Report on WP1/M5: Local cooling effects on fiber thermal noise
M.Alshourbagy2, P. Amico1, S.Bigotta2, L. Bosi1, G.Cagnoli3-4, E.Campagna3, F. Cottone1, A.
Dari1, L. Gammaitoni1, M. Lorenzini3, G. Losurdo3, F. Marchesoni1, F. Martelli3, F.
Piergiovanni3, M.Punturo1, A.Toncelli2, M. Tonelli2, F. Travasso1, F. Vetrano3, H. Vocca1
1
INFN, Perugia, Italy
2
INFN, Pisa, Italy
3
INFN, Florence, Italy
4
IGR, Glasgow, UK
Coordinators: M. Punturo (INFN) and G. Cagnoli (Glasgow and INFN)
Introduction
The suspension system of the main optics in the current GW interferometric detectors is based
on a single or double metal wire loop. Only the GEO600 detector uses a different suspension
system, based on a monolithic fused silica design. Fused silica is a good material for low
thermal noise suspensions because of its low intrinsic loss angle and its low thermo-elastic
effect.
Crystalline materials have structural losses as low as, or even lower than silica but, due to
their relatively large thermal expansion, the thermo-elastic loss dominates by far over the
sensitive frequency range. For this reason crystalline materials have never been considered
suitable for the construction of low thermal-noise suspensions at room temperature.
The thermo-elastic dissipation angle te for a cylindrical fiber can be expressed like:
E 2T

unloaded fibre
cv
2
cv d w
2

te    
,  
,

 
2
 T
E     
2.16  2  k
1   
2

r
E



loaded fibre
cv
Eq 1
where dw is the wire diameter, T the temperature, cv is the specific heat, k is the thermal
conductivity, E the Young’s modulus,  the wire tension and  is the Young’s modulus
temperature gradient.
The contribution to the pendulum thermal noise budget due to the thermo-elastic effect is
given mainly by the dissipation occurring in the suspension fiber in the flexural points and by
the equation (Eq 1) it is dominant the role of the thermal expansion coefficient .
Some material, like the crystalline Silicon, shows a large thermal expansion coeeficient at
room temperature that, instead, decreases dramatically at low temperature. Silicon, for istance,
at 120K and about 20K shows a null thermal expansion coefficient.
Hence, cooling down only the flexural points of a suspension fibre, made by a material
showing a similar behaviour, it could be possible to reduce the thermo-elastic contribution to
the thermal noise.
Noise evaluation
Before to invest large efforts in the optical cooling of a suspended fibre, it is necessary to
model the possible noise contribution of this cooling method to the sensitivity curve of a
gravitational wave detector. This model has been developed with the hypothesis that the noise
is mainly due to the power noise of the laser that is coupled to the thermal expansion
coefficient of the suspension fibre.
The first step has been to evaluate the temperature distribution on a fiber where the flexural
point is cooled through the optical cooling method (or “anti-Stokes” method). The cooling
scheme is reported in Figure 1.
T0=300K
Laser
T0=300K
Figure 1 - Local cooling scheme
The amount of heat extracted in the time dt is given by:
dqoc  e(T )  P  dT
Eq 2
where e(T) is the optical cooling efficiency law and P is the laser power. e(T) depends on the
material used for the fiber, but the general behaviour is that it decreases quickly at low
temperature. A simulation performed with reasonable values for the parameters permits to
evaluate the temperature distribution T(y) along the wire length. In the hypothesys that the length
fluctuation of the fiber is given only by the power fluctuation P(f) of the laser, it is possible to
write the integral length fluctuation of the fiber:
eT f   P f 
LT f , f     L  
m  cv T f 
Eq 3
where Tf is the temperature of the flexural point, m is the mass of the wire and  is the average
thermal expansion coefficient:
L
1
    T  y dy
L0
Eq 4
If the filtering effect of the thermal conduction is taken in account, the integral length
fluctuation is given by:
eT  P f 
1
  L   f
LT f , f  
m  cv T f 
1  2f   c 
Eq 5
and the spectral fluctuation of the suspension wire is given by:
y   02  ( y  L)  0
y    L  

 02
2
0
  2    02 
2
2
Eq 6
Substituting in the equation (Eq 6) the characteristics of a suspension similar to the Virgo one,
the dash-dotted curve in Figure 2 is obtained. It is evident that the noise introduced in this way
is smaller than other contributions. This result permits to enumerate the optical cooling in the
list of possible technologies for the thermal noise reduction in gravitational wave experiments.
-18
10
Current Virgo
Pendulum thermal noise
Steel Wire Creep
Optical Cooling on high k
Pend.Th.Noise FS suspension
-19
10
h(f) [1/sqrt(Hz)]
-20
10
-21
10
-22
10
-23
10
-24
10
-25
10
1
10
100
1000
Frequency [Hz]
Figure 2 - Noise evaluation
First experimental tests
The experimental apparatus used in cooling consists of two diode lasers mounted with the
junctions perpendicular to each other. The output wavelength is slightly tunable by changing
the temperature of the diode junctions and is centered approximately around 1030 nm. A
polarizing beam splitter and a 10 cm focal length lens have been used to recombine and focus
the beams onto the crystal. The maximum power available just before the focusing lens is ~3
W. A ~3410 mm3 BaYF single crystal doped with 2.5% at. Yb3+ was placed in vacuum
chamber and suspended on two crossed microscope cover slips in order to reduce parasitic
heat loading from the surroundings, that is mainly due to conduction and convection
mechanisms. Moreover, chamber was kept at pressures less than 10-1 Pa by use of a cryogenic
pump.
A thermal image of the sample through a barium fluoride window on the vacuum chamber by
means of a IR Raytheon 2500AS thermal camera was used in order to get the temperature of
the sample. A maximum temperature drop of about 4 K starting from room temperature has
been achieved in a single pass configuration when the sample is irradiated with 3 W at 1024
nm, the shorter wavelength available with our experimental set-up. For such a temperature
drop starting from 293 K, the estimated cooling power is 2.4 mW and the cooling efficiency is
~3%.
The full potentiality of this results is still to be determined since we could not scan the whole
cooling wavelength range, being limited by the restricted tunability range of the laser diodes.
A new solid-state laser based on a Yb:LiYF4 with a larger tunability crystal is currently under
development. By using this laser to pump the crystal at < 1024 nm, we may expect to find a
larger temperature drop.