40m Simulation Results

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)

Results

R_Mft0.9980.9960.9940.9920.990.9880.9860.9840.9820.980.9780.9760.9740.9720.97
T_Mft1.95e-33.95e-35.95e-37.95e-39.95e-31.195e-21.395e-21.595e-21.795e-21.995e-22.195e-22.395e-22.595e-22.795e-22.995e-2
finesse3040.1543.1033.776.621.2517.7443.6388.344.7310.281.6258.237.9220.7205.8
TauS1.235e-46.271e-54.201e-53.158e-52.529e-52.109e-51.808e-51.582e-51.406e-51.265e-51.15e-51.054e-59.726e-69.028e-68.423e-6
fpole644.41269.1894.2520.3147.3774.4402.5030.5659.6289.6919.7550.8182.8814.9447.
PrcCarr004.7359.0513.3617.6821.9826.2830.5734.8739.1543.4347.7151.9756.2460.564.76
ArmCarr004325.4317.4310.4303.4296.4289.4281.4275.4268.4261.4254.4247.4240.4233.4226.
AsymCarr006.941e-91.287e-81.879e-82.47e-83.059e-83.648e-84.235e-84.822e-85.408e-85.992e-86.576e-87.158e-87.74e-88.32e-88.9e-8
AsymCarr3.092e-46.259e-49.421e-41.258e-31.573e-31.888e-32.203e-32.517e-32.83e-33.144e-33.456e-33.768e-34.08e-34.392e-34.703e-3
PrcSB004.4028.65812.6516.8421.0227.8140.676.0238.7845.8357.2174.8853.4257.1460.93
AsymSB000.99470.99530.99440.99310.99180.98970.98560.97440.9860.98340.97980.97420.98110.97980.9786
AsymSB0.99490.99550.99460.99340.99210.98990.98580.97480.98620.98360.98040.97430.98130.980.9789
R_MRec0.78940.88910.92470.94330.95440.96190.96720.97130.97440.97690.9790.98070.98220.98340.9845
1-C1.656e-41.555e-41.524e-41.509e-41.5e-41.494e-41.489e-41.486e-41.484e-41.481e-41.48e-41.478e-41.477e-41.476e-41.475e-4
Lasymm8.847e-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
gamma0.16890.20110.22240.23890.25250.26410.27450.28440.29180.29960.30680.31370.31930.32510.3306
h(f)1.93e-222.689e-223.288e-223.802e-224.262e-224.682e-225.073e-225.441e-225.787e-226.119e-226.439e-226.746e-227.041e-227.329e-227.609e-22

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

Notes

  1. 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.
  2. 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.
  3. 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).
  4. TauS is output of TauArm function in Bochner's Mathematica program.
  5. fpole = 1/(4*Pi*TauS)
  6. gamma is gammaNormSizeNormDensity in Bochner's Mathematica program. He also computes another parameter called gammaNormSizeNormDensityMclean which we did not record.
  7. h(f) is hDCNormSizeNormDensity in Bochner's Mathematica program. He also computes another parameter called hDCNormSizeNormDensityMclean which we did not record.
  8. 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.
  9. 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.