Assumes perfect mirrors.

See notes following the table.

(In the table "power" = "gain" since laser power = 1.0 nominally in fft.x simulations)

- R_Mft = Intensity reflectivity of interior FP mirrors Mft and Mft
- T_Mft = Intensity transmittivity of interior FP mirrors
- finesse = finesse
- TauS = storage time
- fpole = cavity pole freq.
- ArmCarr00 = Carrier TEM00 power in inline FP cavity
- AsymCarr00 = Carrier TEM00 power at antisymmetric beamsplitter port
- AsymCarr = total carrier power at antisymmetric beamsplitter port
- PrcSB00 = Sideband TEM00 power in power recycling cavity
- AsymSB00 = Sideband TEM00 power at antisymmetric beamsplitter port
- AsymSB = Total Sideband power at antisymmetric beamsplitter port
- R_MRec = Optimum intensity reflectivity of power recycling mirror
- 1-C = contrast defect
- Lasymm = Schnupp asymmetry
- gamma = Optimum modulation depth? (see note 6)
- h(f) = Strain sensitivity at DC? (see note 7)

R_Mft | 0.998 | 0.996 | 0.994 | 0.992 | 0.99 | 0.988 | 0.986 | 0.984 | 0.982 | 0.98 | 0.978 | 0.976 | 0.974 | 0.972 | 0.97 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

T_Mft | 1.95e-3 | 3.95e-3 | 5.95e-3 | 7.95e-3 | 9.95e-3 | 1.195e-2 | 1.395e-2 | 1.595e-2 | 1.795e-2 | 1.995e-2 | 2.195e-2 | 2.395e-2 | 2.595e-2 | 2.795e-2 | 2.995e-2 |

finesse | 3040. | 1543. | 1033. | 776. | 621.2 | 517.7 | 443.6 | 388. | 344.7 | 310. | 281.6 | 258. | 237.9 | 220.7 | 205.8 |

TauS | 1.235e-4 | 6.271e-5 | 4.201e-5 | 3.158e-5 | 2.529e-5 | 2.109e-5 | 1.808e-5 | 1.582e-5 | 1.406e-5 | 1.265e-5 | 1.15e-5 | 1.054e-5 | 9.726e-6 | 9.028e-6 | 8.423e-6 |

fpole | 644.4 | 1269. | 1894. | 2520. | 3147. | 3774. | 4402. | 5030. | 5659. | 6289. | 6919. | 7550. | 8182. | 8814. | 9447. |

PrcCarr00 | 4.735 | 9.05 | 13.36 | 17.68 | 21.98 | 26.28 | 30.57 | 34.87 | 39.15 | 43.43 | 47.71 | 51.97 | 56.24 | 60.5 | 64.76 |

ArmCarr00 | 4325. | 4317. | 4310. | 4303. | 4296. | 4289. | 4281. | 4275. | 4268. | 4261. | 4254. | 4247. | 4240. | 4233. | 4226. |

AsymCarr00 | 6.941e-9 | 1.287e-8 | 1.879e-8 | 2.47e-8 | 3.059e-8 | 3.648e-8 | 4.235e-8 | 4.822e-8 | 5.408e-8 | 5.992e-8 | 6.576e-8 | 7.158e-8 | 7.74e-8 | 8.32e-8 | 8.9e-8 |

AsymCarr | 3.092e-4 | 6.259e-4 | 9.421e-4 | 1.258e-3 | 1.573e-3 | 1.888e-3 | 2.203e-3 | 2.517e-3 | 2.83e-3 | 3.144e-3 | 3.456e-3 | 3.768e-3 | 4.08e-3 | 4.392e-3 | 4.703e-3 |

PrcSB00 | 4.402 | 8.658 | 12.65 | 16.84 | 21.02 | 27.81 | 40.6 | 76.02 | 38.78 | 45.83 | 57.21 | 74.88 | 53.42 | 57.14 | 60.93 |

AsymSB00 | 0.9947 | 0.9953 | 0.9944 | 0.9931 | 0.9918 | 0.9897 | 0.9856 | 0.9744 | 0.986 | 0.9834 | 0.9798 | 0.9742 | 0.9811 | 0.9798 | 0.9786 |

AsymSB | 0.9949 | 0.9955 | 0.9946 | 0.9934 | 0.9921 | 0.9899 | 0.9858 | 0.9748 | 0.9862 | 0.9836 | 0.9804 | 0.9743 | 0.9813 | 0.98 | 0.9789 |

R_MRec | 0.7894 | 0.8891 | 0.9247 | 0.9433 | 0.9544 | 0.9619 | 0.9672 | 0.9713 | 0.9744 | 0.9769 | 0.979 | 0.9807 | 0.9822 | 0.9834 | 0.9845 |

1-C | 1.656e-4 | 1.555e-4 | 1.524e-4 | 1.509e-4 | 1.5e-4 | 1.494e-4 | 1.489e-4 | 1.486e-4 | 1.484e-4 | 1.481e-4 | 1.48e-4 | 1.478e-4 | 1.477e-4 | 1.476e-4 | 1.475e-4 |

Lasymm | 8.847e-2 | -1.785e-2 | -6.179e-2 | -8.943e-2 | -0.1081 | -0.1289 | -0.1526 | -0.1875 | -0.15 | -0.1593 | -0.1746 | -0.1826 | -0.1672 | -0.1705 | -0.1735 |

gamma | 0.1689 | 0.2011 | 0.2224 | 0.2389 | 0.2525 | 0.2641 | 0.2745 | 0.2844 | 0.2918 | 0.2996 | 0.3068 | 0.3137 | 0.3193 | 0.3251 | 0.3306 |

h(f) | 1.93e-22 | 2.689e-22 | 3.288e-22 | 3.802e-22 | 4.262e-22 | 4.682e-22 | 5.073e-22 | 5.441e-22 | 5.787e-22 | 6.119e-22 | 6.439e-22 | 6.746e-22 | 7.041e-22 | 7.329e-22 | 7.609e-22 |

Graph of transmittivity v.s. finesse, TauS, fpole, ArmCarr00, PrcCarr00, h(f).

Notes

- R_Mft is set independently for each simulation. Except for R_Mft = R_Mfr and the initial reflectivity of Mrec all other reflectivities in the ligo.dat file are the same in all simulations: Mbs = .49995, Mtback = Mrback = .999935. Base REF side losses are Mrec = Mft = Mfr = Mtback = Mrback = 5.0e-5 and Mbs = 1.0e-4.
- T_Mft, PrcCarr00 - AsymCarr and R_MRec are taken from the fft.x output files 40m_perf_carr.out. PrcSB00 - AsymSB and Lasym are taken from the fft.x output files 40m_perf_sb.out.
- finesse = Pi*Sqrt[r1*r2]/(1-r1*r2) where r1 = Sqrt[R_Mft] and r2 = Sqrt[.999935] are amplitude reflectivities of mirrors at ends of FP cavity (equation 6.20 pp. 96 in Saulson's book).
- TauS is output of TauArm function in Bochner's Mathematica program.
- fpole = 1/(4*Pi*TauS)
- gamma is gammaNormSizeNormDensity in Bochner's Mathematica program. He also computes another parameter called gammaNormSizeNormDensityMclean which we did not record.
- h(f) is hDCNormSizeNormDensity in Bochner's Mathematica program. He also computes another parameter called hDCNormSizeNormDensityMclean which we did not record.
- Laser power was nominally set at 1.0 watt for all fft.x simulation runs (following Bochner's instructions) and changed to 6.0 watt (the value in 40m_design.ps) for calculating TauS, fp, 1-C, gamma, and h(f) in Bochner's Mathematica post-processing routine.
- FP arm lengths and reflectivity of Mrec were optimized simultaneously in the first (carrier) fft.x run. Laser moculation frequency (not reported here) and Lassym were both optimized in the second (sideband) fft.x run.