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Gravitational wave detectors and the IMPACT and simulation of optical defects ETMY ITMY PRM BS ITMX SRM Daniel Töyrä ETMX Supervisor: Andreas Freise Nottingham 26/10/2015 1 Overview • Gravitational wave interferometers ! • Modelling of optical defects ! • Finding operating points for gravitational wave detectors ! Daniel Töyrä Nottingham 26/10/2015 2 Optical configuration of LIGO ETMY Michelson interferometer ! BS ETMX Daniel Töyrä Nottingham 26/10/2015 3 Optical configuration of LIGO ETMY Michelson interferometer • with Fabry-Pérot armcavities. ! ITMY BS ITMX Daniel Töyrä Nottingham 26/10/2015 ETMX 4 Optical configuration of LIGO ETMY Michelson interferometer • with Fabry-Pérot armcavities. ! !sb = !c ± !gw ITMY BS ITMX Daniel Töyrä Nottingham 26/10/2015 ETMX 5 Optical configuration of LIGO ETMY Michelson interferometer • with Fabry-Pérot armcavities. • with recycling cavities ! ITMY PRM BS ITMX ETMX SRM Daniel Töyrä Nottingham 26/10/2015 6 Optical configuration of LIGO ETMY Michelson interferometer • with Fabry-Pérot armcavities. • with recycling cavities ! ITMY Need signals to control the interferometer. PRM BS ITMX ETMX SRM Daniel Töyrä Nottingham 26/10/2015 7 Ideal laser beams The gaussian beam ! • A solution to Helmholtz equation (time independent wave equation) under the paraxial approximation Daniel Töyrä Nottingham 26/10/2015 8 Distorted beam Daniel Töyrä Nottingham 26/10/2015 9 Mirror defects Figure measurement Numerical modelling Daniel Töyrä Nottingham 26/10/2015 10 Daniel Töyrä Nottingham 26/10/2015 11 Hermite-Gauss modes • Hermite-Gauss modes form a complete set of functions in a plane ! • Any laser beam in a well behaved interferometer can be described by a sum of Hermite-Gauss modes. Daniel Töyrä Nottingham 26/10/2015 12 Beam distortions ⌦ Knm,n0 m0 = unm e2ikz(x,y) un0 m0 Daniel Töyrä Nottingham 26/10/2015 13 ↵ Operating points laser A point in parameter space suitable for operation. EOM BS ITM ETM PD refl • Maximum power Measured by photo diode. • Zero crossing of the error signal Demodulation on modulation frequency. Double-demodulation on modulation and amplitude noise frequencies. • Minimum noise in the error signal Daniel Töyrä Nottingham 26/10/2015 14 Operating points laser A point in parameter space suitable for operation. EOM BS ITM ETM PD refl • Maximum power Measured by photo diode. • Zero crossing of the error signal Demodulation on modulation frequency. Double-demodulation on modulation and amplitude noise frequencies. • Minimum noise in the error signal Daniel Töyrä Nottingham 26/10/2015 15 Operating points Daniel Töyrä Nottingham 26/10/2015 16 Operating points ETMY laser EOM ITMY BS ITM ETM PD refl PRM BS ITMX SRM laser EOM BS PRM ITM ETM PD refl Daniel Töyrä Nottingham 26/10/2015 17 ETMX Thank you! Daniel Töyrä Nottingham 26/10/2015 18 Daniel Töyrä Nottingham 26/10/2015 19 Helmholtz equation Daniel Töyrä Nottingham 26/10/2015 20 PhD in Birmingham ▪ Maintain and Develop ▪ Frequency domain INterfErometry Simulation SoftwarE ▪ Open source ▪ Used for commissioning of GEO 600 and LIGO ▪ Handles various defects e.g: ▪ Quantum noise ▪ Imperfect optics Running Finesse Finesse-file Daniel Töyrä Pisa 20/04/2015 Interferometer Mirror map of LIGO ETM [Charlotte Bond] 21 PhD in Birmingham ▪ Maintain and Develop ▪ Model interferometric techniques for ET and LIGO Proposed geometry of ET Daniel Töyrä The planned ET (ASPERA) Pisa 20/04/2015 22
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