1. Stefan Hild, Andreas Freise, Simon Chelkowski University of Birmingham Roland Schilling, Jerome Degallaix AEI Hannover Maddalena Mantovani EGO, Cascina April 2008, Virgo R&D Review Update on the Advanced Virgo Arm Cavity Design

2. Stefan HildVIRGO R&D review, April 2008Slide 2 Overview  At January’s Virgo week we presented a new concept for arm cavity design of advanced Virgo (www.sr.bham.ac.uk/~hild/presentations/etalon_vs_wedges.ppt)  The new concept combines advantages of wedges and etalon effect.  What is new since last talk?  Numerical simulations and Analytical approximations  Quantitative evaluation of etalon imperfection  Temperature stability requirement  Influence onto alignment signals  Higher order mode buildup See Maddalenas talks

3. Stefan HildVIRGO R&D review, April 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 HildVIRGO R&D review, April 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 HildVIRGO R&D review, April 2008Slide 5 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.

6. Stefan HildVIRGO R&D review, April 2008Slide 6 What can we gain by using the proposed arm cavity design?  Experience from current detectors: Reflectivities of coatings accurate, but unexplained losses.  We concentrate on the differential losses => Optimal solution: adjusting end mirror transmittance. (Changing the input mirror would also change the amount of directly reflected light)  Several technical noises (such as laser frequency and laser intensity noise) couple proportional to the asymmetry of the arms.  Illustrating example:  30 ppm differential losses  Using the etalon effect it should be possible to reduce the differential losses to 1 ppm  Reduce the noise coupling by a factor of 30 !!

7. Stefan HildVIRGO R&D review, April 2008Slide 7 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 merrits = intra cavity power or loss compensation or cavity finesse or transmittance of EM. Parameters taken from these 2 documents:

8. Stefan HildVIRGO R&D review, April 2008Slide 8 Optimal solution: curved Etalon  Examples of figures of merrit:  Transmittance of end mirror (etalon)  Finesse of arm cavity

9. Stefan HildVIRGO R&D review, April 2008Slide 9 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.

10. Stefan HildVIRGO R&D review, April 2008Slide 10 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.

11. Stefan HildVIRGO R&D review, April 2008Slide 11 Everything fine as long Etalon matches the specs… … but what if not ?? => need to check !!

12. Stefan HildVIRGO R&D review, April 2008Slide 12 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 …

13. Stefan HildVIRGO R&D review, April 2008Slide 13 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/  Cross checking with DarkF.  Parameters:  Field: 256x256  Computing 3000 roundtrips  End mirror front:  50ppm transmission  R_c = 1910m  End mirror back:  Varying three parameters  Reflectance  Misalignment (parallelism)  Curvature

14. Stefan HildVIRGO R&D review, April 2008Slide 14 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

15. Stefan HildVIRGO R&D review, April 2008Slide 15 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

16. Stefan HildVIRGO R&D review, April 2008Slide 16 Curvature deviation of etalon back surface  Curvature mismatch has only moderate influence to tuning range of the etalon.

17. Stefan HildVIRGO R&D review, April 2008Slide 17 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.  Investigations of influence onto alignment signals and higher order mode buildup: See Maddalena’s talk.

18. Stefan HildVIRGO R&D review, April 2008Slide 18 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 …

19. Stefan HildVIRGO R&D review, April 2008Slide 19 E N D

20. Stefan HildVIRGO R&D review, April 2008Slide 20 Common Mode Rejection Factor  Finesse and losses are coupled.  Probably the differential losses will be the driving element. Flaminio et al, VIR-NOT-LAP-1390-313 Finesse assymetryDifferential losses