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) 07/12/2018 EGO

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). 07/12/2018 EGO

Sidebands measurement (2/2) 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

Locking instability with Finesse ITF is locked for ROC = 200 km. Then locking is always active. => locking loops don’t converge for ROC = 30km 07/12/2018 EGO

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? 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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. 07/12/2018 EGO

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 30-20 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). 07/12/2018 EGO

Dark fringe image of the carrier as simulated by DarkF 07/12/2018 EGO