1. Jean-Yves Vinet CNRS-ARTEMIS Observatoire de la Côte d’Azur Effects In cavity mirrors

2. Recall Flat beam of radius 11.3 cm  ~3.3 gain factor J-Y. Vinet Classical and Quantum Gravity 22 (2005) P.1395 LG55 beam, w=3.5 cm  ~5 gain factor B. Mours, E. Tournefier, J-Y. Vinet Classical and Quantum Gravity (2006) p.5777-5784 Thermal noise @ 100Hz for Exotic optical modes What about temperature effects ??

3. Incoming Power flow coating substrate thermalization ~16 kW 1ppm = 16 mW Non homogeneous temperature: -Index gradients -Distortions mirror Coating absorption Heat flow

4. Bulk absorption Passing Power flow ~ 500 W 1ppm/cm = 5 mW Heat flow mirror

5. Three examples of optical modes TEM00 w=2cm (Virgo/inputM) « Flat top » b=11.3 cm LG55 w=3.5 cm Axial symmetry: easy analytical calculations

6. Temperature field in the substrate (coating absorption) TEM00 w=2 cm (Virgo/inputM) « Flat top » b=11.3 cm LG55 w=3.5 cm T(r,z)

7. TEM00 w=2 cm (Virgo/inputM) « Flat top » b=11.3 cm LG55 w=3.5 cm Temperature field in the substrate (bulk absorption) T(r,z)

8. Profiles of thermal lenses (coating or bulk absorption) TEM00 w=2 cm Flat b=11.3 cm LG55 w=3.5 cm Curvature radii: R= 328 m.W R=17 165 m.W R=27 396 m.W A factor of ~100 in thermal focal length

9. Temperature field Due to coating absorption  dilatation of substrate *Distortion of the reflecting face *Extra optical path

10. Temperature field Due to internal absorption  dilatation of substrate

11. 1) Extra optical path : renormalization of the temperature index Linear dilatation coefficient Poisson ratio Refractive index n ~1.46 Correction ~ 3%

12. TEM00 w=2 cm Flat b=11.3 cm LG55 w=3.5 cm 2) Thermal aberration (heating by coating) (=coating displacement) Curvature radii: R= 5 842 m.W R=295 114 m.W R=477 565 m.W A factor of ~100 in focal length

13. 2) Thermal aberration (internal heating) (=coating displacement) R= 21 982 m.W R=573 749 m.W R=937 379 m.W Curvature radii: A factor of ~40 in focal length

14. Example of a non axisymmetrical mode LG55 w=3.5 cm Is axial symmetry essential ? Analytical calculation still possible!

15. Temperature field (heating from coating absorption) coating 1 cm depth 2 cm depth Back (10 cm)

16. Temperature field (heating from bulk absorption) Meridian plane 3 cm depth 2 cm depthface

17. Thermal lensing ex : heating by coating absorption axisym Non axisym  very weak difference

18. Calculation of thermal noise is much more difficult for Non axisymmetical beams. But we can guess that the numerical results are weakly different from axisymmetrical results Consequence (conjecture) LG55 axisym/nonaxisym, or HG55 as well are good candidates Final remark

19. Splitter recycler North West Dark fringe

20. Heat source On the coating TEM00 w=2 cm Splitter 45° incidence angle  elliptical spot

21. Temperature On the reflective coating Temperature on the antireflective coating  Very weak asymmetry

22. Face avantFace arrière Longitudinale  z

23. Temperature field x y x z Optical path:  -a a -h/2h/2

24. Thermal lens Numerical integration

25. Thermal lensing After splitter (Heat source on The coating) TEM00 w=2 cm x