1. Stefan Hild, Andreas Freise, Simon Chelkowski University of Birmingham Roland Schilling, Jerome Degallaix AEI Hannover Maddalena Mantovani EGO, Cascina March 2008, GEO-simulation WS Advanced Virgo optical design: Arm cavities with adjustable Finesse

2. Stefan HildGEO Simulation WS, March 2008Slide 2 Overview  Requirements for Advanced Virgo arm cavities: Etalon effect vs wedges.  New concept for advanced GW detectors that combines wedges and etalon effect.  Performance of an ideal etalon  Example of optical system design: Influence of etalon imperfections  Numerical simulations  Analytical approximations  Influence onto alignment signals  Higher-order mode buildup

3. Stefan HildGEO Simulation WS, March 2008Slide 3 Motivation: Input mirror without wedge  Initial Virgo has no wedges in the input mirrors  The etalon effect could be used for adjusting the cavity finesse (compensating for differential losses)  If etalon effect is not controlled it might cause problems

4. Stefan HildGEO Simulation WS, March 2008Slide 4 Motivation: Input mirror featuring a wedge  Used by initial LIGO  Reflected beams from AR coating can be separated from main beam => pick-off beams provide additional ports for generation of control signals.  No etalon effect available.

5. Stefan HildGEO Simulation WS, March 2008Slide 5 What to use for Advanced VIRGO? Etalon or Wedges ??  For AdV possibility to adjust cavity finesse gets more important (higher cavity finesse, DC-readout).  For AdV possibility to create more and better control signals seem desirable. Is there a possibilty to have both for Advanced Virgo ??

6. Stefan HildGEO Simulation WS, March 2008Slide 6 Advanced Virgo: symmetric beam geometry  Increase beam size at mirrors => reduce thermal noise contribution of the test masses.  Move beam waist away from input test mass Is there still an etalon effect in the (flat/curved) input mirror ?

7. Stefan HildGEO Simulation WS, March 2008Slide 7 Etalon effect: flat/flat vs curved/flat  Flat/flat etalon:  Perfect overlap of wavefronts  Curved/flat etalon:  Mismatch of wavefront curvature  Fortunately mirror curvature of a few km is not so far from “flat”.  Simulations show: a reduced etalon effect in curved/flat input mirror is still present

8. Stefan HildGEO Simulation WS, March 2008Slide 8 Etalon effect: flat/flat vs curved/flat  Flat/flat etalon:  Perfect overlap of wavefronts  Curved/flat etalon:  Mismatch of wavefront curvature  Fortunately mirror curvature of a few km are not so far “flat”.  Simulations show: a reduced etalon effect in curved/flat input mirror is still present Still we have to choose: either wegde in input mirror (Pick-off beams available) or no wedge in input mirror (Etalon effect available)

9. Stefan HildGEO Simulation WS, March 2008Slide 9 Overview  Requirements for Advanced Virgo arm cavities: Etalon effect vs wedges.  New concept for advanced GW detectors that combines wedges and etalon effect.  Performance of an ideal etalon  Example of optical system design: Influence of etalon imperfections  Numerical simulations  Analytical approximations  Influence onto alignment signals  Higher order mode buildup

10. Stefan HildGEO Simulation WS, March 2008Slide 10 IDEA: Wedges at input mirrors and etalon effect at end mirrors  Wedge at input mirrors:  Allows for additional pick-off beams  (Concentrate on compensating thermal lensing in input mirror)  Use etalon effect at end test mass  Replace AR-coating by a coating of about 10% reflectivity.  Ideally use a curved back surface (same curvature as front).  End mirror behaves similarly to flat/flat etalon.

11. Stefan HildGEO Simulation WS, March 2008Slide 11 Now let’s have a look at numbers for Advanced Virgo

12. Stefan HildGEO Simulation WS, March 2008Slide 12 Overview  Requirements for Advanced Virgo arm cavities: Etalon effect vs wedges.  New concept for advanced GW detectors that combines wedges and etalon effect.  Performance of an ideal etalon  Example of optical system design: Influence of etalon imperfections  Numerical simulations  Analytical approximations  Influence onto alignment signals  Higher order mode buildup

13. Stefan HildGEO Simulation WS, March 2008Slide 13 Starting with a single AdV arm cavity  Using a single AdV arm cavity (no IFO).  Parameters used:  IM trans = 0.007  IM loss = 50 ppm  EM trans = 50 ppm  EM loss = 50 ppm  AR coatings = 0ppm  IM curvature = 1910m  EM curvature = 1910m  Input = 1W  Figure of merrit = intra cavity power, i.e. loss compensation. Parameters taken from these 2 documents:

14. Stefan HildGEO Simulation WS, March 2008Slide 14 Influence of losses inside the cavity  Imperfection of optics (surface + coatings) might cause different losses in the arm cavities := differential losses.  What are the expected differential losses of AdV ? 5ppm? 50ppm?  A differential loss of 15ppm corresponds to a change of 2W intra cavity power in this example.

15. Stefan HildGEO Simulation WS, March 2008Slide 15 End mirror as curved etalon (optimal solution)  Simulation done with Finesse.  Back surface of end mirror curved (1910m).  AR coating replaced by coating of 10% or 20% reflectivity.  R=0.1 allows adjustment range of 10W (65ppm)  R=0.2 allows adjustment range of 16W (95ppm)

16. Stefan HildGEO Simulation WS, March 2008Slide 16 Optimal solution: curved Etalon  Alternative figures of merrit:  Transmittance of end mirror (etalon)  Finesse of arm cavity

17. Stefan HildGEO Simulation WS, March 2008Slide 17 Etalon changes optical phase  When changing the etalon tuning the optical-phase changes as well. (noise!)  The two etalon surfaces build a compound mirror, whose apparent position depends on the etalon tuning.

18. Stefan HildGEO Simulation WS, March 2008Slide 18 Requirement for temperature stability of etalon substrate  Can calculate require- ment for temperature stability for Advanced Virgo etalon  Using ‘worst case’: 1.22pm/deg  dn/dT = 1.09e-5/K  Substrate thickness = 10cm Example @100Hz: 4e-11K/sqrt(Hz) This requirement is still 2 orders of magnitude above (safer) than temperature stability required from dL/dT of the substrates.

19. Stefan HildGEO Simulation WS, March 2008Slide 19 Everything fine as long Etalon matches the specs… … but what if not ?? => need to check !!

20. Stefan HildGEO Simulation WS, March 2008Slide 20 Overview  Requirements for Advanced Virgo arm cavities: Etalon effect vs wedges.  New concept for advanced GW detectors that combines wedges and etalon effect.  Performance of an ideal etalon  Example of optical system design: Influence of etalon imperfections  Numerical simulations  Analytical approximations  Influence onto alignment signals  Higher order mode buildup

21. Stefan HildGEO Simulation WS, March 2008Slide 21 Optical design: Check system integrity for deviations from specs  A deviation in the reflectivity of the etalon coating:  Only changes tuning range (no problem)  A deviation in the relative misalignment (parallelism) and relative curvature of the two etalon surfaces:  Imperfect wave front overlap…  Reduces tuning range …  Beam shape distortions …

22. Stefan HildGEO Simulation WS, March 2008Slide 22 FFT-simulation of a non- perfect etalon  Using R. Schilling’s WaveProp, (http://www.rzg.mpg.de/~ros/WaveProp/)http://www.rzg.mpg.de/~ros/WaveProp/  Parameters:  Field: 256x256  Computing 3000 roundtrips  End mirror front:  50ppm transmission  R_c = 1910m  End mirror back:  Varying three parameters  Reflectance  Misalignment (parallelism)  Curvature

23. Stefan HildGEO Simulation WS, March 2008Slide 23 Analytic Approximations using Higher-Order Modes  For small misalignments the coupling coefficients k nmnm can be approximated. The amount of light which remains in a TEM 00 mode is given by: (q is the Gaussian beam parameter of the light at the mirror)  Reflection at a (slightly) misaligned component can be characterised by scattering into higher order TEM modes  This model is valid for misalignments below half the diffraction angle (paraxial approximation)  The amplitude in the outgoing fields is given by coupling coefficients k nmnm

24. Stefan HildGEO Simulation WS, March 2008Slide 24 Misalignment of etalon back surface  Strong influence of relative alignment of etalon surfaces.  Question: What accuracy can state of the art manufacturing provide?  Example: Initial Virgo input mirrors (flat/flat) = 1urad

25. Stefan HildGEO Simulation WS, March 2008Slide 25 Curvature deviation of etalon back surface  Curvature mismatch has only moderate influence to tuning range of the etalon.

26. Stefan HildGEO Simulation WS, March 2008Slide 26 !!! KEEP IN MIND !!! For this example…  Numerical simulations and analytical approximation:  Can used to understand optics  Are used to derive specifications  Both do not necessarily represent the reality in all cases  Optimal solution (if feasible):  Test concept in a prototype experiment

27. Stefan HildGEO Simulation WS, March 2008Slide 27 Investigating alignment signals for Advanced Virgo with etalons  Aim: Checking influence of perfect and non- perfect etalon to alignment signals  Performed FINESSE simulation  Investigating Ward and Anderson techniques

28. Stefan HildGEO Simulation WS, March 2008Slide 28 Alignment signals for perfect etalon Signal in transmission: Anderson technique Signal in reflection: Ward technique 150 % variation 10 % variation

29. Stefan HildGEO Simulation WS, March 2008Slide 29 Non perfect etalon: TEM01-buildup in the arm cavity  Misalignment of etalon back surface induces 1st order modes inside the arm cavities.  TEM01 from etalon imperfection is negligible compared to misalignment of the whole end test mass.

30. Stefan HildGEO Simulation WS, March 2008Slide 30 Summary  Advanced Virgo CAN feature wedges in the input mirrors AND use the etalon effect at the end mirrors.  Proposed concept allows us to build ‘arm cavities with adjustable losses’.  A curved/curved etalon would be ideal.  Evaluated and quantified the influence of etalon imperfections using numerical simulations and analytical approximations (tuning range, alignment signals)

31. Stefan HildGEO Simulation WS, March 2008Slide 31 Outlook Potential issues to be investigated:  Need a control system for etalon tuning (error signal + actuator).  Need a value for the expected differential losses in Advanced Virgo in order to choose the reflectivity of the etalon. More details can soon be found in …

32. Stefan HildGEO Simulation WS, March 2008Slide 32 E N D