Excess Noise and Photoinduced Effects in Highly Reflective Crystalline Mirror Coatings

Thermodynamically induced length fluctuations of high-reflectivity mirror coatings put a fundamental limit on sensitivity and stability of precision optical interferometers like gravitational-wave detectors and ultrastable lasers. The main contribution—Brownian thermal noise—is related to the mechanical loss of the coating material. ${\mathrm{Al}}_{0.92}{\mathrm{Ga}}_{0.08}\mathrm{As}/\mathrm{GaAs}$ crystalline mirror coatings are expected to reduce this limit. The first measurements of cryogenic silicon cavities revealed the existence of additional noise contributions exceeding the expected Brownian thermal noise. We describe a novel, nonthermal, photoinduced effect in birefringence that is most likely related to the recently discovered birefringence noise. Our studies of the dynamics and power dependence are an important step toward uncovering the underlying mechanisms. Averaging the anticorrelated birefringent noise results in a residual noise that is shown to be substantially different from Brownian thermal noise. To this end, we develop a new method for analyzing the coating noise in higher-order transverse-cavity modes, which makes it possible for the first time to determine the contribution of Brownian thermal noise to the total cavity noise. The new noise contributions must be considered carefully in precision interferometry experiments using similar coatings based on semiconductor materials.

Popular Summary

Optical interferometers, such as those used in gravitational wave detectors, are currently the most sensitive measurement devices. Their sensitivity and stability are limited by thermodynamically induced length fluctuations, or Brownian noise, of high-reflectivity mirror coatings. As this fundamental noise is determined by the material’s mechanical loss, optical coatings based on crystalline materials with low mechanical loss have been developed. However, the spectral noise of such coatings has yet to be accurately measured, as this would require measurement devices with an unprecedented level of precision in the zeptometer regime. Here, we carry out the first detailed noise characterization of crystalline coatings at cryogenic temperatures.

In our experiments, we used crystalline coatings in two independent cryogenic silicon optical resonators. We confirmed the expected low Brownian noise from the mechanical loss, but also unexpectedly discovered novel noise mechanisms that are much larger than the Brownian noise limit. These noise sources pose an obstacle to a straightforward improvement of the next generation of cryogenic gravitational wave detectors and ultrastable lasers. The observed spectral and spatial properties of the noise provide an important basis to develop an understanding and subsequent optimization of these semiconductor-based high-reflectivity mirror coatings.

Further investigations on crystalline coatings will be performed over a wider range of temperature and wavelength to help expose the underlying physical mechanisms. With an improved understanding, methods for noise reduction may be developed to finally fulfill the high expectations placed on these coatings for future ultrasensitive interferometers.

Figure 1

Schematic of experiment: two lasers are stabilized to the silicon resonator with crystalline mirror coatings. The lasers can be stabilized to different polarization- and transverse-cavity modes independently. Local and global noise sources are depicted in arbitrary units. The frequency fluctuations are measured by comparing the two lasers against a third laser stabilized to a similar reference cavity with dielectric coatings (Si2) [7].

Figure 2

Single-polarization transient response of the 21-cm cavity to a step change of intracavity power measured in succession. The optical path length changes of the fast (blue) and the slow (orange) axes are symmetric.

Figure 3

Frequency dependence of optical path length changes to intracavity power variations for fast (blue) and slow (orange) axes and for their average (red) at mean intracavity power of 0.54 W in comparison to the theoretical photothermal optic response (green) calculated according to Ref. [47]. The error bars indicate the 95% confidence interval. It includes statistical uncertainty and possible contributions due to slowly varying electronic offsets in the measurement. The latter contribution is estimated by forwarding typical electronic offsets to the slope of PDH error signal. For the red curve, only one representative error bar is shown.

Figure 4

Normalized response of the optical path length $\mathrm{\Delta }d$ (slow axis) to a step $\mathrm{\Delta }P$ in intracavity optical power. Both amplitude and time constant show a strong dependence on the final intracavity power $P_{\text{final}}$.

Figure 5

(a) Optical path length fluctuations of the 21-cm cavity measured with the beat signal between Si2 and the two polarization eigenmodes with intracavity power of 1.3 W in the fast and 0.7 W in the slow axis (blue, orange). The noise from Si2 is below the average of the two polarization eigenmodes (red). (b) Power spectral densities $S_d$ of the length fluctuations in the 21-cm cavity. Birefringent noise (purple), noise of an individual polarization eigenmode (orange), and average of two polarizations (red). The sum of technical noise contribution and the predicted Brownian thermal noise for the Hermite-Gaussian ${\mathrm{HG}}_{00}$ mode (green) is included for comparison. (c),(d) Power spectral densities $S_d$ of the length fluctuations in the 6-cm cavity at 16 (c) and 4 K (d). Frequency stability of individual polarization eigenmodes (orange) of the average of two polarization eigenmodes (red) and the predicted Brownian thermal noise (green). The contribution of reference lasers is removed from the PSDs (see Appendix pp1).

Figure 6

(a) Measured optical path length fluctuations of polarization-averaged the ${\mathrm{HG}}_{00}$ (blue) and ${\mathrm{HG}}_{01}$ modes (orange) referenced to another cavity (Si2), and the difference between the two HG modes (red). For clarity, the curves are shifted by an arbitrary amount. (b) Spectral power densities of the individual displacement noise of the ${\mathrm{HG}}_{00}$ (blue) and ${\mathrm{HG}}_{01}$ modes (orange) determined by three-cornered-hat (TCH) method, and of their difference (red). The estimated differential Brownian noise between the two modes is shown in green.

Figure 7

Thermal noise contributions in the Si5 resonator. Br, Brownian thermal noise; TE, thermoelastic noise; TO, thermo-optic noise.

Figure 8

Technical noise contributions for Si5 in comparison to the Brownian noise of the $\mathrm{AlGaAs}/\mathrm{GaAs}$ coating with ${\varphi }_{124\mathrm{K}}=2.5\times {10}^{-5}$.

Figure 9

Obtained by the three-cornered-hat analysis: PSD of fractional frequency noise of Si5 (blue), Si2 (yellow), and the 48-cm ULE cavity (gray). The expected thermal noise of Si5 (green) is included for reference.

Figure 10

Top: experimental setup of the locking scheme. The additional EOM1 and its driver LO1 required for dual-frequency locking are shown in the red box. EDFL, erbium-doped fiber laser; ISO, optical isolator; EOM, electro-optic modulator; (P)BS, (polarization) beam splitter; FR, Faraday rotator; HWP, half wave plate; PD, photodetector; LP, loop filter; LO, local oscillator. Bottom: frequency components of the light (green), and the cavity resonances of fast (purple) and slow (red) axes in units of the free spectral range $\mathrm{\Delta }{\nu }_{\mathrm{FSR}}$.

Figure 11

PSD of dual-frequency locking (blue) compared to that achieved by averaging with two independent laser setups. The PSD of the difference between two lasers stabilized to adjacent ${\mathrm{HG}}_{00}$ modes with dual-frequency locking indicates the quality of this technique. Both methods suppress the birefringent noise by at least a factor of 10.

Figure 12

Correlation coefficient of birefringent noise between the ${\mathrm{HG}}_{00}$ and ${\mathrm{HG}}_{01}$ modes (red). It agrees well with the expectation value for local noise (green) and is significantly different from the expectation value for global noise (yellow).

Figure 13

Small-signal transfer function measured with different modulation amplitude (slow axis) at 0.62 and $1.72\mathrm{\mu }\mathrm{W}$ mean transmitted power in the fast and slow axes, respectively. The error bars indicate the 95% confidence interval, with contributions from slowly varying electronic offsets, which is estimated by forwarding typical electronic offsets to the slope of PDH error signal.

Figure 14

Small-signal transfer function from optical power modulation in transmission $\mathrm{\Delta }P$ to optical path length changes $\mathrm{\Delta }d$ for different averaged transmitted power $P_{\text{trans}}$. The error bars have the same meaning as those described in Fig. 13.