Beam shaping for thermal noise reduction
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Transcript of 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
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 3
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
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 4
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
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 5
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
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 6
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]
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 7
Flat beams in GW community
SimulationExperimentaldata
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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
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 8
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.
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 9
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
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 11
GWADW Kyoto 18.05.2010
Experimental setup for mode generation and cleaning
P. Fulda, A. Freise Slide 12
GWADW Kyoto 18.05.2010
Lab optical path for mode conversion
P. Fulda, A. Freise Slide 13
GWADW Kyoto 18.05.2010
Generated LG beams
P. Fulda, A. Freise Slide 14
Phase modulation Phase + amplitude modulation
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 15
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 16
1
Chelkowski, S. et al, ‘Prospects of LG modes in GWDs’, Phys Rev D, 79, 122002, 20091
GWADW Kyoto 18.05.2010
PDH error signal for LG33 mode
P. Fulda, A. Freise Slide 17
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 18
GWADW Kyoto 18.05.2010
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)
P. Fulda, A. Freise Slide 19
Input and transmitted LG33 beams
P. Fulda, A. Freise GWADW Kyoto 18.05.2010 Slide 20
Sinusoidal LG33
Helical LG33
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 21
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 22
Output beam residualInput beam residual Finesse residual
GWADW Kyoto 18.05.2010
Mode decomposition result
P. Fulda, A. Freise Slide 23
Since the output mode is very pure, we can therefore estimate input mode purity as :
Input purity = output power input power x LMC throughput
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 24
purity~66%
purity>99%
purity~51%
purity>99%
GWADW Kyoto 18.05.2010
Locked to even higher-order LG modes...
P. Fulda, A. Freise Slide 25
LG33 LG55 LG88
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 26
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 27
GWADW Kyoto 18.05.2010
Helical modes in TMCs Helical mode composed of vertically symmetric
and anti-symmetric sinusoidal modes TMC separates these out; only one can pass
P. Fulda, A. Freise Slide 28
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 29
Contrast enhanced for clarity Contrast enhanced for clarity
GWADW Kyoto 18.05.2010
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
P. Fulda, A. Freise Slide 30
GWADW Kyoto 18.05.2010P. Fulda, A. Freise Slide 31
GWADW Kyoto 18.05.2010
Helical modes in TMCs Helical modes are not vertically (anti-)symmetric Sinusoidal modes can be either vertically
symmetric or anti-symmetric
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Sinusoidal LG33 Cosinusoidal LG33 Helical LG33
vertical symmetry vertical anti-symmetry vertical asymmetry
LG33 phase fronts