The Mesa Beam Juri Agresti 1 2 Erika

The Mesa Beam Juri Agresti 1, 2, Erika D’Ambrosio 1, Riccardo De. Salvo 1, Danièle Forest 3, Patrick Ganau 3, Bernard Lagrange 3, Jean-Marie Mackowski 3, Christophe Michel 3, John Miller 1, 4, Jean-Luc Montorio 3, Nazario Morgado 3, Laurent Pinard 3, Alban Remillieux 3, Barbara Simoni 1, 2, Marco Tarallo 1, 2, Phil Willems 1 LIGO-G 050 XXX-00 -R 1. Caltech/ LIGO 2. Universita’ di Pisa 3. LMA Lyon/ EGO 4. University of Glasgow Gingin’s Australia-Italia workshop on GW Detection

Why mesa beams l Detectors limited by fundamental thermal noise l Spectral density scales as 1/wn » n = 1 for the dominant coating losses LIGO-G 050 XXX-00 -R l Diffraction prevent dramatically increasing beam size l Gaussian beams sample only a few percent of the mirror’s surface Gingin’s Australia-Italia workshop on GW Detection 2

Why mesa beams Wider, flatter, and steeper edges beams Better average over the mirror surface depress thermal noise without compromising diffraction losses LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 3

Mesa Beam l Optimisation produces the mesa beam rim (same integrated beam power) Ste ep Higher peak power Slow exponential fall Steeper fall LIGO-G 050 XXX-00 -R Aspheric profile Spherical profile Gingin’s Australia-Italia workshop on GW Detection 4

Molecular beam deposited mirror • Profiled Deposition: • Coating the desired Mexican Hat profile using a pre-shaped mask • precision ~60 nm Peak to Valley • Corrective coating: 1. Compare achieved to desired shape Correct with molecular pencil precision <10 nm. 2. • LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 5

The test Cavity l 7. 32 m folded cavity l Rigid structure l Suspended in custom vacuum tank Flat input mirror Flat folding mirror MH mirror . 5 3 x 2 m INVAR rod Vacuum pipe LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 6

Cavity Suspensions V~ 0. 6 Hz H ~ 1 Hz Suspension System: GAS spring wires LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 7

Cavity Vacuum & Thermal Shield Suspension view Suspension wires Vacuum pipe Thermal shield Spacer plate INVAR rod LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 8

“Mexican hat” mirrors Numerical eigenmodes for a ideal MH Fabry-Perot interferometer: The fundamental mode is the socalled “Mesa Beam”, wider and flatter than a gaussian power distribution Cylindrical symmetry yields TEMs close to the Laguerre-Gauss eigenmodes set for spherical cavities LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection

“Mexican hat” mirrors l LMA laboratories provided three mirror prototypes l All affected with several imperfection » Due to the excessively small mirror size l Beam Tested one with a not negligible slope on the central bump l First simulated using paraxial approximation to evaluate how mirrors with these imperfections would affect the resonant beam LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 10

FFT simulations l The slope on the central bump can be corrected applying the right mirror tilt LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 11

Tilts of Spherical Mirrors l Tilts of spherical mirrors only translate optical axis LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 12

MH Cavity Alignment Tilt on MH mirrors destroys cylindrical symmetry -> resonant beam phase front changes with the alignment l Folded cavity: no obvious preferential plane for mirrors alignment -> very difficult align within required rad precision => TEM 00 difficult to identify l LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 13

Experimental Results l l No stable Mesa beam profile was initially acquired Higher order modes were found very easily LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 14

Results l These modes exhibit good agreement with theory MH 10 Good fit l LIGO-G 050 XXX-00 -R TEM 10 LG 10 Bad fit l Gingin’s Australia-Italia workshop on GW Detection 15

Results - other HOM Diffraction around beam baffle eliminated LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 16

Chasing the TEM 00 l - - - Apply FP spectrum analysis: TEMs identification and coupling analysis Non-symmetric spacing: as expected TEM 00 is the first of the sequence, independently of its profile appearance LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 17

Chasing the TEM 00 2 -dimensional nonlinear regression: Definitively not Gaussian LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 18

Experimental Results l TEM 00 tilt simulation 4 rad tilt LIGO-G 050 XXX-00 -R TEM 00 data Gingin’s Australia-Italia workshop on GW Detection 19

Systematic and next steps l l l Any attempt to “drive” the beam in a centered configuration failed cylindrical symmetry is definitely not achievable FP spectrum analysis: peaks are separated enough -> we are observing the actual TEM 00 cavity modes LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 20

Cause of cylindrical symmetry loss l l Mechanical clamping stress deform the folder and input mirrors ~ 60 nm deformation -> three times the height of the MH central bump Marked astigmatism is induced FFT simulation with actual IM profile confirm problem LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 21

Solving the problem l Flat mirrors too thin (1 cm) Temporary fix: Distributed stress with aluminum rings l Thicker substrates ordered l LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 22

Other improvements l Improved atmospheric isolation l Better stability ‘in lock’ LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 23

Passing from Side to Dither lock l Bad spectrum l l l Improved spectrum More power in the fundamental mode Now can lock on the TEM 00 mode LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 24

Improving Alignment l The reference during alignment was changed from the intensity profile to the transverse mode spectrum LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 25

The First Mesa Beam LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 26

Non-Linear Fit X LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 27

Non-Linear Fit Y LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 28

Alignment LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 29

Best Mesa Beam l Rsq = 0. 996 LIGO-G 050 XXX-00 -R l Rsq = 0. 992 Gingin’s Australia-Italia workshop on GW Detection 30

Best Mesa Beam Jagged top due to imperfect mirrors LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 31

Tilt Sensitvity l Controllability of beam is key l Decided to first investigate tilt sensitivity l Tilt MH mirror about a known axis LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 32

Profiles l Profiles along tilt axis 2 rad simulated 3. 85 rad experiment 2. 57 rad experiment LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 33

Excuses l Lack of temporal stability » vacuum? l Stiction l PZTs are bad LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 34

Summary l We are able to produce acceptable flat-topped beams with imperfect optics l We have begun to make a quantitative analysis of mesa beam » Beam size appears correct » Tilt sensitivity shows correct trends but less than expected by a factor of two LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 35

Further Work With This Set Up l Improve profile using new, stiffer flat mirrors l Repeatability/ stability – vacuum operations l Complete tilt sensitivity measurements l Test other two MH mirrors – mirror figure error tolerances l Long term – design and build half of a nearly concentric MH Cavity LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 36

Concentric cavity MH mirror profile LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 37

LIGO-G 050 XXX-00 -R Gingin’s Australia-Italia workshop on GW Detection 38