faraday thermal lensing numerical simulations
DESCRIPTION
Faraday thermal lensing numerical simulations. Slim Hamdani EGO LIGO-G070358-00-Z. Faraday Thermal Lensing. Virgo: 10W + 3W mismaching:~0.5%. Virgo +: 40W + 10W mismaching:~5%. Advanced Virgo: 150W + 50W mismaching:~37%. When heated, the Faraday isolator: - PowerPoint PPT PresentationTRANSCRIPT
Thermal lensing simulationLSC meeting, 25/05/07 1
Faraday thermal lensingnumerical simulations
Slim HamdaniEGO
LIGO-G070358-00-Z
Thermal lensing simulationLSC meeting, 25/05/07 2
Faraday Thermal Lensing
When heated, the Faraday isolator:When heated, the Faraday isolator:-Changes its polarization (isolation)Changes its polarization (isolation)-Change non uniformly its refraction index (lensing)Change non uniformly its refraction index (lensing)-Change non uniformly its dimensions (lensing)Change non uniformly its dimensions (lensing)
Virgo:Virgo:-10W + 3W10W + 3W- mismaching:~0.5%mismaching:~0.5%
Virgo +:Virgo +:- 40W + 10W40W + 10W- mismaching:~5%mismaching:~5%
Advanced Virgo:Advanced Virgo:- 150W + 50W150W + 50W- mismaching:~37%mismaching:~37%
Thermal lensing simulationLSC meeting, 25/05/07 3
Finite elements
Gaussian beam
conduction
Vacuum or not
air c
oolin
g
air c
oolin
g
heat radiation
Shield or not
radiationM. Punturo Matlab’s algorithm
Thermal lensing simulationLSC meeting, 25/05/07 4
Finite elements simulation
Heat transfer equations
conduction Q=AT/d
Q [Watt/sec] rate of heat flow
[Wm-1K-1] thermal conductivity
A [m2] contact area
T temperature difference
d [m] distance of heat flow
radiation Q=A(T4-T04)
Q [Watt/sec] rate of heat flow
A [m2] contact area
[Wm-2K-4] Stefan Boltzmann cst
emissivity
T [K] temperature
Thermal lensing simulationLSC meeting, 25/05/07 5
External conditions simulation
convection Q=(T-Tair)A
Q [Watt/sec] rate of heat flow
[Wm-1K-1] flux caracterization
T[K] sample temperature
Tair[K] air temperature
A [m2] contact area
=[10:100] turbulent or laminar flux
Air or vacuum Shield or free
Radiation transfer(with the shield
considered always thermalized)
radiation Q=A(T4-T04)
Thermal lensing simulationLSC meeting, 25/05/07 6
TGG heated by a 150 + 50 Watt Yag
Temperature map
PR aligned
Temperature map
Refraction index map&
Verdet cst map
Thermal lensing simulationLSC meeting, 25/05/07 7
Phase
Mean phase change
Refraction index
Thermal expansion
TGG heated by a 150 + 50 Watt Yag
Thermal lensing simulationLSC meeting, 25/05/07 8
N index fit -> Zmax
GaussianGaussianweightedweighted
mean 2mean 2ndnd order fit order fit66thth order radial order radialpolynomial fitpolynomial fit
ZmaxZmax
Thermal lensing simulationLSC meeting, 25/05/07 9
Focal approximation
fit limits~+- 1waist
Circle fit
Radius of curvature
focal
Thermal lensing simulationLSC meeting, 25/05/07 10
Virgo+ and Advanced Virgo thermal lensing
VIRGO+ (50Watt)Thermal lens: f=66mMismatch: 5%
Advanced VIRGO (200Watt)Thermal lens: f=13mMismatch: 37%
E. Geninlogbook entry 13988
tunable withthe input telescope
Thermal lensing simulationLSC meeting, 25/05/07 11
TGG characterization
TGG
emissivity 0.89
thermal conductivity[K W/m]
7.4
density[g/cm3]
7.32
specific heat [J/(K kg)]
385
substrate losses [1/cm]
1.65e-3
thermal expansion [1/K]
9.4e-6
refraction index 1.94
dn/dT [1/K] 1.9e-5
Depending of the sample+- 4 times
Preliminary test with a650mWatt Yag, waist: 180m
Next test wit a0-200 Watt Yag
waistFlip mirror
95% reflection
Cold-Hot: R~24m.Simulation: R=24.3m.
SH
Yag
TGG
2.70e-3
Thermal lensing simulationLSC meeting, 25/05/07 12
Faraday compensation
Thermal lensing:Thermal lensing: converging lensconverging lensCompensator:Compensator: thermal diverging lensthermal diverging lens
VIR
GO
+
Adv
ance
d A
dvan
ced
VIR
GO
VIR
GO
° rotator
Kazanov et al 2004
polarizer polarizer
DKDP ?
22.5
°
22.5
°
?
?
TGG
45°polarizer polarizer
DKDP ?
VIR
GO
+V
IRG
O+
ringheater
plate
Thermal lensing simulationLSC meeting, 25/05/07 13
To do
- Depolarization measurements @ 50W and 200W on TGG, DKDP or others
-Physical parameters characterization of TGG
-Validation of the simulation with the metallic shield and under vacuum
- Test final design for VIRGO+
- Studying the design for Advanced VIRGO