1. April 24 2004GR fun @ Cornell1 A new family of flat-topped beams interesting for future LIGO interferometers Mihai Bondarescu California Institute of Technology

2. April 24 2004GR fun @ Cornell2 Collaborators and Consultants K. Thorne (Caltech) Pavlin Savov (Caltech) Erika D’Ambrosio (Caltech) S. Vyatchanin (MSU, Moscow) S. Strigin (MSU, Moscow) R. O’Shaughnessy (NWU, Chicago) P. Kazarian (GCC)

3. April 24 2004GR fun @ Cornell3

4. April 24 2004GR fun @ Cornell4 International Network of Interferometric Detectors Network Required for: »Detection Confidence »Waveform Extraction »Direction by Triangulation LIGO Hanford, WA LIGO Livingston, LA GEO600 Hanover Germany TAMA300 Tokyo VIRGO Pisa, Italy Slide adapted from a talk by Kip

5. April 24 2004GR fun @ Cornell5 LIGO Collaboration of ~350 scientists at ~30 institutions Hanford Washington 4 km 2 km Slide adapted from a talk by Kip

6. April 24 2004GR fun @ Cornell6 Livingston, Louisiana 4 km Slide adapted from a talk by Kip

7. April 24 2004GR fun @ Cornell7 LIGO’s International Partners VIRGO: Pisa, Italy [Italy/France] GEO600, Hanover Germany [UK, Germany] TAMA300, Tokyo [Japan] AIGO, Jin-Jin West Australia Slide adapted from a talk by Kip

8. April 24 2004GR fun @ Cornell8 How a LIGO Interferometer Works Fabry-Perot Cavity Fabry-Perot Cavity Beam Splitter Slide adapted from a talk by Kip

9. April 24 2004GR fun @ Cornell9 Slide adapted from Rejean J Dupuis talk from http://www.ligo.org/results/

10. April 24 2004GR fun @ Cornell10 Noise in LIGO Adopted from Kip’s Talk (LIGO-G030137-00-Z)

11. April 24 2004GR fun @ Cornell11 What is Thermoelastic Noise and How to Reduce It? Random Thermal Fluctuations (~0.5 mm) Hot Regions Expand; Cold Contract Beam Intensity Averages Over Mirror Surface Imperfect Averaging = Thermoelastic Noise Gaussian Beam Slide from a talk prepared by Pavlin Savov for PCGM

12. April 24 2004GR fun @ Cornell12 What is Thermoelastic Noise and How to Reduce It? Random Thermal Fluctuations (~0.5 mm) Hot Regions Expand; Cold Contract Beam Intensity Averages Over Mirror Surface Imperfect Averaging = Thermoelastic Noise Mesa Beam Slide from a talk prepared by Pavlin Savov for PCGM

13. April 24 2004GR fun @ Cornell13 Building a MESA beam Minimal Gaussian

14. April 24 2004GR fun @ Cornell14 Building a MESA beam Minimal Gaussian

15. April 24 2004GR fun @ Cornell15 Building a MESA beam Minimal Gaussian

16. April 24 2004GR fun @ Cornell16 Building a MESA beam Minimal Gaussians

17. April 24 2004GR fun @ Cornell17 Building a MESA beam Mesa

18. April 24 2004GR fun @ Cornell18 Flat and Concentric Configurations (O’Shaugnessy, Thorne) (Bondarescu, Kazarian,Savov)

19. April 24 2004GR fun @ Cornell19 Flat and Concentric Configurations (O’Shaugnessy, Thorne) (Bondarescu, Kazarian,Savov)

20. April 24 2004GR fun @ Cornell20 My proposal Mirror Overlap minimal Gaussians centered on these lines

21. April 24 2004GR fun @ Cornell21 What’s different? Surfaces of constant phase Mimimal Gausian’s axis

22. April 24 2004GR fun @ Cornell22 What’s different? Flat Mirrors Confocal Mirros D

23. April 24 2004GR fun @ Cornell23 Mesa Beams Comparison

24. April 24 2004GR fun @ Cornell24 Mexican-Hat Mirrors’ Corrections

25. April 24 2004GR fun @ Cornell25 Tilt Instability Reduce Thermoelastic Noise Evaluate Tilt Instability for New Mirrors’ Shapes Compare to Conventional Spherical Mirrors Fabry-Perot Cavity

26. April 24 2004GR fun @ Cornell26 The Eigenvalue Problem

27. April 24 2004GR fun @ Cornell27 Mesa Beam Profiles

28. April 24 2004GR fun @ Cornell28 Flat-Concentric MB Comparison Eigenstates Comparison Eigenvalues Comparison

29. April 24 2004GR fun @ Cornell29 Again Flat-Concentric Configurations Relation (Yanbei Chen) G=1-L/R

30. April 24 2004GR fun @ Cornell30 Results and Conclusions Thermoelastic Noise ( O,Shaughnessy, Strigin, Vyatchanin ) Tilt Instability ( Mode Mixing ) Nearly Flat  Concentric Duality ( in Progress )