Transcript G080328-00
Reducing Thermal Noise with Mesa Beams J. Miller [email protected] Caltech 21/3/2008 Overview Why non-Gaussian? Mesa beams Previous/ ongoing work Possible future work Other options 2 Thermal Noise Many precision measurements are limited by thermal noise Two approaches to thermal noise » change coating » change beam 3 Mesa beam - Construction Idea: Big, flat beams are better Achieve compromise between flatness of top and diffraction losses Top hat – delta functions Mesa beam – minimal Gaussians 4 Thermal noise reduction Noise Source Fused Silica (34x20cm) Ratio of displacement noise Gaussian/Mesa in mHz-1/2 Single fused silica test mass Coating Brownian ~1.9 Substrate Brownian ~1.6 Coating Thermoelastic ~1.9 Substrate Thermoelastic ~2.2 Conclusion....noise down by x2 No measured values yet 5 Comparison 6 Mirror Construction Ion source Robot Mask Substrate in rotation Sputtered atoms Silica target Two step process Step 1 » Rotation gives rough shape 500 nm/mm 7 Mirror Construction Ion source Stage 2 Substrate in translation Robot Atomic pencil Mask Large diameter optics are easy Technique limited by metrology Sputtered atoms Silica target interferometer Magnetorheological finishing is also an option 8 MH Coating Before corrective coating After 9 Experiment Design and construction of single prototype cavity Begin evaluation of mesa beams as an option for future GW detectors 10 Fundamental SIMULATION – idealised optics and alignment EXPERIMENTAL DATA mm 11 Coupling and Locking Theoretical coupling with Gaussian beam: » ~94% at MH mirror » ~91% at waist Pound Drever Hall locking Standard techniques still work 12 Higher order modes Odd contribution upon mirror tilts is just like HG01/10 ‘Hermite’ and ‘Laguerre’ families as for GB Differential wavefront sensing » successfully modelled - student project 13 Mirror tilts Data plus simulation from maps 1.39 rad 0.8 rad 0.48 rad Solid – theory Dashed – experimental 14 Alternatives Mesa beams are non-optimal Hyperboloidal beams » finite mirror effects High order LG modes Fully optimised beams Conical beams 15 Summary Mesa beams can reduce thermal noise effects by around a factor of two Work is ongoing to study the properties of these beams Moderately more susceptible to cavity perturbations Standard techniques still applicable There are other options but (to me) at present seem less favourable Main hurdle is construction of small optics 16 Thank you 17 Why non-Gaussian? Interferometry is only a means of measuring position of test masses Gaussian mode doesn’t provide optimal method of reading out test mass position Stochastic fluctuations » thermal noise Narrow, steeply sloping Gaussian beam provides poor spatial average of fluctuations 18 Mesa Beams - Motivation Well known that wider Gaussian modes are less susceptible to test mass thermal noise » penalty is higher diffraction loss Wider beams are better In order to best average the dynamic fluctuations a more uniform intensity profile is desirable Flatter beams are better Ideal beam would be a rectangular ‘top hat’ mode 19 Comparison of Modes x10 20 Benefits 21 Benefits h noise down by x1.8 @100Hz NS/NS range » 170 → 205 Mpc BH/BH range » 990 → 1143 Mpc Stochastic ΩGW » 2.34e-9 → 1.98e-9 Event rate Thermal effects less significant Good coupling to Gaussian relative to other candidates - Up by ~1.75 22 Possible Disadvantages So far no show stoppers for mesa beams Construction of mirrors is more costly, figure errors must be x2 smaller Thermal compensation may be more difficult Tilt must be controlled more tightly (x3) but mesa beams are less susceptible to instabilities Coupling to gaussian beams, much better than other candidates 23 Work so far Resonated mesa beam Implemented robust locking scheme Investigated properties of fundamental mode including tilt sensitivity Recent theoretical exploration of thermal effects Auto-alignment work in progress 24 Possible Future Work Investigate properties of coupled Gaussian and non-Gaussian cavities Conduct full theoretical study of dual-recycled mesa beam interferometer Implement mesa beams in a fully suspended interferometer Evaluate alternatives to mesa beams 25 Alternatives Optimised mesa beams – finite mirror effects Hyperboloidal beams High order TEM modes Conical/Fully optimised beams Gains are available but at increasing cost to the experimenter 26 Thermal noise Brownian » internal friction » impurities, dislocation of atoms Thermoelastic Thermorefractive » refractive index changes with temperature dn 0 dT » random heat flow in substrate and coating » non-null coefficient of thermal expansion » thermodynamic fluctuations result in displacements 0 27 Motivation Dynamical surface fluctuation Sensitive to test mass position as sensed by laser Test Mass Steep gradient provides a poor spatial avg. For Gaussian Beams (GB) bigger is better » diffraction loss S ~ 1 / wn 28 Ideal beam Dynamical surface fluctuation Wide Flat-topped beam Not really a valid picture for finite masses 29 Mesa beam/MexHat Mirrors Mesa Field at Mirror U [( x x0 ) 2 ( y y0 ) 2 ][1 i ] dx0 dy0 C exp 2w0 D INTENSITY MIRROR Gaussian Mesa •Also Hyperboloidal, Bessel & Laguerre-Gauss beams amongst others 30 The experiment Like an ‘arm’ cavity Transforms GB to MB 31 Our experiment Rigid, suspended, FP cavity Folded once Alignment controlled by PZTs Vacuum possible 3.657 m 32 Our experiment 33 MH mirror map 34 MH mirror map Central bump 35 ‘Flat’ mirror map Our cavity has two flat mirrors in addition to Mexican hat 5nm peak to valley Thanks to GariLynn 36 Tilts of Spherical Mirrors Tilts of spherical mirrors translate optical axis 37 Tilt sensitivity Measure max tilt using lock in detection Use chopper and secondary laser to align and capture beam at correct tilt Laser Chopper Optical lever PZT 38 Tilt sensitivity - results 1.39 rad 0.8 rad 0.48 rad 39 Gaussian? Modes resemble Hermite and Laguerre sets MH10 fit LG10 fit 40 Future work - coupled cavity 3-mirror coupled system mechanics simulation and design fields, coupling, alignment locking » » » » single side band amplitude modulation phase modulation sub-carrier 41 ‘3-mirror’ coupled cavity 42 Tilt Instability Serious tilt instability for nearly flat cavity (Sidles, Sigg) » Similar to Gaussian beam cavity Problem is mitigated by nearly concentric cavities Ratio of torques for concentric mesa (CM) and concentric Gaussian (CG) cavities TCM / TCG = 0.91 43 Concentric cavity • • Flat mirrors - Add MH profile to flat substrate Concentric mirrors - Subtract MH profile from spherical substrate (gr-qc/0409083) 44 Concentric cavities Mirror profile must not be as steep as the maximum resolvable slope 45 Thermal effects Study deformation of arm cavity mode with absorbed power » power limit for mesa beams? Thermal noise implications Thermal compensation system (TCS) thoughts Model » » flat-flat, mesa, AdLIGO cavity no substrate absorption. 5x less power absorbed vs. coating » no lensing » input beam fixed » instant response Static FFT model and Mathematica AdLIGO TCS Thanks to Hiro 46 Heating - Gaussian For Gaussian beam - mirrors become less concave and spot size goes from 6 to ~5.4cm Total thermal noise increases by ~11% Thermoelastic deformation for AdvLIGO Pcirc = 850kW, Coating absorption=0.5ppm 0.425 W ~50nm 47 Heating - Mesa 2.5ppm ~90nm 1.5ppm ~60nm 1ppm ~40nm 0.5ppm ~20nm 48 Heating - mesa 0ppm 0.5ppm 1ppm 1.5ppm 2.5ppm 49 MH thermal noise Semi analytical model – numerical integrals Noise goes DOWN with increased absorption! To be checked by FEM Results are surprising but similar has been seen before... 50 MH losses Other things discovered during this study Insertion (mode-matching) loss lower than expected » always good news Diffraction loss higher » wide parameter space for tuning 51 TCS Strategy Make ‘bad’ mirrors which achieve the correct figure at operating power Turned off for science mode – no noise injected Need to know optics very well – single point solution Deformable OR Mirror LASER Scanning laser Ring heaters 52 TCS Gaussian 53 TCS Mesa 54 Other beams – LG55 LG beams » x2.5 better HG beams » formalism breaks down 55 Other beams - hyperboloidal FLAT CONCENTRIC 56 Other beams - hyperboloidal Intensity h(r) 57 ‘Conical’ Beams Conical Concentric Flat mesa M. Bondarescu 58 Other beams – fully optimised 59 Other beams – fully optimised Substrate Brownian Optimisation is difficult – done for single noise sources Realistic constraints makes large difference MB non optimal up to x3 better achievable Coating Substrate Thermoelastic 60 TCS Gaussian 61 TCS Mesa 62 Gaussian vs. Mesa Mirror tilts: 3-4x more susceptible Transverse displacement: Equal Figure errors – 2x more sensitive Need to control to 10-8 rad. level gr-qc/0409075 63 Thermal noise - Gaussian 64