Direct measurement of coating thermal noise in optical resonators

The best measurements of space and time currently possible (e.g., gravitational-wave detectors and optical reference cavities) rely on optical resonators, and are ultimately limited by thermally induced fluctuations in the reflective coatings which form the resonator. We present measurements of coating thermal noise in the audio band and show that for a standard ion-beam sputtered coating, the power spectrum of the noise does not have the expected power-law behavior.

Figure 1

A high-finesse cavity configuration, with a folding mirror (the sample to be measured) equidistant from the input and output mirrors. The inset image shows the TEM20 and TEM02 modes used to make the coating thermal noise measurement. Since these modes overlap only in a small central area, noise in the coating causes changes in the difference between their resonant frequencies, while most other noises sources cancel in this difference.

Figure 2

The experimental setup involves a Nd:YAG laser (far left) and an in-vacuum high-finesse cavity (far right). A laser beam is split into three paths, two of which are shifted in frequency with acousto-optic modulators. The laser frequency is controlled to lock the TEM00 mode to the cavity length with the PDH locking scheme while the TEM02 and TEM20 modes are DC locked to the cavity. Beams 2a and 2b are intensity stabilized by actuating RF power on acousto-optic modulators using intensity stabilization servo (ISS) loops. The primary output of the experiment is the difference between the TEM02 and TEM20 resonant frequencies (labeled BEAT NOTE). Note, beams 1, 2a, 2b are the fundamental TEM00 modes. A conversion of beams 2a, 2b into TEM02 and TEM20 takes place in the cavity.

Figure 3

The noise spectrum measured for three samples. Note that the plotted fit is the sum of CTN and the stationary noise contributions. Nonstationary noise below 30 Hz from environmental vibrations and above 2 kHz from down-converted RF interference, limit the extent of the fit.

Figure 4

The noise budget for Advanced LIGO that incorporates a new measured value of the loss angle and the slope for coating thermal noise. A previous estimate of coating thermal noise (${\varphi }_{{\mathrm{SiO}}_2}=5.0\times {10}^{-4}$, ${\varphi }_{\mathrm{Ti}:\mathrm{Ta}}=2.3\times {10}^{-4}$, slope index $=0.5$) is included in the plot and marked as “CTN-old.”