Beam shaping for thermal noise reduction

Beam shaping for thermal noise reduction

Paul Fulda, Andreas Freise GWADW, Kyoto, 18.05.2010

Foto by Nickster2000

…advantages in using Laguerre-Gauss modes

P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 2

Overview

Alternative beam shapes Laguerre modes versus other beam shapes Experimental results with LG modes


Possible Thermal Noise Reduction

thermal noise

(Coating) Brownian thermal noise dynamically distorts the surface of the mirrors

This results in noise in the dark fringe, proportional to the magnitude of the `average’ phase change in the reflected wave fronts

This `average’ can be improved by widening and flattening the beam size on the mirror


Design of flat beams: clipping loss Take three example beams: the basic Gaussian (LG00), a

higher-order Laguerre-Gauss mode (LG33) and a super-Gaussian (SG) beam:

Compute clipping loss in order to scale the beam radius relative to a mirror size


Design of flat beams: divergence Now propagate beams and and look for a small

divergence and a remaining flat profile This is why we do not plan to use super-Gaussian

beams

Propagate


Other flat beams A more successful approach to create low-diffraction flat-top

beams is to think of it as of a sum of multiple small Gaussian beams (FMGB = Flat-top Multiple Gaussian Beam)

FMGBs suggested by Tovar (JOSA A, 18, 2001) and successfully used experimentally and theoretically (e.g. analytic equations for their propagation through ABCD systems in Gao et al JOSA A, 26, 10, 2009)

Procedure adopted by GW community

[D'Ambrosio et al]


Flat beams in GW community

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FMGBs can be used to suppress

all types of thermal noise (abouta factor of 1.5 in typical examples) and also to reduce thermal lensing

The first type of FMGBs (also called Mesa beams in the GW community) were analysed using FFT simulations

Experimental verificationhas been done in a dedicatedprototype


Optimised beams

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Intensity profile

Mirror profile

Bondarescu et al (and others) have theoretically optimised the beam shapefor low thermal noise for a given clippingloss.

Expected thermal noise reduction: 2.3 (compared to 1.5 with Mesa beams) forthe case of Advanced LIGO.

Challenges come from non-spherical mirrorprofile: e.g. need to control DC position to 4 um and/or 3nrad to keep losses below 10ppm.


Why Laguerre-Gauss modes instead? The full GW detector might include mode cleaners, signal

recycling cavities, filter cavities, squeezed light generators

For QND schemes the light must be mode-matched to different cavities with low losses

No experience how to do that with conical beams or mesa beams

Noise reduction factor slightly smaller for LG beams (ET note by Janyce Franc et al: ‘Role of high-order Laguerre-Gauss modes on mirror thermal noise in gravitational wave detectors’)

Also LG beams introduce new problems: the degeneracy of higher order modes. Still work to do but so far LG modes seem the easiest challenge of all flat beams

GWADW Kyoto 18.05.2010

Experimental LG mode interferometry Generate LG modes with a spatial light modulator

Observe length control signals for a LG33 mode in a linear mode cleaner (LMC)

Demonstrate locking a LMC to LG33 mode

Estimate the purity increase upon transmission

Investigate compatibility of LG modes with the ‘standard’ triangular pre-mode cleaner design

P. Fulda, A. Freise Slide 10


Experimental setup for mode generation and cleaning



Lab optical path for mode conversion



Generated LG beams


Phase modulation Phase + amplitude modulation


Length control signals for LG33 modes in a linear mode cleaner

Simulations show that length and alignment control should work as well as for a LG00

Modulate laser at RF modulation of light, then demodulate reflected/transmitted light to get longitudinal error signal


1

Chelkowski, S. et al, ‘Prospects of LG modes in GWDs’, Phys Rev D, 79, 122002, 20091


PDH error signal for LG33 mode



PDH locking of linear mode cleaner (LMC)

Input beam manually aligned to LMC optic axis Lock acquisition is easy and repeatable Lock is stable for long time scales (~1hr) LMC stays in lock when input is switched from

helical to sinusoidal mode LMC could be locked to transmit modes up to

order 24 (LG88)


Input and transmitted LG33 beams


Sinusoidal LG33

Helical LG33


Estimating cleaned mode purity Best-fits made of measured and ideal intensities Simulated setup with input beam misaligned by

αx=-100µrad and αy=60µrad recreated output beam intensity residual

Decompose theoretical field to estimate mode content of measured output beam


Output beam residualInput beam residual Finesse residual


Mode decomposition result


Since the output mode is very pure, we can therefore estimate input mode purity as :

Input purity = output power input power x LMC throughput


Input mode purity estimations Measured LMC throughput efficiency = 63% Helical input power = 2.93mW, output = 1.21mW Sine input power = 1.53mW, output = 0.496mW


purity~66%

purity>99%

purity~51%

purity>99%


Locked to even higher-order LG modes...


LG33 LG55 LG88


Helical modes in triangular mode cleaners (TMCs)

We expected that helical modes will not pass through a cavity with an odd number of mirrors

Only vertically (anti-)symmetric modes can pass



Helical modes in TMCs Helical mode composed of vertically symmetric

and anti-symmetric sinusoidal modes TMC separates these out; only one can pass



Astigmatism in TMCs In a TMC, the beam is incident upon a curved

mirror at non-normal angle The cavity eigenmode is therefore astigmatic LG modes cannot describe astigmatism, so the

eigenmode cannot be a pure LG mode


Contrast enhanced for clarity Contrast enhanced for clarity


Conclusions Simulations have shown LG modes to be compatible with standard

interferometer control signals We achieved the generation of LG modes up to the order 24 We experimentally demonstrated the locking of LG modes to a LMC

see http://arxiv.org/abs/1005.2990 The spatial mode purity increased significantly after transmission

through the LMC, estimated mode purity >99% Experimental demonstration that helical LG modes do not pass

TMCs, but are split into the sinusoidal LG mode components The next step: experimental demonstration of a LG33 mode in a

Michelson interferometer with arm cavities Theoretical investigations into mode degeneracy and mirror surface

figure requirements ongoing


http://arxiv.org/abs/1005.2990

http://arxiv.org/abs/1005.2990

GWADW Kyoto 18.05.2010P. Fulda, A. Freise Slide 31


Helical modes in TMCs Helical modes are not vertically (anti-)symmetric Sinusoidal modes can be either vertically

symmetric or anti-symmetric


Sinusoidal LG33 Cosinusoidal LG33 Helical LG33

vertical symmetry vertical anti-symmetry vertical asymmetry

LG33 phase fronts

Beam shaping for thermal noise reduction

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