Multimaterial coatings with reduced thermal noise

The most sensitive measurements of time and space are made with resonant optical cavities, and these measurements are limited by coating thermal noise. The mechanical and optical performance requirements placed on coating materials, especially for interferometric gravitational wave detectors, have proven extremely difficult to meet despite a lengthy search. In this paper we propose a new approach to high performance coatings, the use of multiple materials at different depths in the coating. To support this we generalize previous work on thermal noise in two-material coatings to an arbitrary multimaterial stack, and develop a means of estimating absorption in these multimaterial coatings. This new approach will allow for a broadening of the search for high performance coating materials.

Figure 1

The numbering of coating layers, interfaces and fields is shown above. The z-coordinate is zero at the coating surface, and is positive moving away from the coating. Note that the E-fields are evaluated just inside each coating layer (e.g., $E_1$ is evaluated at $z=-\epsilon$ in the limit of $\epsilon \to 0$).

Figure 2

The contribution of coating layers to the total coating absorption varies with depth in the coating. Deeper layers make a smaller contribution, as seen by the rapidly decreasing value of ${\overline{\rho }}_j$ with increasing $j$. The two ingredients of $\overline{\rho }$, absorption of each layer relative to the power arriving at that layer, ${\rho }_j$, and power attenuation as a function of depth $P_j/P_0$, are also shown [see Eqs. (14)–(16)]. The coating used to generate this figure consists of 10 ${\mathrm{SiO}}_2\text{−}{\mathrm{Ta}}_2{\mathrm{O}}_5$ quarter-wave doublets.

Figure 3

The contribution of coating layers to Brownian noise increases with depth in the coating. This figure shows the coating phase sensitivity to fluctuations in each layer, $\partial {\varphi }_c/\partial {\varphi }_j$, and the weight of each layer in the total Brownian noise, $b_j$ [see Eqs. (1) and (9)].

Figure 4

Brownian thermal noise dominates in this example coating, in part thanks to the cancellation of the thermo-elastic (TE) and thermo-refractive (TR) components of thermo-optic noise. The noise level of $4.6\times {10}^{-21}\mathrm{m}/\sqrt{\mathrm{Hz}}$ at 100 Hz is a useful benchmark for the impact of coating thermal noise on gravitational wave detectors. The coating used to generate this figure consists of 10 ${\mathrm{SiO}}_2\text{−}{\mathrm{Ta}}_2{\mathrm{O}}_5$ quarter-wave doublets.