Experimental Measurement of the Dynamic Photothermal Effect in Fabry-Perot Cavities for Gravitational Wave Detectors

We report the experimental observation of the frequency dependence of the photothermal effect. The measurements are performed by modulating the laser power absorbed by the mirrors of two high-finesse Fabry-Perot cavities. The results are very well described by a recently proposed theoretical model [M. Cerdonio, L. Conti, A. Heidmann, and M. Pinard, Phys. Rev. D 63, 082003 (2001)], confirming the correctness of such calculations. Our observations and quantitative characterization of the dynamic photothermal effect demonstrate its critical importance for interferometric displacement measurements towards the quantum limit, as those necessary for gravitational wave detection.

Figure 1

Scheme of the experimental setup. C1, C2: Fabry-Perot cavities; OI: optical isolator; HW: half-wave plate; EOM1, EOM2: electro-optic modulators; P: polarizer; BS: beam splitter; D1–D3: photodetectors; M: mixer. The dashed lines mark out active thermal stabilization.

Figure 2

Differential length variation $\delta l$ as a function of the relative modulation amplitude $P_{\mathrm{m}}/P_0$, for a fixed modulation frequency ${\nu }_{\mathrm{m}}=0.05\mathrm{H}\mathrm{z}$. The error bars are due to the uncertainty of the slope of the Pound-Drever signal, which calibrates the length scale.

Figure 3

Differential length variation $\delta l$ as a function of the modulation frequency ${\nu }_{\mathrm{m}}$. The solid line is the fitting curve of the experimental data with the expression of Eq. (4). The dashed line is the best fit of the experimental data with a single-pole, low-pass function.