Coating-free mirrors for high precision interferometric experiments

Thermal noise in mirror optical coatings may not only limit the sensitivity of future gravitational-wave detectors in their most sensitive frequency band but is also a major impediment for experiments that aim to reach the standard quantum limit or cool mechanical systems to their quantum ground state. We present the design and experimental characterization of a highly reflecting mirror without any optical coating. This coating-free mirror is based on total internal reflection and Brewster-angle coupling. In order to characterize its performance, the coating-free mirror was incorporated into a triangular ring cavity together with a high quality conventional mirror. The finesse of this cavity was measured using an amplitude transfer function to be about $\mathcal{F}\simeq 4000$. This finesse corresponds to a reflectivity of the coating-free mirror of about $R\simeq 99.89\%$. In addition, the dependence of the reflectivity on rotation was mapped out.

Figure 1

(Color online) Left: Sketch of the CFM with all dimensions. Right: Photograph of a coating-free mirror alongside an Australian five cent coin.

Figure 2

(Color online) Setup to characterize the CFM reflectivity (not to scale).

Figure 3

(Color online) Measured frequency (top graph) and phase (bottom graph) response of the cavity for the optimum rotational alignment angle of the CFM. The solid line represents the measured data while the dashed line is the result of a least-squares fit used to determine the reflectivity of the CFM. The $-3\text{dB}$ point, corresponding to half the cavity linewidth (HWHM), of the frequency response is marked along with the equivalent 45° phase point.

Figure 4

(Color online) Reflectivity of the CFM versus its rotational alignment angle. The error bars arise from the relative calibration of the power meter used. Error bars in the rotational angle are too small to be displayed. The solid line represents the calculated change of reflectivity of the CFM due to deviation from the Brewster angle of the in- and outcoupled beams. The calculated curve is normalized in such a way that its maximum coincides with the maximum reflectivity of the CFM as experimentally obtained.

Figure 5

(Color online) Power reflected from the front face of the CFM (the beam hitting the power meter in Fig. 2) as a function of rotational alignment. The solid line is derived under the assumption that no cavity mismatch occurs, and changes in intracavity power are caused only by deviations of the beams from the Brewster angle at the CFM front face. Thus, the difference between this curve and the experimental values corresponds to the power lost from the ${\text{TEM}}_{00}$ mode.