1. S. ChelkowskiSlide 1LSC Meeting, Amsterdam 09/2008

2. Overview  Motivation for using Higher-Order Laguerre modes  Summary of length and alignment sensing with higher order Laguerre-Gauss modes  Arm cavity mirror radii of curvature trade-off analysis  Using advanced Virgo as an example  Use inspiral ranges as figure of merit  Three scenarios lead to four different comparisons of the fundamental LG 00 and the proposed LG 33 mode S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 2

3. S. ChelkowskiSlide 3 Thermal noise in future GW detectors LSC Meeting, Amsterdam 09/2008 Advanced Virgo Conceptual Design VIR–042A–07

4. Integrated beam power for modes with 1ppm loss on a mirror with d =35cm S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 4 by M. Laval and J.-Y. Vinet

5. LG nm modes: Flat beams: Thermal noise of LG and Flat beams S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 5 HG 00 mode: Bondu et al. Physics Letters A 246 (1998) 227 J.-Y. Vinet CQG 22 (2005) 1395 Bondu et al. Physics Letters A 246 (1998) 227 formulas valid for infinite media only

6. TN scaling factors of LG nm modes S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 6 01 234 5 0 1 2 3 4 5 n m 10.69 0.500.60 0.410.46 0.31 0.37 0.57 0.44 0.27 0.25 numbers shown are for an infinite mirror size LG 33 personal communication J.-Y. Vinet LG 55

7. Expected thermal noise improvements All values given for beam sizes corresponding to 1ppm clipping losses S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 7 References: C. TN: personal communication J.-Y. Vinet S. TN: Mours et al.. CQG 23 (2006),5777 T. E. N: personal communication J.-Y. Vinet

8. Comparison of LG and Flat beams  Spherical phase fronts  Compatible with current interferometers  Beam shape and phase fronts change on propagation  Mirror surfaces are more complex S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 8 By M. Laval and J.-Y. Vinet E0 Eref Etr Ecav M1M2 L=3km HG & LG mode cavity design Flat top beam cavity design E0 Eref Etr Ecav M1M2 L=3km

9. S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 9 Comparison of length and alignment signals for a single cavity LG33 LG00  0.4º  5.0º 1mrad for more details see my Elba talk about higher order LG modes

10. Clipping loss comparison S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 10

11. Arm cavity mirror radii of curvature trade-off analysis S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 11 Simulation parameters:  Bench version 4.1  Latest IFO model of Adv.Virgo  Rescaled beam size for LG modes  Used thermal noise scaling factor by J-.Y. Vinet  Thermo-elastic TN compensation included  Coating radius 17cm according to Virgo note VIR-038A-08 (2008) Figure of merit: Inspiral ranges

12. Advanced Virgo sensitivity S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 12

13. Three Scenarios 1.We buy one a set of optimized mirrors for each mode configuration; same clipping losses 2.We buy mirrors which are compatible with both mode configurations; same radii of curvature 3.We buy mirrors optimized for the LG00 mode and use the TCS system to optimize them later for LG33 and vice versa S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 13

14. Scenario 1: Same clipping losses Problem: The mirrors are not compatible! S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 14 17% 27% 24% 25% 23% 32% Reference configuration

15. Scenario 2: Same radii of curvature  Trade-off concerning clipping loss  LG 00 configuration much worse than current baseline S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 15 Problem: -21% -24% 21% 32% 28% Not a good option!

16. Scenario 3: Use thermal compensation system to the change RoC S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 16 Credit to S. Hild

17. Scenario 3a: Use thermal compensation system to the change RoC S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 17 Advanced LIGO TCS TCS range of 120m

18. Scenario 3a: Change RoC with TCS, optimisation for fundamental mode Problem: Implementation of such TCS might be difficult S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 18 0% 21% 32% 29% Looks promising!

19. Scenario 3b: Use thermal compensation system to the change RoC S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 19 TCS range of 120m Advanced LIGO TCS

20. Scenario 3b: Change RoC with TCS, optimisation for LG33 mode Problem: Implementation of such TCS might be difficult S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 20 -15% -18% 17% 27% 24% Looks promising!

21. Conclusion  LG modes reduce the thermal noise in the IFO  LG modes compatible with current IFO designs  Beam parameters are different  RoC have to be matched, or clipping loss are different  Length and alignment signals of LG 33 better than LG 00 for the same mirror sizes  Inspiral ranges of RoC compatible IFO configuration (Scenario two) are low for fundamental LG 00 mode  Best solution uses Thermal Compensation System to adapt RoC to the desired mode S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 21

22. Higher order Laguerre Gauss modes in triangular cavities S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 22

23. Behaviour of LG modes in triangular cavities S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 23 Two possible solutions for this problem 1.Do not use triangular cavities 2.Use sinusoidal LG modes  Thermo-elastic noise of sinusoidal LG modes needs to be investigated! For more details see talk by M. Barsuglia Virgo Biweekly Meeting 1/7/2008

24. Conclusion LG modes in triangular cavities  Helical LG modes are not compatible with triangular cavities  Either use sinusoidal LG modes or use modecleaner cavities with an even number of mirrors  Helical and sinusoidal LG modes have the same brownian thermal noise  Thermo-elastic noise of sinusoidal LG modes unknown  should be investigated S. ChelkowskiLSC Meeting, Amsterdam 09/2008Slide 24