Matrix Heater in the Gravitational Wave Observatory GEO 600
Holger Wittel, Christoph Affeldt, Aparna Bisht, Suresh Doravari, Hartmut Grote, James Lough, Harald Lück, Emil Schreiber, Kenneth A. Strain, Karsten Danzmann
MMatrix Heater in the Gravitational WaveObservatory GEO 600
H Wittel , C Affeldt , A Bisht , S Doravari , H Grote ,J Lough , H L¨uck , E Schreiber , K A Strain andK Danzmann E-mail:
[email protected] Max Planck Institute for Gravitational Physics and Gottfried Wilhelm LeibnizUniversit¨at Hannover, D-30167 Hannover, Germany SUPA, School of Physics and Astronomy, The University of Glasgow,G12 8QQ, United Kingdom School of Physics and Astronomy, Cardiff University, United Kingdom
Abstract.
Large scale laser interferometric gravitational wave detectors(GWDs), such as GEO 600 require high quality optics to reach their designsensitivity. The inevitable surface imperfections, inhomogeneities and light-absorption induced thermal lensing in the optics can convert laser light fromthe fundamental mode to unwanted higher order modes, and pose challenges tothe operation and sensitivity of the GWDs.Here we demonstrate the practical implementation of a thermal projectionsystem which reduces those unwanted effects via targeted spatial heating of theoptics. The thermal projector consists of 108 individually addressable heatingelements which are imaged onto the beam splitter of GEO 600. We describe theoptimization of the spatial heating profile and obtained results. a r X i v : . [ a s t r o - ph . I M ] J un atrix Heater in GEO 600
1. Introduction
The gravitational wave (GW) observatory GEO 600 [1][2][3] is a 600 m long dual-recycled [4] Michelson interferometer with folded arms, located south of Hanover,Germany.As all other current GWDs, GEO 600 uses the DC-readout method [5] forobtaining a GW measurement signal; a self-homodyne scheme, in which a photodetector measures the DC power of the output beam of GEO 600. The output beamhowever, is dominated by unwanted high order spatial modes (‘HOMs’) of laser light.Typically, the output beam of GEO 600 consists of 6 mW of TEM carrier light for theDC-readout, about 1 mW of TEM sidebands used for controlling the interferometer,and about (depending of the alignment state of the interferometer) 30 mW of unwantedHOMs.To prevent HOMs from reaching the main photo detector, a small optical cavity,the output mode cleaner (‘OMC’) [6] as mode selective element is placed in frontof the main photo detector (see Figure 1). The OMC is mode-matched to themain interferometer beam and its length is controlled to be resonant to the TEM fundamental mode of the beam. HOMs (and control sidebands) are then reflected offthe OMC. A simplified optical layout of GEO 600 is shown in Figure 1. Imperfect optics and thermal effects such as thermal lensing can convert TEM light into HOMs. Even though an OMC is an effective way preventing HOMs fromreaching the main photo detector, they can still adversely affect the operation ofthe interferometer in several ways. For one, they can introduce spurious signals onauxiliary photo detectors which are used for the alignment of the detector subsystemsand optical cavities [7].Stray light is a challenge for all GWDs. Since the spatial extent of HOMs dependson their order ‡ , large order HOMs extend further than the optics of GEO 600. Theycan bounce off the (partly reflective) inside walls of the vacuum system, and a fractionof them may eventually recombine with the main beam.The walls of the vacuum system are not isolated from ground motion. Theyare, however, partly reflective and any light that reflects or scatters from them willexperience strong phase modulation. If high order modes reach the walls they willpick up varying phase shifts from the vibrating surface. A fraction of this light caneventually recombine with the main beam where the noise may affect the measurement[8]. At the limit of very large conversion of light from the TEM mode to HOMs,they will act as a loss channel and limit the possible power build up in the powerrecycling cavity, thus lowering the (usually photon shot noise limited) sensitivity.At GEO 600 we identified four main sources of HOMs.(i) Misalignment of the suspended optics.
While automatic alignment systems keep the optical system aligned over longtimescales ( >
10 s), at timescales of a Hertz and faster, misalignments can causefluctuations in the power of HOMs, as can be seen by the spikes in the dark port ‡ it generally varies with square root of the mode order atrix Heater in GEO 600 Wrong curvature of the East end mirror MFE.
The radius of curvature of the mirror MFE deviates from its design value (686 mvs designed 666 m), and made the initial operation of GEO 600 with this mirrorimpossible. This was corrected by installing a ring heater [9] behind this mirror.By thermal radiation it creates a thermal gradient in the mirror. Due to thermalexpansion of the bulk material, the mirror’s radius of curvature gets closer to thedesired value.While this made the operation of GEO 600 possible, it was discovered later thatthe heating ring creates astigmatism in the mirror, i.e. it curves the mirrordifferently in horizontal and vertical direction. Additional heaters were installed atrix Heater in GEO 600
Other imperfection of the optics, such as micro-roughness and dustparticles.
Even though GEO 600 uses the highest quality optics that were available at thetime of installation, and is set up in a clean room environment, small imperfectionsand contamination on the optics are unavoidable. At low circulating power, whenthermal effects are insignificant, we attribute all HOMs to imperfections of theoptics. We expect these ‘cold’ HOMs to scale linearly with the circulating powerin GEO 600, with a scaling factor of roughly 30 mW of HOMs at the output portper 2.2 kW circulating power.(iv)
Thermal effects, in particular thermal lensing in the beam splitter.
Due to the high circulating laser power in the power recycling cavity (PRC) ofGEO 600, thermal effects and thermally induced HOMs have to be considered. Inparticular the beam splitter is a strong source of thermally induced HOMs, sincedue to GEO’s unique optical layout without arm cavities, the PRC has a veryhigh power build up, and thus a high power passing the beam splitter substrate.Additionally, the compact layout of the central building led to an optical designplacing the waist of the interferometer near the beam splitter, further increasingpower density. As an optically transmissive element inside the PRC, the beamsplitter exhibits a power dependent thermal lens which converts TEM lightinto HOMs. While the reflective optics in the PRC also show thermal lensingeffects, we expect the beam splitter to have the largest contribution, for severalreasons: In the highly reflective mirrors, absorption in the coating will introducea bulging of the mirror surface due to thermal expansion. In the beam splitterhowever, we get an additional effect due to the substrate absorption and thethermal change of the refractive index § . Also (equal) absorption in both endmirrors would constitute a common mode effect, which would at least partlycancel in the (differential) output port.Furthermore, since the beam passes the beam splitter at an angle, the resultingthermal lens is astigmatic. For an increase in the circulating laser power inGEO 600 we will attribute all non-linear increase in HOMs to be of thermalorigin. This work investigates a method of counteracting the effects mentioned above byutilizing thermal actuation; more specifically by projecting a specific heating patternto the beam splitter of GEO 600. By this means, it is possible to selectively delayareas of the laser beam wavefront, mostly due to the thermo-refractive effect. In thisway – with an appropriately shaped spatial heat distribution – it may be possible tocorrect both thermal lensing effects and mirror imperfections.Similar approaches have been investigated in the past. The heater setup at the endmirror of GEO 600 has been mentioned above, but also other GWD have investigated § roughly ten times the size of the thermal expansion effect [12] atrix Heater in GEO 600 laser projectors with masks are usedto correct the laser beam wavefront [15]. However, technical noise of the CO lasershas to be considered, hence they are used for small corrections using a mask, heating acompensation plate outside of the highly sensitive arm cavities, while the ring heatersdo the bulk of the compensation.Different approaches that do allow arbitrary heating profiles have also beenproposed: [16] discusses the use of a scanning CO projector, and [17] providessimulations for a projector using a grid of 3 ×
2. Setup
The thermal projection system consists of an array of 9 ×
12 small heating elementslocated outside of the vacuum system of GEO 600, and an imaging system to projectsaid array to the surface of the main beam splitter of GEO 600.
The heater array is a custom PCB with 108 small heating elements mounted on it.The individual heaters are re-purposed commercial platinum resistance temperaturedetectors (‘Pt100’). Each Pt100 can produce a Planck spectrum with about 1 W ofthermal radiation (at 900 K) in the desired wavelength range (cid:107) which is being projectedonto the beam splitter.The Pt100 resistors are arranged in a rectangular grid of 9 ×
12 (height × width),with a center-to-center spacing (‘pixel size’) of 7.5 mm × × w). The heatersare standing upright on the PCB, facing angled and polished aluminum surfaces ofa reflector grille, such that radiation from both flat surfaces of the Pt100s can beutilized. The setup of the heater array is shown in Figure 2. Each heater can beindividually controlled via multiplexed driving.The heater array is imaged to the surface of the beam splitter via the imagingsystem. In this case, we used an off axis parabolic aluminum mirror and a potassium-bromide (KBr) lens, which project the image through a zinc-selenide (ZnSe) vacuum-window onto the beam splitter. All of the materials for the optics were chosen for good(broadband) transmission of thermal radiation from the heater array. The projectionsystem is chosen to have a magnification factor of two. The throughput of the opticalsystem is limited by the solid angle between the vacuum viewport and the beamsplitter to a numerical aperture NA of 0.06. (cid:107) The wavelength range that is absorbed by the beam splitter substrate material (Suprasil 311 R (cid:13) ),i.e. longer than 4 µ m. atrix Heater in GEO 600 (a) Photograph of the heater array.(b) Cross section of the heater array. Figure 2: Photograph and cross section of the heater array.
3. Procedure
As a first step in the operation of the thermal projection system, it is necessary toalign the projected image of the heater array to the beam path in the beam splitterof GEO 600.The scheme we have devised for doing this works by designating a specific heateras ‘center pixel’ and modulating its driving current, which will result in modulated(spatially limited) heating on the beam splitter. Due to the dn/dT effect, the samemodulation will couple into the differential arm length signal of GEO 600, dependingon the overlap of the heated area with path of the main laser beam. In the alignmentprocess, the overlap of the central pixel with the laser is maximized.Furthermore, we can use this method to map out the overlap of each individualpixel with the fundamental TEM mode of the laser beam in the beam splitter, asshown in Figure 3. As expected, due to the laser beam hitting the beam splitter atan angle close to 45 degrees, the beam profile appears to be oval.Finally we try to reduce the amount of HOMs produced in GEO 600. For this,it is necessary to find a suitable setting for each heating element (‘heating pattern’).Using an approach in which individual heaters are adjusted one by one can be tedious,due to the large number of degrees of freedom and the long thermal timescales.We followed two approaches to determine a suitable heating pattern: atrix Heater in GEO 600 mode of the main laser beam in GEO 600. For comparison,the (1/e in intensity) size of the laser beam spot on the beam splitter is representedvia white dashes, while the outline of the beam splitter is depicted in the background.
1. The naive approach:
Since a large fraction of the HOMs in GEO 600 originatesfrom thermal effects/ thermal lensing at the beam splitter, it should be possible tomitigate this issue by an annular heating pattern, which will create a negative thermallens. Overall the aim is to flatten the thermal gradient caused by the high poweredlaser beam in the beam splitter. Via trial and error, using the total power of HOMs atthe output port of GEO 600 as a measure, we a suited annular heating pattern. Theresult is shown in Figure 4.
2. The actuation matrix approach:
As a second way to find a suitable heatingpattern, we employed a more deterministic technique, as described in [18]. Thistechnique works by defining a base-set of heating patterns. Each pattern of the baseset is applied, and the effect on HOMs is recorded. The relation that is obtained thisway can be expressed in matrix A in the form: (cid:126)HOM = A (cid:126)h, with the (cid:126)HOM being the power in the HOMs, and (cid:126)h being a vector of the basisheating patterns.Once the matrix A is known, it can be inverted, and one can obtain a linearcombination of the basis heating patterns which produces a desired distribution ofHOMs ¶ . A reasonable basis set of heating profiles may be the phase profile of thehigh order Hermite-Gauss (HG) modes that we want to affect. We expect especiallythe second order HG modes to be of importance, since a mode mismatch due to athermal lens in the beam splitter would mostly produce these modes.Due to several practical challenges, we had to adapt the procedure in [18], whichwe will describe in the following.In theory one would use a bias in the heating, i.e. choosing half power for allheaters as zero point, as this would allow for ‘negative’ heating. In our setup however,we noticed an increase in HOMs with all heaters at a constant power, which we ¶ Here we are only interested in the special case of minimizing the amount of HOMs atrix Heater in GEO 600 mode. Bychanging its length, we can make it resonant for HOMs of different orders instead,and measure their power on the main photo detector. A drawback of using the OMCas measurement tool for HOMs is that it is mode-degenerate; all modes of the sameorder will resonate at the same length, i.e. an HG mode cannot be distinguishedfrom an HG mode with this method. Therefore, this method will work best formode orders which are dominated by a single HOM. In GEO 600 this is the case formode orders 2, 7, and 8.
4. Results
We tested the two approaches from above, and judge the outcome by the effect on totalpower at the output port of GEO 600, which is dominated by HOMs. Figure 5 showsa time series of the power at the output port of GEO 600 at the standard operatingpower (2.2 kW circulating power in the PRC) and with an increased circulatingpower (3.5 kW) to increase the influence of the thermal lensing effect. Note thatfor the experiments depicted in Figure 5, the TEM content in the output beamwas intentionally reduced to be < power is keptconstant, any changes in the output power can be attributed to HOMs.With the annular shape, based on the naive approach, we obtain an improvementin HOM power in the order of 10% (‘1’ in Figure 5).As a next step we apply a single heating profile from the chosen basis set, witha shape similar to the HG modes (‘2’ and ‘2a’ in Figure 5), since we expect thismode to be affected the most when raising the interferometer power and it is one ofthe strongest modes even at lower power. With this we achieve an improvement inthe order of 15% (standard power) and 20% (increased power).We also tested the heating profile obtained by the full actuation matrix (‘3’ inFigure 5), but do not achieve a significant improvement in HOMs. We attribute thisto the fact that many of those mode orders are not dominated by a single HOM andtherefore the actuation matrix based on the (mode degenerate) OMC may not beaccurate for the degenerate mode orders. When reducing the actuation matrix tothe mode orders dominated by a single mode (2,7,8 in GEO, ‘4’ in the Figure), weobtain results similar to the HG heating profile. Furthermore, by solving the inverseactuation matrix, we determine that the required heating profile contains elementsthat are greater than the maximum power that the heater array can apply. Therefore,we combined this heating profile with the best annular one to increase the total powertransferred to the beam splitter (by involving more heater elements). This results inan improvement in HOMs of 31% in the high- and 24% in the standard power state(‘5a’ and ‘5’ respectively in Figure 5). atrix Heater in GEO 600 heating, to counteract HG02 moderight: heating profile against HG modes 2,7 and 8, via reduced actuation matrix (a) Dark port power.(b) Cutout view of select areas from above. Figure 5: Plot of the time series of the power at the dark port at GEO 600 (dominatedby HOMs, with < content) at normal and increased (1.6 h – 4.5 h)operating power. Periods during which the thermal projector is used to suppressHOMs are numbered and marked by the colored background. atrix Heater in GEO 600
5. Summary, Outlook and Discussion
We have demonstrated the use of a thermal projector for the generation of arbitraryheating profiles in a large scale GWD, and achieved a reduction of unwanted HOMs,and therefore an improvement in interferometer contrast by 30%. One finding is thatmore power delivered to the beam splitter by the thermal projection system may bebeneficial. Therefore, the thermal projection system is currently being upgraded; Theoptical system outside of the vacuum chamber has been replaced by an in-vacuum lens,which due to the increased opening angle, will allow for a factor of five increase in thepower transmission. Furthermore, the heater matrix in this work used a row-by-rowmultiplexing for driving the heaters, which is easier to build, but produces a signal inGEO 600 at the multiplexing frequency. A new layout will work without multiplexingand instead provide an individual channel for each heater.While the method of determining an ideal heating profile has been shown towork, the measurement of the exact actuation matrix poses a challenge with theexisting infrastructure (i.e. with the mode degenerate OMC). An alternate approachcould be to use the obtained heating profile for the well-defined HOMs, and use it as astarting point for an in-situ optimization, for example via the Newton method. Globaloptimization methods searching beyond local maxima, as e.g. simulated annealing orgenetic algorithms, may be useful as well.
Acknowledgments
We thank the GEO collaboration for the development and construction of GEO 600.The authors are also grateful for support from the Science and Technology FacilitiesCouncil (STFC), the University of Glasgow in the UK, the Max Planck Society, theBundesministerium f¨ur Bildung und Forschung (BMBF), the Volkswagen Stiftung,the cluster of excellence QUEST (Centre for Quantum Engineering and Space-TimeResearch), the international Max Planck Research School (IMPRS), and the State ofNiedersachsen in Germany.This article has been assigned LIGO document number ligo-p1800116.
References [1] H L¨uck et al
The upgrade of GEO600 , 2010, Journal of physics: conference series 228, 012012[2] C Affeldt et al,
Advanced techniques in GEO600 , 2014, Class. Quantum Grav. GEO 600 and the GEO-HF upgrade program: successes and challenges , 2016,Class. Quantum Grav. Dual recycling for GEO 600 , 2004 Class. Quantum Grav. S473[5] S Hild et al,
DC-readout of a signal-recycled gravitational wave detector , 2009 Class. QuantumGrav. The output mode cleaner of GEO 600 , 2012 Class. Quantum Grav. Alignment sensing and control for squeezed vacuum states of light , 2016 Opt.Express , 146-152[8] S Hild, Beyond the first Generation: Extending the science range of the Gravitational WaveDetector GEO 600 , P 31, PhD Thesis, Leibniz University Hannover, Febuary 2007.[9] H L¨uck et al,
Thermal correction of the radii of curvature of mirrors for GEO 600 , 2004 Class.Quantum Grav. S985[10] H Wittel et al,
Thermal correction of astigmatism in the gravitational wave observatoryGEO 600 , 2014 Class. Quantum Grav. Central heating radius of curvature correction (CHRoCC) for use in large scalegravitational wave interferometers , 2013 Class. Quantum Grav. atrix Heater in GEO 600 [12] W. Winkler et al, Heating by optical absorption and the performance of interferometricgravitational-wave detectors , 1991, Phys. Rev. A 44, 7022[13] J Abadie et al,
Advanced LIGO , 2015 Class. Quantum Grav. Advanced Virgo: a 2nd generation interferometric gravitational wave detector ,2015 Class. Quantum Grav. Overview of Advanced LIGO adaptive optics , 2016, Appl. Opt. , 8256-8265[16] R Lawrence et al, Adaptive thermal compensation of test masses in advanced LIGO , 2002 Class.Quantum Grav. Reduction of higher order mode generation in large scale gravitational waveinterferometers by central heating residual aberration correction , Phys. Rev. D 87, 082003(2013)[18] G. Vajente,