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Report on WP3/T2: Measurements of thermo-elastic effects of coatings at room
temperature
O. Arcizet(1), M. De Rosa(2,3), A. Heidmann(1), F. Marin(2,4), F. Marino(2), M. Pinard(1)
1
CNRS - LKB, Paris, France
INFN, Sezione di Firenze, Italy
3
INOA, Sezione di Napoli, Italy
4
Dip. di Fisica, Università di Firenze, Italy
2
Coordinators: Antoine Heidmann (CNRS LKB), Francesco Marin (INFN – FI)
Introduction
The displacement sensitivity of optical interferometers is limited by several dissipative phenomena.
One of such effects is the dynamic photothermal effect due to the fluctuations of the laser power
absorbed by the mirrors and converted into surface displacements through thermal expansion. The
purpose of Task T2 is to carry out a deep experimental investigation of this photothermal noise by
using the effect induced by an intensity modulation of the light entering a Fabry-Perot cavity. This
measurement can be performed over a wide frequency range, with the temperature ranging between
tenths of Kelvin up to room temperature, and with low-losses optical coatings.
During the last years, we have investigated the photo-elastic effect over a wide frequency range and
different spot sizes, including finite mirror size effects at low frequency and coating effects at high
frequency. We have developed a theoretical model to describe the observed finite size and coating
effects. We have also performed a theoretical investigation of possible instabilities and dynamics in a
high-finesse cavity where both radiation pressure and photothermal effects are considered.
In this third-year report, we present the last improvements in the photothermal measurements at room
temperature and the theoretical studies on mixed radiation pressure and photo-thermal effects.
Measurements of thermo-elastic effects of coatings at room temperature
We have performed two new series of photothermal measurements on a short cavity, changing the
setup (in particular, the locking and measurement system) to verify the absence of systematic errors due
to the measurement technique. In a first series of measurements at intermediate modulation
frequencies, the laser was directly locked to the reference cavity and the one with a modulated intensity
by acting on an AOM with an improved servo loop. In a second series of measurements (at high
frequencies), we used only one cavity with a calibration signal added to the laser frequency driver.
Both series of measurements are in agreement with the old ones.
We have theoretically studied the stability of Fabry-Perot cavities in presence of radiation pressure and
photo-thermal effects. The analysis provides important indications that should be taken into account in
the development of quantum optics experiments and gravitational-wave detectors. We have shown that
the interplay between these nonlinear phenomena may lead to self-oscillatory behavior [1] or to
bistability, even in absence of time-delay effects in the intracavity field buildup. In particular, we show
that, for high mechanical quality factor, an Hopf bifurcation can occur before the limit of the bistable
cycle calculated from stationary state analysis. This phenomenon reduces the useful linear operation
range of pendular cavities. An example is shown in Figure 3, where are shown the stability domains in
the (cold detuning)/(hot detuning) plane. Here ‘cold detuning’ is for vanishing laser power, while ‘hot
detuning’ includes the non-linear cavity displacement due to radiation pressure and photo-thermal
effect. Stationary solutions for different values of input power are shown in dotted lines. The stable
domain defined by the Hopf bifurcation is the shaded region, while the usual bistability border is drawn
with a solid line. A complete analysis applied to different kinds of optical cavities and detector
parameters is given in Ref. [2].
Figure 3
[1] "Canard orbits in Fabry-Perot cavities induced by radiation pressure and photothermal effects", F.
Marino, M. De Rosa, and F. Marin, Phys. Rev. E 73, 026217 (2006)
[2] "Thermo-optical nonlinearities and stability conditions of high-finesse interferometers", F. Marino,
F. Marin, in press on Phys. Lett. A (available on line)