Thermally Deformable Mirrors: a new Adaptive Optics scheme for Advanced Gravitational Wave Interferometers Marie Kasprzack Laboratoire de l’Accélérateur Linéaire European Gravitational Observatory

Adaptive optics: Motivation Advanced Virgo: Dual recycling interferometer Increase the sensitivity by a factor 10 with respect to Virgo Gain of factor 1000 in event rate Many improvements, in particular increase of laser power: 125 W at the interferometer input March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Adaptive optics: motivation High laser power brings thermal effects Optical path difference (OPD) Consequences: The wavefront of the beam is modified If the substrate is not perfectly homogeneous, the thermal lens will not be symmetric This leads to apparition of aberrations of high spatial frequencies After propagation, the beam will not be Gaussian any more Opto-mechanical parameters Temperature field Refraction index Thermo-optic coefficient Poisson coefficient Thermal expansion coefficient March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Matching sensitive systems Injection: Need of 99% Matching into the ITF Thermal effects : potentially 10% of mismatch Potential source of noise, power losses All effects unlikely predictable and potentially time varying Need of adaptive optics to reach the design sensitivity Interferometer Pre-stabilized laser March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Requirements for the corrective device High order mode correction: Matching control from 90-95% to better than 99% Environment high power laser: about 200 W high vacuum compatible: 10-6 mbar not be a source of noise (electronic, magnetic, mechanical...) Optics surface roughness: lower than 0.1 nm flatness: better than l /20 Actuation possible at long time scales: min. 10 mHz Need of a new corrective device with thermal actuation and high degree of actuation March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Thermally deformable mirror (TDM) TDM Actuation Control of the optical path length via the substrate temperature Opto-mechanical parameters Temperature field March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Prototype Features Prototype Resistor number 61 Board PCB Resistor type SMD Size (mm2) 2 resistors 0.5x1 = 1x1 Gap (mm) ~ 0.2 R Dispersion < 5% Substrate Fused Silica Animation avec l’image thermique? March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Experimental Characterization Direct observation of wavefront modification with a wavefront sensor pupil actuator nm March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Actuator properties Features Prototype Power absorbed by the substrate (% of dissipated power ) ~ 16 % Stroke of one actuator ~ 200 nm Linearity: Amplitude of response proportional to the dissipated power Time response: a few seconds Experimental data Linear fit Noise level March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Zernike generation Zernike polynomials basis: for description of aberrations in an optical system How well can the TDM reproduce them? Closed-loop control : Least square algorithm with boundaries optimization of the dynamic range nm nm nm Sensing Noise level March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Zernike Generation Order 2 & 3 Order 4 Order 5 March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Wavefront correction Characterization: Efficiency: evaluation of the dynamic range Accuracy: evaluation of the inter-mode coupling nm nm nm March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Wavefront correction Efficiency: Highly limited above the 4th order Accuracy: Limited coupling observed for the 5 orders 3rd order 4th order 5th order March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Wavefront correction Efficiency: Highly limited above the 4th order Accuracy: Limited coupling observed for the 5 orders 3rd order 4th order 5th order March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Wavefront correction Results: the TDM is able to correct phase aberrations Ability to reproduce the Zernike polynomials Very good accuracy and efficiency up to the 3rd order with 80 nm RMS up to the 4th order with 30 nm RMS But ideally the dynamic range must be at least 50 nm RMS for all How to control the matching into a resonant cavity? HG02 HG11 HG20 HG12 HG21 HG30 HG03 HG01 HG10 HG00 March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Suppresion of a High order mode (HOM) TDMs only act on the phase Small correction of the beam phase in two planes we want this term = 0 March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Suppresion of a HOM Analytical computation of the amplitude real coefficients b1 and b2 To perform the correction of the mn HOM mode we need: 2 corrective patterns with Hmn polynomial shapes 2 corrective devices separated by z2 – z1 With the Gouy phase for the m+n order March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Mode Matching Setup Setup with a triangular cavity Laser frequency locked on the cavity One TDM for creation of aberrations Gouy phase difference ~20 deg Mode Cleaner Cavity F = 50 FSR = 2 GHz March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors SETUP In The calva ROOM TDM0 TDM1 TDM2 reflection transmission Cavity March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Mode Matching Setup Actuation maps: projection of the Hermite-Gauss onto the TDM basis HG02 HG11 HG20 HG12 HG21 HG30 HG03 HG13 HG22 HG31 HG04 March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Mode Matching Setup Correction of the mode HG11: mode reduced by a factor 3 coupling to other modes: defocus, tilt and mode 30 Mode 11 Mode 30 focus tilt March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Mode Matching Setup Correction of the mode HG30: mode reduced by a factor 1.9 increase of defocus and tilt Mode 30 focus tilt March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Prospects The setup is limited by the coupling to the tilt and focus Necessary next steps: Implementing an automatic alignement system to: Determine the limits of the setup by systematic tests: Determine the limits of correction for each mode Perform simultaneous correction of several modes Compare with simulations Improving the sensing to keep the cavity locked: Direct estimation of the HOM content via cameras Reduction of the convergence time March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors

Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors Conclusion The TDM is an innovative device with many advantages: Thermal actuation High optical quality High order mode correction Further steps are necessary before installation in Advanced Virgo: End the matching characterization Make a vacuum compatible prototype Check the performance under vacuum Check the noise compatibility March 26, 2015 Moriond 2015 - Marie Kasprzack - Thermally Deformable Mirrors