Outline l Motivations l Diffractive optics for Laguerre-Gauss

Outline l Motivations l Diffractive optics for Laguerre-Gauss (LG) beams l Experimental setup l Generated LG mode analysis l preliminary results: LG 33 interferometry l Summary and conclusions M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 1

Motivations l GW interferometers of the 2 nd and 3 rd generation will be limited by mirrors’ thermal noise in the central part of the detection band, around 102 Hz [1][2] LG 00 l Laguerre-Gauss (LG) beams [3][4] : ü wider power distribution on mirror surface ü lower thermal noise ü compatible with spherical mirrors [3] Mours B. & al. , Class. Quant. Grav. 23 , 2006 [4] Vinet J. Y. , Living Rev. Relativity 12 , 2009 l Need to test the generation of LG beams and their application to interferometry therm. noise [m/sqrt(Hz)] [1] Virgo coll. , Advanced Virgo baseline design, VIR-027 A-09 [2] Punturo M. & al. , Class. Quant. Grav. 27 , 2010 LG 33 frequency [Hz] J. Franc, WP 3 meeting 09/06/09 M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 2

Generation of Laguerre-Gauss beams l l Spiral phase plates, cylindrical mode converters, computer generated holograms, fibers, spatial light modulators, … Diffractive optical elements (DOEs) = etched plates of glass: l l stable passive optics ✔ DOE simple technique ✔ (in principle) can handle high power ✔ LG 00 LG 33 We have chosen a DOE for the generation of LG 33 M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 3

LG 33 diffractive optical element l l single transmission blazed element of fused Si DOE 2400*2400 pixels 1 pixel = 5. 9 μm l 16 phase levels etched l ~ 20 mm M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 4

LG 33 generated mode DOE LG 00 w 0 = 2. 15 mm Pin Pout w 0 ~ 288 μm Pout / Pin = 91. 4 % (DOE without AR coating) AR coating is foreseen M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 5

Mode purity upper limit l mode purity ≡ 2 D-amplitude overlap integral at a given point along propagation: l power coupling losses: l purity upper limit: the phase is not considered possible reasons: intrinsic DOE efficiency, input LG 00 beam matching & shape (astigmatic), DOE alignm. , . . M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 6

Experimental setup • LG 33 filtering with a mode-cleaner FARADAY ISOLATOR EOM LASER MODE MATCHING TELESCOPE LG 00/LG 33 switch LG 00 MODE CLEANER X/Y/Z mount DOE LG 00 DOE transmitted LG 33 lens M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 7

Mode-cleaner lock on LG 33 PD • plano/concave monolithic cavity • Finesse = 103 , FSR = 500 MHz • stable locking (hours) on LG 33 Faraday isolator CCD 30 cm EOM LG 00 path Laser mode-matching telescopes radiofrequency PD mode-cleaner DOE servo mixer PD M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 8

Alignment issues • • the LG 00 beam is initially aligned on the cavity the LG 33 is aligned on the LG 00 the cavity is locked on the LG 33 • alignment fine tuning is made using the reflected beam • measured reflected field: aligned mode X misal. Y misal. M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 9

Transmitted power PD LG 33 CCD Pout Pin 30 cm LG 33 transmission: Pout / Pin = 37 % throughput = 90 % Pin LG 33 = 41 % LG 1 l LG 4 l LG 2 l other modes: Pother / Ptotal = 45. 7 % towards higher conversion efficiency: • DOE design optimization • input LG 00 optimization, DOE alignment • cavity mode-matching optimization M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 10

Transmitted beam (far field – 1. 3 m) LG 33 - theory 1. 2 cm LG 33 - measure 1. 2 cm M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 11

Transmitted beam (far-field) analysis l mode purity : l power coupling losses: intensity [a. u. ] measured cross sect. – hor. measured cross sect. – vert. analytical intensity cross sect. NOT A FIT position [mm] M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 12

Summary and conclusions l we have generated a high-purity LG 33 beam using a diffractive element (etched glass plate) and a mode-cleaner (spatial filter): 98 % purity , 37 % generated mode transmission through mode-cleaner l this technique (stable component which can handle high power) is scalable to GW interferometers next steps: higher purity and conversion efficiency: • input LG 00 optimization, DOE alignment • cavity mode-matching optimization • DOE design optimization • high-finesse mirrors interferometry: • simple Michelson • Fabry-Perot arm cavities • control • contrast defect M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 13

LG 33 Michelson interferometer mirror LASER MODE CLEANER LG 00/LG 33 switch mirr. + PZT BS LG 33 MICH. ITF M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 14

LG 33 Michelson ITF locking screenshot I L I M E R P A N Y R dark fringe visibility: V = (Pmax-Pmin) / (Pmax+Pmin) = 97 % M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 15

Summary and conclusions l we have generated a high-purity LG 33 beam using a diffractive element (etched glass plate) and a mode-cleaner (spatial filter): 98 % purity , 37 % generated mode transmission through mode-cleaner l this technique (stable component which can handle high power) is scalable to GW interferometers next steps: higher purity and conversion efficiency: • input LG 00 optimization, DOE alignment • cavity mode-matching optimization • DOE design optimization • high-finesse mirrors interferometry: • simple Michelson • Fabry-Perot arm cavities • control • contrast defect M. Granata, M. Barsuglia, C. Buy, R. Ward – GWADW 2010 , Kyoto 16

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