LIGO-G050XXX-00-R Gingin’s Australia-Italia workshop on GW Detection

The Mesa Beam

Juri Agresti1,2, Erika D’Ambrosio1, Riccardo DeSalvo1, Danièle Forest3, Patrick Ganau3, Bernard Lagrange3, Jean-Marie Mackowski3, Christophe Michel3,

John Miller1,4, Jean-Luc Montorio3, Nazario Morgado3, Laurent Pinard3, Alban Remillieux3, Barbara Simoni1,2,

Marco Tarallo1,2, Phil Willems1

1. Caltech/ LIGO 2. Universita’ di Pisa

3. LMA Lyon/ EGO 4. University of Glasgow

2LIGO-G050XXX-00-R Gingin’s Australia-Italia workshop on GW Detection

Why mesa beams Detectors limited by

fundamental thermal noise

Spectral density scales as 1/wn

» n = 1 for the dominant coating losses

Diffraction prevent dramatically increasing beam size

Gaussian beams sample only a few percent of the mirror’s surface

1h nS

w

2

2exp 2clip

m

w

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Why mesa beams

Wider, flatter, andsteeper edges beams

Better average overthe mirror surface

depress thermal noisewithout compromising

diffraction losses

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Mesa Beam

Optimisation produces the mesa beam

Steeper fall

Slow exponential fall Ste

ep ri

m

Aspheric profile

Higher peak power

(same integrated beam power)

Sphericalprofile

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Molecular beam deposited mirror

• Profiled Deposition:• Coating the desired Mexican Hat profile using a pre-shaped mask• precision ~60nm Peak to Valley

• Corrective coating:1. Compare achieved to

desired shape2. Correct with molecular

pencil• precision <10 nm.

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The test Cavity

7.32 m folded cavity

Rigid structure

Suspended in custom vacuum tank

INVAR rod

MH mirrorFlat input mirror

Flat folding mirror

Vacuum pipe

2x 3.5 m

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Cavity Suspensions

Suspension System:

V~ 0.6 Hz

H ~ 1 Hz

GAS spring

wires

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Cavity Vacuum & Thermal Shield

Thermal shield

Vacuum pipe

INVAR rodSpacer plate

Suspension wires

Suspension view

LIGO-G050XXX-00-R Gingin’s Australia-Italia workshop on GW Detection

“Mexican hat” mirrors

Numerical eigenmodes for a ideal MH Fabry-Perot interferometer:

The fundamental mode is the so-called “Mesa Beam”, wider and flatter than a gaussian power distribution

Cylindrical symmetry yields TEMs close to the Laguerre-Gauss eigenmodes set for spherical cavities

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“Mexican hat” mirrors LMA laboratories provided three mirror prototypes

All affected with several imperfection» Due to the excessively small mirror size

Beam Tested one with a not negligible slope on the central bump

First simulated using paraxial approximation to evaluate how mirrors with these imperfections would affect the resonant beam

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The slope on the central bump can be corrected applying the right mirror tilt

FFT simulations

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Tilts of Spherical Mirrors

Tilts of spherical mirrors only translate optical axis

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MH Cavity Alignment

Tilt on MH mirrors destroys cylindrical symmetry

-> resonant beam phase front changes with the alignment

Folded cavity: no obvious preferential plane for mirrors alignment

-> very difficult align within required rad precision

=> TEM00 difficult to identify

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Experimental Results

No stable Mesa beam profile was initially acquired Higher order modes were found very easily

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Results These modes exhibit good agreement with theory

TEM10

MH10

Good fit

LG10

Bad fit

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Results - other HOM

Diffraction around beam baffle eliminated

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Apply FP spectrum analysis:

- TEMs identification and coupling analysis

- Non-symmetric spacing: as expected

- TEM00 is the first of the sequence, independently of its profile appearance

Chasing the TEM00

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Chasing the TEM00

2-dimensional nonlinear regression:

Definitively not Gaussian

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TEM00 tilt simulation 4rad tilt TEM00 data

Experimental Results

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Systematic and next steps

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 TEM00cavity modes

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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

Cause of cylindrical symmetry loss

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Solving the problem Flat mirrors too thin (1 cm) Temporary fix: Distributed stress

with aluminum rings

Thicker substrates ordered

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Other improvements Improved atmospheric

isolation

Better stability ‘in lock’

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Passing from Side to Dither lock

More power in the fundamental mode

Now can lock on the TEM00 mode

Improved spectrum

Bad spectrum

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Improving Alignment The reference during alignment was changed from the intensity profile

to the transverse mode spectrum

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The First Mesa Beam

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Non-Linear Fit X

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Non-Linear Fit Y

6.68theoryw mm

7.60 1.19experimentw mm

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Alignment

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Best Mesa Beam

Rsq = 0.996 Rsq = 0.992

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Best Mesa Beam

Jagged top due to imperfect mirrors

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Tilt Sensitvity

Controllability of beam is key

Decided to first investigate tilt sensitivity

Tilt MH mirror about a known axis

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Profiles

Profiles along tilt axis

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2 rad simulated

3.85 rad experiment2.57 rad

experiment

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Excuses

Lack of temporal stability » vacuum?

Stiction

PZTs are bad

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Summary

We are able to produce acceptable flat-topped beams with imperfect optics

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

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Further Work With This Set Up

Improve profile using new, stiffer flat mirrors

Repeatability/ stability – vacuum operations

Complete tilt sensitivity measurements

Test other two MH mirrors – mirror figure error tolerances

Long term – design and build half of a nearly concentric MH Cavity

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Concentric cavity MH mirror profile

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