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Photothermal and thermo-refractive effects in high reflectivity mirrors at room and cryogenic temperature
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Image of FIG. 1.
FIG. 1.

(Color online) Scheme of the experimental apparatus. O.I.: Optical isolator; AOM: Acousto-optic modulator; EOM: Electro-optic modulator; H: Half-wave plate; Q: Quarter-wave plate; PD: Photodiode; PBS: Polarizing beam-splitter; BS: Beam-splitter.

Image of FIG. 2.
FIG. 2.

(Color online) (a) Amplitude of the photothermal response as a function of the modulation frequency at room temperature. The solid red line is the fit through the complex response function (78) for both silica and silicon mirrors, keeping fixed the substrate parameters (see Table I). Other curves refer to the fused silica (green) and silicon (blue) mirrors. Dashed lines: Substrate contributions; dash-dotted lines: Coating expansion contributions; dotted lines: Thermo-refractive contributions. (b) Phase of the photothermal response and its corresponding fit. Blue curves are traced neglecting some effects, in order to show their relevance: The dashed line corresponds to a response of just homogeneous substrates (calculated from Eq. (2), the dotted line considers just δXs and δXc in Eq. (A51), thus neglecting the thermorefractive effect.

Image of FIG. 3.
FIG. 3.

(Color online) The same as in Fig. 2, at cryogenic temperature.


Generic image for table
Table I.

Substrate parameters used in the fitting procedure. The expressions for the low-temperature thermal capacitance and expansion coefficient of silica are, respectively, (T) = (0.64 + 0.54 T − 0.021T 2)T 3 × 10−3 and (T) = (2.6–5.2 T + 2.9T 2 −0.91T 3 + 0.044T 4) × 10−9. The Poisson factors for Si are averaged over the respective planes.

Generic image for table
Table II.

Coating parameters in the fitting procedures. For αc at low temperature, the first quoted uncertainty reflects the spread in the assumed thermo-optic coefficient of tantala.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Photothermal and thermo-refractive effects in high reflectivity mirrors at room and cryogenic temperature