Beam shaping for thermal noise reduction

Beam shaping for thermal noise reduction …advantages in using Laguerre-Gauss modes Foto by Nickster2000 Paul Fulda, Andreas Freise GWADW, Kyoto, 18.05.2010

Overview • Alternative beam shapes • Laguerre modes versus other beam shapes • Experimental results with LG modes GWADW Kyoto 18.05.2010

Possible Thermal Noise Reduction • (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 thermal noise GWADW Kyoto 18.05.2010

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 GWADW Kyoto 18.05.2010

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 GWADW Kyoto 18.05.2010

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] GWADW Kyoto 18.05.2010

Simulation Experimentaldata Flat beams in GW community • 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 [Agresti et al JPCS 2006] [Talks by J. Miller 2008] GWADW Kyoto 18.05.2010

Optimised beams [Bondarescu et al PRD 2008] [VinetLiv. Rev. in Relativity, 2009] Bondarescuet al (and others) havetheoretically optimisedthe 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. Intensity profile Mirror profile GWADW Kyoto 18.05.2010

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 GWADW Kyoto 18.05.2010

Experimental setup for mode generation and cleaning GWADW Kyoto 18.05.2010

Lab optical path for mode conversion GWADW Kyoto 18.05.2010

Generated LG beams Phase modulation Phase + amplitude modulation 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 1 1 Chelkowski, S. et al, ‘Prospects of LG modes in GWDs’, Phys Rev D, 79, 122002, 2009 GWADW Kyoto 18.05.2010

PDH error signal for LG33 mode 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) GWADW Kyoto 18.05.2010

Input and transmitted LG33 beams Sinusoidal LG33 Helical LG33 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 Input beam residual Output beam residual Finesse residual GWADW Kyoto 18.05.2010

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 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 purity >99% purity ~66% purity >99% purity ~51% GWADW Kyoto 18.05.2010

Locked to even higher-order LG modes... LG33 LG55 LG88 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 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 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 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 LMCsee 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 GWADW Kyoto 18.05.2010

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 LG33phase fronts Sinusoidal LG33 Cosinusoidal LG33 Helical LG33 vertical symmetry vertical anti-symmetry vertical asymmetry GWADW Kyoto 18.05.2010

Beam shaping for thermal noise reduction