1. Some features of NV.
Vincent Loriette

2. NV main objectives
Evaluate the effect of imperfections on the shot-noise limited sensitivity.
Fix some tolerances.
Find free parameters optimal values (modulation depth, démodulation phase, etc.)

3. NV main features All optical parameters can be varied.
Free mirror shapes.
Free orientation and shape of the incident beam.
Free modulation amplitude and frequency. …
Fields are represented as finite sums of HG functions (no FFT).
Fast code.
No diffraction in free space.
Not suited to work with exotic beam shapes.
Optimization steps use realistic error signals.
Realistic resonnance and antiresonnance seeks.
Not necessarilly optimal (in the math sense).

4. Computation example : north arm refectance
ORFP_n=ORni_o+OTni_i*inv(OId-exp(-i*phi_n)*OFPn)*(OPna*ORne_i*OPna*exp(-i*phi_n))*OTni_o;
Edges diffraction
Mode réfléchi
Airy peak,…
Mode incident
Roughness indiced mode coupling

5. Effects of heating
North arm reflectance without… and with thermal effects (stable)

6. Various optimizations can be performed
NV main window
Various optimizations can be performed
Each optical parameter can be associated with an experimental measurement datafile

7. Result window : north arm example

8. Result windows : beam example

9. Output beam shape (before OMC)

10. Sensitivity & modulation

11. Typical results Scalar defects Maps Maps+thermal Opt mod index 0.068
0.172±0.001
0.215 ±0.001
Opt demod phase
2 ±0
17 ±1
Finesse N
49.26
49.1 ±0.2
49.3 ±0.2
Finesse W
49.79
49.6 ±0.2
49.7 ±0.2
dF/F [%]
0.27
0.23 ±0.12
0.24 ±0.12
Asymmetry [%]
1.05
1.00 ±0.3
2.78 ±0.5
Stored power N [kW]
15.38
10.82 ±0
11.15 ±0
Lost power N [W]
0.23
4.11 ±1
3.70 ±1
Surtension N
31.37
31.18 ±0.02
31.15 ±0.02
Stored power W [kW]
15.55
10.91 ±0
11.27 ±0.3
Lost power W [W]
0.19
6.05 ±0.02
5.85 ±0.04
Surtension W
31.70
31.42 ±0.01
31.48 ±0.1
Carrier power on BS [W]
978.5
684.5 ±0.5
725.1 ±2
Sideband power on BS [W]
1.70
8.56 ±0.1
10.9 ±0.2
Reflected carrier [W]
17.84
8.42 ±0.01
9.82 ±0.08
Reflected sb [W]
0.027
0.24 ±0
0.26 ±0.01
CITF surtension Carrier
49.04
34.74 ±0.03
37.10 ±0.08
CITF surtension SB
36.49
29.01 ±0.02
24.0 ±0.1
Transmitted (detected) carrier [mW]
0.064 (0.064)
359 ±6 (1.6 ±0)
324 ±40 (3.5 ±0.1)
Transmitted (detected) sb [mW]
18.7 (17.9)
93.0 ±0.8 (70.0 ±1)
125 ±2 (100 ±2)
Sensitivity [*1E-23]
2.48
2.87 ±0.01
2.96 ±0.02