1. Thermal lensing effect: Experimental measurements - Simulation with DarkF & Finesse J. Marque (Measurements analysis: M. Punturo; DarkF simulation: M. Laval) o Scanning Fabry-Perrot direct measurements o Thermal lensing model (DarkF/Finesse) o Thermal lensing effect zone interest (DarkF/Finesse) o Longitudinal control instability zone (DarkF/Finesse) o Sidebands vs alignment (Finesse)
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2. Sidebands measurement (1/2)
Some evidence of thermal drifts when reaching the dark fringe in the RF signals. In particular pick up at the BS demodulated at 2f (“B5_2f”) Need to monitor sidebands amplitude for better understanding (as this signal is said to be proportional to sidebands amplitude).
=> Scanning Fabry Perrot installed on dark fringe beam (video).
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3. Sidebands measurement (2/2)
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4. The DarkF simulation (Laval, Vinet)
DarkF code uses FFT to propagate field into the cavities. Fields and mirror maps are sampled on a grid.
The locking of the cavities is done by changing a phase propagator in the cavities.
To lock the cavity, at each 100 iterations, we calculate the phase shift between Ecavn and Ecavn+1 and we tune the propagator to cancel it.
Finally, we stop the iterations when we estimate the intracavity field has converged.
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5. The Finesse simulation (Freise)
Finesse is a frequency domain interferometer simulation.
The program computes the light field amplitudes at every point in the interferometer assuming a steady state. Finesse can perform analysis using a plane-wave approximation of Hermite-Gauss modes.
Finesse can optionally lock the interferometer by zeroing the same error signals as it is actually done.
Possible analysis: computation of demodulated error signals, beam shapes… Following results have been computed with n+m=8 higher order modes.
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6. Thermal lensing model DarkF/Finesse
Simulations take into account thermal lensing + HR coating face deformation
The equivalent curvature of the thermal lens is 12 to 16 times higher than the one of the HR coating deformation.
Note: in this talk, for all the following plots, the x-axis is the equivalent ROC of the thermal lens, the y-axis is the recycling gain normalized by the recycling gain of the carrier at the first lock.
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7. Thermal lensing effect zone interest (DarkF)
ITF is locked for ROC = 200km. Then no locking loop is applied.
Recycling gains are clearly affected when ROC lower than 100km.
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8. Thermal lensing effect zone interest (Finesse)
Same plot (ITF is locked for ROC = 200 km. Then no locking loop is applied).
And same result: effect starts at 100km.
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9. Locking instability with DarkF
For several values of curvature of the thermal lens, taking into account the map of the mirrors, the interferometer seems to become unstable (~20km; 8km; 5km)
Moreover, with perfect mirrors it is impossible to make converge DarkF for a thermal lens with a curvature radius close to 35km.
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10. Locking instability with Finesse
ITF is locked for ROC = 200 km. Then locking is always active. => locking loops don’t converge for ROC = 30km
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11. Sidebands vs alignment (1/4)
Many experimental evidences that sidebands amplitude is highly dependent on the alignment of the mirrors of the central interferometer: which range?
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12. Sidebands vs alignment (2/4)
End mirrors have no influence on sidebands amplitude within 1 urad. But the differential mode is critical for the gain of the carrier.
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13. Sidebands vs alignment (3/4)
Input mirrors have no influence on the carrier recycling gain within 1 urad. But the sidebands are highly sensitive. Locking loops don’t converge for misalignment higher than 0.7 urad.
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14. Sidebands vs alignment (4/4)
Power recycling mirror has no influence at all on the carrier recycling gain within 1 urad. But the sidebands are highly sensitive. Locking loops don’t converge for misalignment higher than 0.3 urad.
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15. Conclusion
Simulation results summary: o ROC of input mirrors, if lower than 100km (~HR coating power absorbed higher than 1.6 mW), is affecting the results of the simulation in a non negligible way. o Current thermal lensing (according to the simulations) is equivalent to ROC = 20-40km (all results are converging to this zone). o Simulations are not converging for ROC lower than km.
o Sidebands behaviour highly dependent on central ITF mirrors alignment (alignment has to be better than 0.3 urad!?).
Sidebands monitoring/study: what next? Put one more SFP on the beam reflected by ITF. Wavefront scanning system development: phase camera (improve frequency resolution, get spatial information).
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16. Dark fringe image of the carrier as simulated by DarkF
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