeting, Amsterdam 8
Simulation
·Simulation of complete chain will give us a better understanding.
·This will help a lot during commissioning of the TCS.
·Extensive work already carried out on simulation chains:Ansys: Maurizio Di Paolo Emilio (Tor-Vergata)
Analytical: Jean-Yves Vinet (ARTEMIS)
Developed simulation chain
TCS Optical
Bench Setup
Zemax:
Optical
Simulation
CO2
beam shape
Matlab:
Thermal
Simulation
DarkF:
Interferometer
Simulation
Phase maps:
transmission
& reflection
-SB behaviour
-Locking signals behaviour
-Phase camera images
24 August 2008 LSC-Virgo Meeting, Amsterdam 9
Zemax: optical simulation
·Well known ray tracing software for optical design.
·Construct optical layout surface by surface
·Optical setup developed by Tor-Vergata & EGO
Axicon
Adjust to change ring diameter
Adjust to change ring thickness
24 August 2008 LSC-Virgo Meeting, Amsterdam 10
Zemax: optical simulation
Zemax can produce intensity images and profiles
24 August 2008 LSC-Virgo Meeting, Amsterdam 11
Zemax: optical simulation
· By adjusting two lenses in system we tailor ring shape to our needs
Adjust ring thickness Adjust ring diameter
· Using Matlab toolbox we move lenses and export data
· Automation important for optimizing ring shape.
24 August 2008 LSC-Virgo Meeting, Amsterdam 12
Thermal Simulation
A lot of work already done with direct application to thermal compensation:
•Analytical solution by P. Hello / J-Y Vinet
•Comsol simulations by NIKHEF
•ANSYS simulations by Tor-Vergata
•A lot of work at LIGO (FEMLAB, see thesis R. Lawrence)
•2-D simulation in Matlab by M. Punturo (slices and rings)
We chose to base our simulation on work done by M. Punturo
24 August 2008 LSC-Virgo Meeting, Amsterdam 13
Matlab: Thermal Simulation
Two types of Matlab simulations were developed:
2D simulation: M. Punturo
· 3D problem reduced to 2D
· Assumes cylindrical symmetry
· 24 hrs in ~6 sec
3D simulation: B. Swinkels
· Necessary for simulating decentred and asymmetrical beams
· 24 hrs in ~200 sec
Power transfer:
· YAG Power absorbed in coating and in substrate.
· CO2 power absorbed in coating using profiles from Zemax
· Power emitted by radiation from surfaces of mirror
· Both measure time evolution of temperature in mirror
3D
2D
24 August 2008 LSC-Virgo Meeting, Amsterdam 14
Matlab: Thermal Simulation
Thermal equilibrium reached when Power in = Power out
Time constant of ~ 5 hours
Switch on YAG beam
24 August 2008 LSC-Virgo Meeting, Amsterdam 15
Matlab: Thermal Simulation
Temperature distribution after 12 hours of YAG heating
24 August 2008 LSC-Virgo Meeting, Amsterdam 16
Matlab: Thermal Simulation
Temperature distribution after 12 hours of CO2 ring beam heating (1W)
24 August 2008 LSC-Virgo Meeting, Amsterdam 17
Matlab: Thermal Simulation
Three effects on optical path length due to mirror heating:
1. Thermooptic Effect (thermal lensing)· Change in refractive index with temperature.
· Taken into account.
2. Thermoelastic Deformation
· Curving of surface due to thermal expansion.
· Partially taken into account.
→ Assume that all displacement occurs on absorbing surface.
3. Elastooptic Effect· Change in refractive index with thermal expansion induced strain.
· Not taken into account.
· For Fused Silica these assumptions should give sufficiently accurate results.(see thesis R. Lawrence)
24 August 2008 LSC-Virgo Meeting, Amsterdam 18
Matlab: Thermal Simulation
Comparison with analytical solution (Hello & Vinet)
· Total deformation of ~ 7 nm
· Difference due to assumptions made for thermoelastic deformation
· Agreement to < 1nm in region of interest
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Radial Distance (m)
Surface Deform
ation (nm)
Analytical
Simulation
Thermoelastic
Deformation
24 August 2008 LSC-Virgo Meeting, Amsterdam 19
Matlab: Thermal Simulation
Comparison with analytical solution (Hello & Vinet)
· Total optical path length change of ~ 150 nm
· Extremely good agreement with analytical solution
· This effect (thermal lensing) is the most important for sidebands
0
20
40
60
80
100
120
140
160
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Radial Distance (m)
Optical Path Length (nm)
Analytical
Simulation
Thermooptic
Effect
24 August 2008 LSC-Virgo Meeting, Amsterdam 20
Matlab: Thermal Simulation
Analytical
Simulation
Comparison with analytical solution (Hello & Vinet)
· Transient effects also agree well with analytical solution
· We will see that transient effects are important for our application
Thermooptic
Effect
24 August 2008 LSC-Virgo Meeting, Amsterdam 21
0
500
1000
1500
2000
2500
3000
3500
4000
0 1 2 3 4 5Time (hrs)
Coupling loss (ppm)
YAG
Matlab: Thermal Simulation
We are interested in distortion of YAG beam
→ Compare distorted & undistorted wave front → Coupling Loss (ppm)
Lock interferometer
Time constant ~10 min
Steady state loss 3700 ppm
Remember that time constant of mirror temperature was 5 hours!
24 August 2008 LSC-Virgo Meeting, Amsterdam 22
Matlab: Thermal Simulation
Analytical
Simulation
· Central “bump” forms very quickly
· Afterwards everything rises at the same rate
24 August 2008 LSC-Virgo Meeting, Amsterdam 23
Matlab: Thermal Simulation
What happens if we switch on TCS when interferometer locks?
Steady state loss 190 ppm
· TCS works but things get worse before they get better !!
· 2 hours before things settle down.
· We’re going to have fun trying to lock with things like this!
0
1000
2000
3000
4000
5000
6000
7000
0 1 2 3 4 5
Time (hrs)
Coupling loss (ppm)
YAG
YAG & CO2
24 August 2008 LSC-Virgo Meeting, Amsterdam 24
Central heating spot
But there is a solution:
•Never switch off the CO2 laser ring
•When interferometer not locked heat the centre with CO2 laser beam
In this way the mirror will never see a change
Installation of central heating beam planned before end 2008by Tor-Vergata group with participation from EGO
24 August 2008 LSC-Virgo Meeting, Amsterdam 25
The perfect ring
Many parameters for CO2 ring beam:
•Ring Thickness
•Ring Diameter
•Ring Power
Use optical & thermal simulation
to try all combinations.
Use coupling loss as measure of performance
24 August 2008 LSC-Virgo Meeting, Amsterdam 26
0
100
200
300
400
500
600
700
800
900
1000
1 1.5 2 2.5 3 3.5 4 4.5 5
CO2 Power (W)
Coupling Loss (ppm)
The perfect ring
· Thin rings better at low power.
· Thick rings better overall
For every ring thickness and at every power find best ring diameter
Thin ring
Thick ring
Plateau at 280 ppm
40 ppm
24 August 2008 LSC-Virgo Meeting, Amsterdam 27
0
50
100
150
200
250
300
350
400
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Radial Distance (m)
Relative intensity (a.u.)
The perfect ring
· The rings giving lowest coupling “hug” the YAG beam.
Lowest coupling loss for each ring thickness
YAG beam
24 August 2008 LSC-Virgo Meeting, Amsterdam 28
0
100
200
300
400
500
600
700
800
900
1000
1 1.5 2 2.5 3 3.5 4 4.5 5
CO2 Power (W)
Coupling Loss (ppm)
The perfect ring
Where does this plateau come from?
Thin ring
Thick ring
Plateau at 280 ppm
24 August 2008 LSC-Virgo Meeting, Amsterdam 29
0
50
100
150
200
250
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Radial Distance (m)
Relative intensity (a.u.)
The perfect ring
Optimal heating of 280 ppm when ring is far from center
Just look at thinnest ring. Find best diameter for each power.
Increasing
Power
Not as good as 40 ppm but much less sensitive to alignment (3D simulations)
24 August 2008 LSC-Virgo Meeting, Amsterdam 30
DarkF: Interferometer Simulation
Created by
Mikael Laval & Jean-Yves Vinet
Mikhael Pichot continues work
Optical simulation code in FORTRAN 90
Uses plane wave decomposition to
propagate the wavefronts
We can insert phase maps from thermal simulations
Simulate entire Virgo interferometer to see thermal effects
24 August 2008 LSC-Virgo Meeting, Amsterdam 31
0
5
10
15
20
25
30
35
40
45
50
0 1 2 3 4 5Time (hrs)
Recycling Gain
LSB YAG
USB YAG
DarkF: Interferometer Simulation
Preliminary results
· Fast reduction in sidebands gain with time constant ~ 10 min
Lock interferometer
24 August 2008 LSC-Virgo Meeting, Amsterdam 32
DarkF: Interferometer Simulation
Preliminary results
· Sidebands only get back to a stable state after about 2 hours
Switch on TCS when interferometer locks
0
5
10
15
20
25
30
35
40
45
50
0 1 2 3 4 5
Time (hrs)
Recycling Gain LSB YAG
LSB YAG & CO2
USB YAG
USB YAG & CO2
24 August 2008 LSC-Virgo Meeting, Amsterdam 33
Conclusions & Further work
Conclusion
� Assembled complete simulation chain of Thermal compensation for Virgo.
� Better understanding of temporal evolution.
� Tools to choose best ring and calculate alignment tolerances.
� First results of simulated interferometer with thermal effects.
Further work
� Add central heating spot to simulation.
� Use of finesse interferometer simulation: comparison DarkF.
� Compare interferometer simulations with experimental data.
� Use experience gathered from simulations to help with installation and commissioning of Thermal Compensation System.
24 August 2008 LSC-Virgo Meeting, Amsterdam 34
Conclusions & Further work
Conclusion
� Assembled complete simulation chain of Thermal compensation for Virgo.
� Better understanding of temporal evolution.
� Tools to choose best ring and calculate alignment tolerances.
� First results of simulated interferometer with thermal effects.
Further work
� Add central heating spot to simulation.
� Use of finesse interferometer simulation: comparison DarkF.
� Compare interferometer simulations with experimental data.
� Use experience gathered from simulations to help with installation and commissioning of Thermal Compensation System.