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Investigating Thermal Lensing Effect in Optical Interferometers: Measurements and Simulations

Explore experimental measurements and simulations using DarkF and Finesse software to analyze thermal lensing impact on interferometer performance. Understand the effects on sidebands, control instability, and cavity locking. Discover ways to improve alignment and monitoring for better results.

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Investigating Thermal Lensing Effect in Optical Interferometers: Measurements and Simulations

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  1. Thermal lensing effect:Experimental measurements -Simulation with DarkF & FinesseJ. Marque(Measurements analysis: M. Punturo; DarkF simulation: M. Laval)o Scanning Fabry-Perrot direct measurementso 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) EGO

  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). EGO

  3. Sidebands measurement (2/2) EGO

  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. EGO

  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. EGO

  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. EGO

  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. EGO

  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. EGO

  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. EGO

  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 EGO

  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? EGO

  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. EGO

  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. EGO

  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. EGO

  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 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). EGO

  16. Dark fringe image of the carrier as simulated by DarkF EGO

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