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Thermal noise reduction through LG modes

Explore the effectiveness of Laguerre-Gauss modes combined with cryogenic temperatures for reducing thermal noise in next-gen GW detectors. Detailed simulations, reference parameters, and conclusions on substrate and coating noise sources presented.

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Thermal noise reduction through LG modes

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  1. Thermal noise reduction through LG modes Janyce Franc, Raffaele Flaminio, Massimo Galimberti Laboratoire des Matériaux Avancés-LYON Simon Chelkowski, Andreas Freise University of Birmingham Stefan Hild University of Glasgow 2nd ET General Meeting-ERICE 15th October 2009 Janyce Franc-ET meeting-Erice

  2. Contents • Introduction • Motivations • Objectives • Laguerre-Gauss advantages • Simulations • References and Parameters • Influence of LG mode on Brownian and TE Noises • LG modes and different substrates • LG modes and different mirror sizes • Conclusion and future work Janyce Franc-ET meeting-Erice

  3. Thermal noise in 3rd generation of GWD All these thermal noise sources are at least at some frequencies above the ET target • The ideas to reduce thermal noise : • Arm lengths • New coating materials • Cooling mirror @ cryogenic T° • Change beam mode and beam size Janyce Franc-ET meeting-Erice

  4. Motivation for using LG modes • Advantages : Best power distribution on the mirror surface • Lower Thermal Noise • Lower Thermal Lensing The idea is to prove the efficiency of the combination of cryogenic temperature and the use of Laguerre-Gauss modes to decrease the thermal noise for future GW detector. Janyce Franc-ET meeting-Erice

  5. Introduction to simulations Unless otherwise specified Reference : S. Hild et al. arXiv:0906.2655v2 [gr-qc] Janyce Franc-ET meeting-Erice

  6. Parameters values @ 10K COATING SUBSTRATE L : Low index material H : High index material Janyce Franc-ET meeting-Erice

  7. References for formula For Infinite Mirrors with Gaussian Beam: 1. M. L. Gorodetsky Phys. Lett. A 372 (2008) 6813-6822 Summary of all thermal noise formula 2. Cerdonio et al. Phys. Review D, 63, 082003 Description of substrate TE Noise without adiabatic assumption 3. Braginsky, Gorodetsky, Vyatchanin arXiv:cond.mat/9912139v1 1999 Helpful to determine substrate TE Noise without adiabatic assumption applicable to higher LG modes For Finite Mirrors with LG modes: 4. B. Mours et al CQG 23 (2006), J.-Y.Vinet : Living Rev. Relativity12,  (2009) Provides all formula for finite/infinite mirrors and for gaussian and LG beams 5. V.B. Braginsky, S.P. Vyatchanin, physics letter A 312 (2003) 244-255 Gives details of calculation for Coating TE Noise. Janyce Franc-ET meeting-Erice

  8. Coating Brownian Noise Conclusions on Coat. Brownian Noise : -No difference between finite and infinite mirrors -LG33 and LG55 give the same results NB: ‘Finite mirror’ is 62 cm diameter mirror Janyce Franc-ET meeting-Erice

  9. Substrate Brownian Noise Conclusions on Sub. Brownian Noise : - No difference between finite and infinite mirrors for Gaussian Beam - TN decreases in finite mirror for LG33 and LG55 - A small advantage for LG55 compare to LG33 Janyce Franc-ET meeting-Erice

  10. Coating Thermoelastic Noise Work in progress and in discussion with Jean-Yves Vinet Some problems have been identified in comparing formula from different references Janyce Franc-ET meeting-Erice

  11. Substrate Thermoelastic Noise Conclusions on Sub. TE Noise : - No difference between finite and infinite mirror - Advantage for LG33 - Calculation for LG55 is in progress Janyce Franc-ET meeting-Erice

  12. Substrates Comparison Study of two limiting Noises : Coating and Substrate Brownian Noise Coating Brownian Noise Substrate Brownian Noise Finite Mirror Ø=62 cm h=30cm COATING BROWNIAN NOISE ADVANTAGE SAPPHIRE SUBSTRATE BROWNIAN NOISE ADVANTAGE SILICON Janyce Franc-ET meeting-Erice

  13. Total Thermal noise in Interferometer Mirror sizes effects : Diameter dependency For 1 ppm diff. losses Silicon substrate Arm = 10 km T=10K BETTER RESULT FOR Ø=45cm with LG33 than Ø=62cm with LG00 Janyce Franc-ET meeting-Erice

  14. Total Thermal Noise TARGET • Thermal Noise for 2nd generation GWD • Interferometer arms : 3 km • Temperature : 300K • Large beams : 6.7 cm (gaussian beam) • Thermal Noise for 3rd generation GWD • Long interferometer arms : 10 km • Temperature : 10K • 2 cases : Ø=62 cm LG00 & Ø= 45 cm LG33 Low T° + High Mirror Size + LG33 = Thermal noise Target confirmed Janyce Franc-ET meeting-Erice

  15. Conclusion and future work - Impact of different thermal noises depends on the considered LG modes but the main results does not change: coating Brownian noise remains the limit - LG33 mode appears as a good solution in order to decrease the total thermal noise (thermal noise reduced by 1.71 for LG33 compared to LG00). - A study of LG55 does not demonstrate a better result than LG33. - Writing up of an ET note in progress - A proposition of ET design, using large dimension mirror and LG33 mode, gives good sensitivity: Stefan Hild et al. arXiv: 0906.2655v2 [gr-qc] Janyce Franc-ET meeting-Erice

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