1. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 281 Generation of flat-top beam in a “Mexican hat” Fabry-Perot cavity prototype for advanced GW detectors Marco G. Tarallo 1 (Universita` di Pisa – INFN Pisa) In collaboration with J.Agresti 1, E.D’Ambrosio 1, R. DeSalvo 1, D.Forest 2, B.Lagrange 2, J.M.Mackowsky 2, C. Michel 2, J.Miller 1, J.L. Montorio 2, N.Morgado 2, L.Pinard 2, A.Remilleux 2, B.Simoni 1, P.Willems 1 1 LIGO Laboratory, Caltech 2 LMA Laboratory/EGO

2. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 282 Mesa beam for advanced GWID Advanced GWIDs aim: sensitivity beyond the SQL Test mass TN will be the fundamental limit in the frequency band with highest sensitivity Gaussian beams sample a relatively small fraction of the mirror surface  widening and flattening the light probe will depress TN Mirror surface fluctuations Fused Silica TM

3. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 283 It is possible to have a nearly optimal flat top beam reshaping the FP arm cavity mirrors The “Mesa beam” is a multi-gaussian laser field designed as superposition of minimal Gaussians with w 0 =  (L/k) The obtained wavefront phase gives the “Mexican hat” profile to the phase graded mirror Mesa beam for advanced GWID Profiles normalized for Same Integrated power  EM field second momentum almost x2 larger Slow exponential fall Steeper fall Mesa beam/MH FP Gaussian beam/Spherical FP

4. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 284 Thermal Noise Prospects [ref. Agresti LIGO-G050310-00-R] Gaussian beam TN Mesa beam TN Sensitivity Gain: x 1.7 (f=100 Hz) Theoretical investigations: thermal noise reduction NS-NS inspiral Reach 193 Mpc 251 Mpc x 1.3 Detection Event Rate x 2.2 !! Mesa beam noise reduction is an additional factor to any other mirror development (optimized coatings, cryogeny, ecc.)

5. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 285 Mesa beam cavity prototype Experimental work before a direct application to a GWID : - Starting the design of a prototype to generate flat “Mesa” beams (summer 2003, Willems, D’Ambrosio, DeSalvo) - Design and construction of a suspended rigid FP cavity at Caltech (autumn 2003 – summer 2004, Simoni, DeSalvo et al.) - Manufacturing first test Mexican hat (MH) mirrors (2004-2005, LMA laboratory) - Full prototype experimental set up (autumn 2004 – spring 2005, Tarallo, Willems, Agresti, DeSalvo) - Testing MH mirrors and achieving the first flat Mesa beam (summer 2005, Miller, Tarallo, Willems et al. )

6. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 286 Mesa beam cavity prototype l Necessity to verify the behavior of the mesa beam and study its generation and control before its possible application to GW interferometers l We built a rigid, folded, suspended, 7.32m long FP cavity supporting a MH mirror to investigate the modes structure and characterize the sensitivity to perturbations mirrors imperfections misalignments INVAR rod MH mirror Flat input mirror Flat folding mirror Vacuum pipe Thermal shield Spacer plate 2x 3.5 m

7. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 287 Input/output optics bench: Nd:YAG Mephisto laser Mode match telescope Fast photodiode for transmitted power readout CCD camera to control the locked TEM Suspended FP cavity, F ~ 100 Profile readout bench (CCD camera, high resolution) Feedback control electronics & cavity mirrors DC driving Mesa beam cavity experimental setup CCD camera

8. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 288 “Mexican hat” mirrors We can characterize how mirrors imperfections affects the beam in such a interferometer l LMA laboratories provided three mirror samples l C05004 (test run): - Thin substrate (20 mm) - large offset on the central bump l C05008 & C05009: - Thick substrate (30 mm) - Both affected with a not negligible slope on the central bump Mexican hat C05008

9. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 289 FFT simulations Using paraxial approximation, FFT codes can simulate the propagation of actual TEM patterns on optical cavities A Mathematica FFT routine has been dedicated to simulate our cavity beam behavior: it gave us the best tool to choose the best MH: C05008 First implementation of MH C05008 map FFT EM field on a ideal MH mirror

10. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2810 The slope on the central bump can be corrected applying the right mirror tilt FFT simulations  5 nm error central area

11. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2811 MH Cavity Alignment Spherical optics: tilt is translated in a change of the optical axis MH mirrors: only cylindrical symmetry -> resonant beam phase front change with the alignment Folded cavity: no preferential plane for mirrors alignment -> very difficult align within  rad precision

12. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2812 First Experimental Results Experimental setup (electronics, beam acquisition, locking…) tested with 8m r.o.c. spherical end mirror MH installation: no stable Mesa beam profile was acquired at the beginning Higher order modes were found very easily, good agreement with numerical prediction! ‘TEM10’‘TEM11’ ‘TEM20’

13. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2813 ‘TEM10’ 1D profile fit: Fit function: Mesa ‘TEM10’ Rsq = 0.990 Fit function : Laguerre-Gauss TEM10 Rsq = 0.929 First Experimental Results

14. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2814 TEM00 tilt simulation TEM00 data First Experimental Results Misalignments and mismatching effects has been modeled to recognize “strange” resonant modes

15. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2815 Strange evidence: every time we tried to align the cavity, mode shapes became worse and worse (as with spherical end mirror) Central part of the cavity seems “unstable”: maybe the problem is not the MH but the other two mirrors Systematics and following steps Mechanical clamping, PZTs and screws stress ~ 60 nm deformation -> three times the height of the MH central bump - We changed mirrors mounts reinforcing flexible mirrors with aluminum rings

16. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2816 First Mesa beam observations We were able to stably lock on the Mesa ‘TEM 00 ’ Best Mesa beam CCD Density plot The result is consistent with the best achievable using our current prototype MH mirror

17. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2817 First Mesa beam observations Comparison with FFT results: - Jagged top due to MH bump imperfections both in FFT and in experimental profiles - Deviation from the ideal Mesa field, almost the same - Still same asymmetry due to flat mirrors imperfections - The beam has the expected size within the experimental uncertainty Input and folding mirrors are the second main limitation

18. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2818 MH cavity characterization Remarkable agreement between numerical eigenvalues and experimental spectrum Cavity finesse and coupling are unavoidable depressed by flat mirror deviations (F exp  68 instead of 100)

19. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2819 Tilt sensitivity 2  rad simulated 3.85  rad experiment 2.57  rad experiment A preliminary quantification of beam sensitivity to mirror tilts was carried on Simulations and experimental data shows the same trend but a factor 1.5 of disagreement (TBI)

20. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2820 Conclusions and Future We are able to produce acceptable flat-topped beams with imperfect optics Alignment more taxing than with spherical mirrors MH “profile deposition” technique is actable, but better for larger mirror radius Next steps: Study MH FP coupled with recycling cavities AdLIGO and future high power detectors: nearly-concentric configuration (MHC )  A new 120m interferometer prototype (EGO?)

21. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2821 Thermal noise reduction using Mesa Beam (evaluation for Advanced LIGO mirrors) Advanced LIGO Evaluation conditions: The beam radius is dynamically adjusted to maintain a fixed diffraction loss = 1ppm The mirror thickness is also dynamically adjusted as a function of the mirror radius to maintain a fixed 40 Kg mirror mass. Gaussian beamMesa beam mirror Beam rad. (cm) ~2x

22. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2822 Substrate Thermoelastic Coating Brownian Substrate Brownian Coating Thermoelastic Gain factor Overall thermal noise budget Gaussian beam Mesa beam mirror Comparison between Gaussian and Mesa beam Calculation at the frequency 100 Hz Constraint 40 Kg mirror

23. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2823 The mirror shapes match the phase front of the beams. Mesa beam Gaussian beam Profiles normalized for Same Integrated power Steeper fall Slow exponential fall Higher peak power 0 Flat “mesa” beam profiles require rimmed “Mexican Hat” mirror profiles

24. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2824 Thermal shield Vacuum pipe INVAR rod Spacer plate Suspension wires Mechanical setup GAS springs

25. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2825 Cavity Lock Acquisition Tested with a R=800cm roc spherical mirror Two techniques: - Side locking: control on the injection current -> easier - Dither locking: modulation of the cavity length -> possibility to measure coupling with input beam but more sensitive to noise Results: - TEM patterns characterization - Environment capability to keep a lock

26. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2826 TEMs with spherical end mirrors Hermite-Gauss TEM set Laguerre-Gauss TEM set TEM00 TEM10 TEM20 TEM30 TEM10TEM20 Resonant beams: experimental data

27. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2827 TEMs with spherical end mirrors Qualitative analysis: - Cylindrical symmetry gradually lost - Difference between theoretical Hermite-Gauss and actual TEMs beam profiles (structure in the residual map) - Marked unbalance between the two TEM10 peaks: not avoided with fine PZTs adjustments

28. LIGO-G0200XX-00-M “Mexican hat” mirrors Numerical eigenmodes for a ideal MH Fabry-Perot interferometer: The fundamental mode is the so- called “Mesa Beam”, wider and flatter than a gaussian power distribution Cylindrical symmetry yields TEMs close to the Laguerre-Gauss eigenmodes set for spherical cavities

29. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2829

30. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2830 FP spectrum analysis: - TEMs identification and coupling analysis - Non-symmetric spacing: as expected - More peaks than we should see? Experimental Results

31. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2831 Other resonant TEMs: Experimental Results 2-dimensional nonlinear regression: Definitively not gaussian

32. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2832 Misalignments and mismatching effects has been modeled to recognize “strange” resonant modes No way to distinguish between them Experimental Results

33. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2833 Experimental Results

34. LIGO-G0200XX-00-M GWADW 2006 - Isola d'Elba (Italy), May 2834 Systematic and next steps Any attempt to “drive” the beam in a centered configuration failed FFT: even cylindrical symmetry is definitely lost FP spectrum analysis: peaks are separated enough -> we are observing the actual cavity modes