Deliverable n.65
Report on WP3/T3: Mechanical transfer function of the folded Fabry-Perot cavity
M. Anderlini 1, F. Marin 1, F. Marino 1
1
INFN, Florence, Italy
Coordinators: Paolo Falferi (IFN), Antoine Heidmann (CNRS LKB)
The folded Fabry-Perot (FFP) prototype was mounted in an initial configuration of 9 mirrors, on
two parallel rows: an input (T=130 ppm) plane mirror, a spherical output mirror (R=1m, T=10 ppm)
and 3 intermediate plane mirrors (T=10 ppm) on one row, and 4 intermediate plane mirrors on the
opposite row. The two mirror rows are mounted on separate oscillating masses (more details on the
FFP are given in the 2007 Report).
The experimental scheme for the measurement of the mechanical response function was improved
with respect to the one described in the previous report, and is shown in Fig. 1.
Figure 1 Sketch of the experimental setup
The light source is a cw Nd:YAG laser at 1064 nm. After a 40 dB optic isolator, a resonant electrooptic modulator (EOM1) provides phase modulation at 13.3MHz with a depth of about 1 rad used
for the Pound–Drever–Hall detection scheme. The light is then transmitted within an optical fiber
and passes through an optical isolator. A second beam can be shifted in frequency by means of two
acousto-optic modulators (AOM) and modulated in amplitude by an EOM. The light reflected by
the cavity and a portion of the input light are collected by photodiodes PD1 and PD1 respectively,
In order to characterize the frequency response curve of the Folded Fabry-Perot (FFP), the laser is
locked on the cavity and the injected power is modulated (AM) at different frequencies. The
extraction of the cavity response to the amplitude-modulation of the light power is obtained by
demodulation of the error signal (Pound-Drever signal of PD1) at the AM frequency.
In an optical cavity consisting of two oscillating masses the intracavity optical path depends on the
optical intensity through two competing effects. The first is radiation-pressure, which is significant
in correspondence of the mass resonant frequencies. The second is the thermal expansion of the
mirror due to residual optical absorption (photothermal-effect). The response to a modulation of the
optical intensity (Fig. 2) is the result these two contributions, showing the mechanical resonances
excited by radiation-pressure on top of a nearly constant photothermal background.
b)
Figure 2 a) Phase and b) amplitude of the mechanical response of a FFP. Blue circles: experimental data;
blue line: fit with the complete response function; dotted line: photothermal background; red solid line:
complete mechanical response; red dashed line: mechanical response of two modes.
In the enlargement of Fig. 2b we clearly see that the complete susceptibility is below the level of the
single mechanical modes that compose it, due to the negative interference between modes excited at
frequencies respectively above and below their resonances (‘back-action reduction’).