====== Thermal noise limit ======

===== Parameters needed for thermal noise calculation =====
**Literature**:
  * [1] J. Opt. Soc. Am. B pp 914, Vol. 27, No. 5/May 2010
  * [2] NATURE PHOTONICS Vol.7, 644 (2013)
  * [3] Optics Letters, Vol. 40, Iss. 9, p. 2112 (2015).


^ Description                                               ^ Material      ^ Parameter name  ^ Value                                               ^  Comment                         |   |
| Boltzmann constant                                        |               | kb              | 1.38064852 × 10-23 m2 kg s-2 K-1                    |                                  |   |
| Temperature (K)                                           |               | T               | 300                                                 |                                  |   |
| Poisson Ratio of substrate                                | Fused Silica  | σ<sub>sb</sub>  | 0.16                                                | Fused Silica substrtae [1]       |   |
| Poisson Ratio of coating                                  | AlGaAs        | σ<sub>c</sub>   | 0.32                                                | AlGaAs coating [2]               |   |
| Young's modulus of substrate                              | Fused Silica  | E<sub>sb</sub>  | 72.7 Gpa                                            | Fused Silica substrtae [1]       |   |
| Young's modulus of spacer                                 | ULE           | E<sub>sp</sub>  | 67.6 Gpa                                            | ULE Spacer [1]                   |   |
| Young's modulus of coating                                | AlGaAs        | E<sub>c</sub>   | 100 Gpa                                             | AlGaAs coating [2]               |   |
| Length of cavity                                          |               | L               | 0.48 m                                              | Sr Beast [3]                     |   |
| Spacer radius                                             |               | R<sub>sp</sub>  | 0.045 m                                             | Sr Beast [3]                     |   |
| Central bore radius of spacer                             |               | r<sub>sp</sub>  | 0.0065 m                                            | Sebastian Häfner Thesis page 83  |   |
| Thickness of coating                                      | AlGaAs        | D               | 6.83*10<sup>-6</sup> m                              | AlGaAs coating [2]               |   |
| 1/e<sup>2</sup> mode radius on the mirror                 |               | w               | 0.000488 m for Mirror 1 \\ 0.000677 m for Mirror 2  | Mode calculations                |   |
| Effective coefficient of thermal expansion for substrate  |               | α<sub>sb</sub>  | 1.2* 10-6 K-1                                       | Fused Silica substrtae [2]       |   |
| Effective coefficient of thermal expansion for coating    |               | α<sub>c</sub>   | 1.68* 10-5 K-1                                      | AlGaAs coating [2]               |   |
| Effective thermorefractive coefficient for coating        |               | β<sub>c</sub>   | 5*10-5                                              | AlGaAs coating [2]               |   |
| Thermal conductivity for substrate                        |               | κ<sub>sb</sub>  | 1.38 W/Km                                           | Fused Silica substrate [2]       |   |
| Thermal conductivity for coating                          |               | κ<sub>c</sub>   | 62.9 W/Km                                           | AlGaAs coating [2]               |   |
| Heat capacity per unit volume for substrate               |               | C<sub>sb</sub>  | 1.71*106 J/Km3                                      | Fused Silica substrate [2]       |   |
| Heat capacity per unit volume for coating                 |               | C<sub>c</sub>   | 1.64*106 J/Km3                                      | AlGaAs coating [2]               |   |
|                                                           |               |                 |                                                     |                                  |   |
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