1. Laguerre-Gauss Modes for Future Gravitational Wave Detectors Keiko Kokeyama University of Birmingham 2 nd ET Annual Workshop @ Erice, Sicily, Italy 13-18 Oct 2009

2. Contents  Introduction  Laguerre-Gauss (LG) beams  Advantages of LG beam interferometry  Experimental status  Summary 15 th October 2009Keiko Kokeyama 1/13

3. Introduction Thermal noise will be one of the limiting noise sources in the second and future GW detectors Laguerre-Gauss (LG) mode is proposed to lower the thermal noise in IFOs 15 th October 2009Keiko Kokeyama 2/13 Mours, B.; Tournefier, E. & Vinet, J., Classical and Quantum Gravity, 23, 5777-5784 (2006)

4. Laguerre-Gauss (LG) beams Hermite-Gauss (HG) modesHelical LG modes 15 th October 2009Keiko Kokeyama 3/13. 00 10 20 30 11 21 31 22 32 33 00 10 20 30 01 11 21 31 02 12 22 32 03 13 23 33 00 10 20 30

5. Different Laguerre-Gauss modes Helical LG modes Sinusoidal LG modes 00 10 20 30 11 21 31 22 32 33 00 10 20 30 11 21 31 22 32 33 15 th October 2009Keiko Kokeyama 4/13 cosine mode sine mode Same brownian TN as helical LG modes

6. Power distribution of LG beams on the mirror surfaces 15 th October 2009Keiko Kokeyama 5/13 Integrated beam power for modes with 1ppm loss on a mirror with d =35cm by M. Laval and J.Y. Vinet Any surface deformations are averaged out more smoothly and the temperature increase of the mirror is more uniform thereby reducing thermal deformation effects. More uniform power distribution on a mirror surface than the fundamental mode.

7. Thermal noise of LG and Flat beams J.Y. Vinet, CQG 22 (2005) 1395, Bondu et al. Physics Letters A 246 (1998) 227 LG nm modes: HG 00 mode: Flat beams: LG 33 15 th October 2009Keiko Kokeyama 6/13 formulas valid for infinite media

8. Other features of LG mode The higher order LG modes are fully compatible with the current spherical arm cavity mirrors LG beam IFOs provide the compatible longitudinal control signals Alignment control matrix is also compatible Mirror tilt coupling with the longitudinal degree is less than the HG beam IFOs Chelkowski, S. et al; Phys. Rev. D, 79, 12, 2009 15 th October 2009Keiko Kokeyama 7/13

9. LG beam research at Birmingham  Simulation Work  Table-top experiments 15 th October 2009Keiko Kokeyama 8/13 Purpose of experiment To characterize the conversion from the fundamental mode to the LG33 cosine mode To exam the cavity/IFO performance To Investigate possible problems, like mode degeneracy and phase instability

10. Generating LG cosine mode  To generate the LG33 cosine mode, we utilize a Liquid-crystal-on-silicone spatial light modulator (LCOS-SLM, or phase plate)  A phase plate imprints the phase modulation to the wavefront of the incoming HG00 beam, and converts the beam into LG33 cosine mode holographically Holoeye LC-R2500 15 th October 2009Keiko Kokeyama 9/13 Matsumoto et al, J. Opt.Soc.Am.A 25,7 (2008) phase plate

11. Generating LG cosine mode  To generate the LG33 cosine mode, we utilize a Liquid-crystal-on-silicone spatial light modulator (LCOS-SLM, or phase plate)  A phase plate imprints the phase modulation to the wavefront of the incoming HG00 beam, and converts the beam into LG33 cosine mode holographically Holoeye LC-R2500 15 th October 2009Keiko Kokeyama 9/13 Schematic of a phase plate Matsumoto et al, J. Opt.Soc.Am.A 25,7 (2008)

12. Lab setup The phase image to convert HG00 to LG33 cosine mode Generate the LG33 cosine mode with a simple setup π 0 15 th October 2009Keiko Kokeyama 10/13

13. Preliminary results  Successful to generate the LG33 cosine mode in the lab  The beam profile of the generated LG33 cosine mode was measured ● Fitting tool was developed (written in Matlab) ● Beam profile of the generated beam w0 = 0.3 mm, zR = 0.34 m  We have developed a theory and confirmed it by experiment for estimating the beam parameters of the LG33 mode depending on the phase plate characteristics 15 th October 2009Keiko Kokeyama 11/13

14. Future Plans of Tabletop Experiment  Modecleaner to obtain cleaner LG33 cosine mode  Michelson interferometer  Triangular cavity 15 th October 2009Keiko Kokeyama 12/13

15. Summary  The limiting thermal noise can be reduced and therefore the IFO sensitivity can be improve by using LG higher order mode  Normal optics, compatible control and alignment signals are available  Table-top demonstrations are in progress  LG33 cosine mode is successfully generated Our simulation / experiment works will be the milestone of the LG mode technology for future GW detectors. 15 th October 2009Keiko Kokeyama 13/13

16. Thank you Acknowlidgements Simon Chelkowski Paul Fulda Andreas Freise

17. Types of LG modes Behaviour of LG modes in triangular cavities  “helical” LG modes  Continuous ring structure  Helical phase distribution  “sinusoidal” LG modes  Radial dark sections  Number of sections corresponds to l in LG pl  Spherical phase front  Same brownian TN as helical LG modes S. ChelkowskiLSC Meeting, Amsterdam 09/2008 Slide 17 Thermo-elastic noise of sinusoidal LG modes needs to be investigated!

18. Behaviour of LG modes in triangular cavities S. ChelkowskiLSC Meeting, Amsterdam 09/2008 Slide 18 Symmetrical and asymmetrical modes behave differently in triangular cavities symmetrical modesasymmetrical modes