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Advanced Virgo optical design: Arm cavities with adjustable Finesse

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

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Advanced Virgo optical design: Arm cavities with adjustable Finesse

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

  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 GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

  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. GEO Simulation WS, March 2008

  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 ?? Fortunately: YES ! GEO Simulation WS, March 2008

  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 ? GEO Simulation WS, March 2008

  7. Curved/flat etalon: • Mismatch of wavefront curvature Etalon effect:flat/flat vs curved/flat • Flat/flat etalon: • Perfect overlap of wavefronts • 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 GEO Simulation WS, March 2008

  8. Etalon effect:flat/flat vs curved/flat • Flat/flat etalon: • Perfect overlap of wavefronts Still we have to choose: either wegde in input mirror (Pick-off beams available) or no wedge in input mirror (Etalon effect available) • 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 GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

  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. GEO Simulation WS, March 2008

  11. Now let’s have a lookat numbers for Advanced Virgo GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

  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: GEO Simulation WS, March 2008

  14. 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. Influence of losses inside the cavity • Imperfection of optics (surface + coatings) might cause different losses in the arm cavities := differential losses. GEO Simulation WS, March 2008

  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) GEO Simulation WS, March 2008

  16. Optimal solution: curved Etalon • Alternative figures of merrit: • Transmittance of end mirror (etalon) • Finesse of arm cavity GEO Simulation WS, March 2008

  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. GEO Simulation WS, March 2008

  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. GEO Simulation WS, March 2008

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

  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 GEO Simulation WS, March 2008

  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 … GEO Simulation WS, March 2008

  22. FFT-simulation of a non-perfect etalon • Using R. Schilling’s 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 GEO Simulation WS, March 2008

  23. Analytic Approximations using Higher-Order Modes • 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 knmnm • For small misalignments the coupling coefficients knmnm can be approximated. The amount of light which remains in a TEM00 mode is given by: (q is the Gaussian beam parameter of the light at the mirror) GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

  25. Curvature deviation of etalon back surface • Curvature mismatch has only moderate influence to tuning range of the etalon. GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

  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 GEO Simulation WS, March 2008

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

  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. GEO Simulation WS, March 2008

  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) GEO Simulation WS, March 2008

  31. More details can soon be found in … 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. GEO Simulation WS, March 2008

  32. E N D GEO Simulation WS, March 2008

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