JRA3: STREGA - TASK M1
Report on optical and Q measurements of Si and CaF2
sample
First year report (04/2004, 04/2005)
Leading group: ESPCI, CNRS-IN2/P3 (2)
The main activity of CNRS UPR5 in the field of gravitational wave research is optical
metrology. Our task within the STREGA framework is to measure optical properties of
different materials that could be chosen to replace fused silica as substrate material for the
next generation gw detectors. The optical properties that are most important to measure (at
least in a preliminary study) are absorption coefficient and birefringence level. Requirements
for the next generation detectors put severe constraints on the optical performances of the
chosen material: the effects of absorption and birefringence on the detector should be at least
one order of magnitude lower than what it is actually in working detectors. Concerning
birefringence, this implies that the maximum tolerable level of coupling between orthogonal
polarisation states of an incoming laser beam should be lower than 10-7. Concerning
absorption, things are a little less straightforward because the pertinent parameter to lower is
not the absorption by itself but the thermal lens effect it induces. This effect depends not only
on the absorption level but also on the value of some thermal parameters (thermal
conductivity ant thermooptic coefficient). If fluorine is chosen, then its absorption coefficient
should be lower than 10-7/cm, while if silicon is chosen, its absorption coefficient could be as
large as a few 10-6/cm if cooled below 100K.
Fluorine absorption at 1064nm at room temperature
One of the first candidate for replacing fused silica was CaF2. It is a cubic crystal, so it is not
birefringent, and the only critical optical parameter to measure was supposed to be absorption
(see the section on silicon birefringence for information). We purchased fluorine samples
from different manufacturers and measured their absorption coefficient at the Nd:YAG
wavelength, using a mirage bench. The results we obtained show that:
 The absorption coefficient strongly depends on the manufacturer, for a given
manufacturing process.
 The absorption fluctuates from point to point in a given crystal. This feature is
common to all samples.
 The absorption level is 10 to 300 times higher than what is required for the next
generation detectors. The following table summarizes the main results that were
obtained
Average absorption
Crystran
Crismatec
unknown
4.6 ppm/cm
1 ppm/cm
24 ppm/cm
Absorption dispersion
inside a given crystal
0.9 ppm/cm
0.2 ppm/cm
10 ppm/cm
Silicon absorption at 1500nm at room temperature
Absorption in silicon can be caused by the presence of impurities, or by free carriers. In the
case of undoped silicon, the free carrier absorption falls well below 10-8 per centimetre (Drude
model), so the use of intrinsic silicon seems at first glance to be the best choice. Nevertheless,
at least two reasons make the testing of slightly doped silicon necessary :
 The very first absorption measurements show that undoped silicon has a unexpectedly
high absorption factor, suggesting that it contains much more impurities that doped
silicon. The reason for this lies in the manufacturing process, but we cannot avoid the
possibility that, whatever the process, it may be difficult to obtain intrinsic silicon with
a higher level of purity than doped silicon.
 If a reasonable amount of free carriers is present in the mirror substrates (1012 to 1014
cm-1 it may help getting rid of the problem of ionization by cosmic radiation, which
seems to be a problem with the current fused silica mirrors.
We have realized a mirage bench working at 1300nm-1500nm, with a sensitivity of
50ppm/cm, limited by the amount of heating laser power.
Figure 1 : The mirage bench. The sample is placed in the blue cryostat.
We started a systematic study of silicon bulk absorption as a function of :
 Doping level
 Doping species
 Manufacturing process
Silicon absorption at 1500nm at 77K
We have started to investigate the effect of cooling on the absorption level of silicon. The
mirage bench has been upgraded by the addition of a He/Na cryostat, and the use of a pulsed
pump laser working at 200kHz-300kHz and delivering 4W of average power. This laser was
bought by EGO, the EC funding not being sufficient. During the last months we have tested
the bench by comparing various results with literature. Figure 2, shows our measurements of
thermal diffusivity compared to previously published results. The bench is now operational
and we should be able to perform absorption measurements at low temperature as early as
month 13. One important point is that, because we still miss a high speed detector (already
purchased but not delivered yet), we cannot evaluate the bench ultimate sensitivity.
Figure 2 : Si thermal diffusivity as a function of temperature. black squares are experimental values.
Silicon intrinsic birefringence.
Although silicon is a cubic crystal, it may exhibit birefringence. We can distinguish three
sources of birefringence: birefringence induced by external strain (typically the substrate
holders and the substrate own weight); birefringence induced by crystalline defects
(dislocations, point defects) that mainly depend on the crystal growth method and on the
manufacturer’s savoir-faire; and intrinsic birefringence. While the two first sources could be
controlled and optimized, the third one puts a lowest value on the achievable birefringence
level. Thanks to the cubic structure of silicon crystal, intrinsic birefringence is very low, but
depending on the orientation of the crystalline axes with respect to the incoming wave vector
(Figure 3), it can induce couplings far higher than the required 10-7 per centimetre. It is thus
necessary to study the angular tolerance of the crystal axes orientation with respect to the
substrate polished faces.
Figure 3 : calculated birefringence losses as a function of the incoming wave vector orientation for S
polarized light. U, V, W are the wave vector coordinates with respect to the crystal {[100],[010],[001]}
axes. The losses are null for two orientations : k along the [100] axis (red square), or along the [111] axis
(green spot).
We started our study with [100] silicon, because its angular tolerance is much larger than
[111] silicon, and because the birefringence signature is much easy to show (Figure 4 and
Figure 5).
Figure 4 : birefringence losses per centimeter as
a function of the substrate orientation ([111]
surface normal) with respect to the incoming
laser beam (the laser is S-polarized)
Figure 5 : birefringence losses per centimeter as
a function of the substrate orientation ([100]
surface normal) with respect to the incoming
laser beam (the laser is S-polarized)
A theoretical model (Figure 3) has been built to calculate the apparent birefringence
amplitude, and the coupling losses, as a function of the crystal orientation with respect to the
incoming light wavevector direction and state of polarization. The maximum birefringence is
an ad-hoc parameter that can only be evaluated experimentally using [110] crystals. We relied
on a previously measured value of 16.76mrad. This allowed to estimate the angular tolerance
of the crystal orientation (Figure 4, Figure 5). A dedicated birefringence bench has been built
to study intrinsic birefringence. It is a linear (non-imaging) bench working at 1.45µm. We
optimized the bench sensitivity to reach birefringence values as small as 30µrad, which
expressed in terms of losses is equivalent to 210-10 for 1 centimetre thick samples. In order to
obtain such a high sensitivity the bench makes use of an acousto-optic modulator which acts
as a dynamic source of birefringence, modulated at 50kHz. The superposition of the sample
induced signal and the modulator signal is sent to a lock-in detection. The 50kHz signal is
proportional to the projection of the birefringence on the incident field polarization (in the
particular measurement scheme which is used). It thus gives immediately the amount of losses
that can be expected in a silicon mirror having the same orientation. The whole bench is set
vertically and the sample lies horizontally on a motorized x-y rotation stage. The
birefringence modulator is placed after the sample, so that the polarization incident on the
sample is always purely linear.
Figure 6 : vertical birefringence bench
Experimental results have confirmed the fact that, as far as only intrinsic birefringence is
present, the angular tolerance for the direction of the [100] axis with respect to the mirror
surface normal is 4° for losses to be lower than 10-8 cm-1. For the [111] direction the tolerance
is 0.1°.
Figure 7 : birefringence measured in [111] silicon as a function of x.