We propose thin single-layer grating waveguide structures to be used as
high-reflectivity, but low thermal noise, alternative to conventional coatings
for gravitational wave detector test mass mirrors. Grating waveguide (GWG)
coatings can show a reflectivity of up to 100% with an overall thickness of
less than a wavelength. We theoretically investigate GWG coatings for 1064nm
based on tantala (Ta2O5) on a Silica substrate focussing on broad spectral
response and low thickness

A Bunkowski

Agresti J

D Friedrich

Harry G M

K Danzmann

Lemarchand F

Moharam M G

O Burmeister

R Schnabel

Sharon A

English

arXiv

We propose thin single-layer grating waveguide structures to be used as high reflectivity, but low thermal noise, alternative to conventional coatings for gravitational wave detector test mass mirrors. Grating waveguide (GWG) coatings can show a reflectivity of up to 100% with an overall thickness of less than a wavelength. We theoretically investigate GWG coatings for 1064 nm based on tantala (Ta2O5) on a silica substrate focusing on broad spectral response and low thickness

Bunkowski, A.

Burmeister, O.

Friedrich, D.

Danzmann, K.

Schnabel, R.

MPG.PuRe

INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITYClass. Quantum Grav. 23 (2006) 7297–7303 doi:10.1088/0264-9381/23/24/007High reflectivity grating waveguide coatings for1064 nmA Bunkowski, O Burmeister, D Friedrich, K Danzmann and R SchnabelMax-Planck-Institut fu¨r Gravitationsphysik (Albert-Einstein-Institut) and Institut fu¨rGravitationsphysik, Leibniz Universita¨t Hannover, Callinstr. 38, 30167 Hannover, GermanyE-mail: alexander.bunkowski@aei.mpg.deReceived 1 August 2006, in final form 8 October 2006Published 3 November 2006Online at stacks.iop.org/CQG/23/7297AbstractWe propose thin single-layer grating waveguide structures to be used as highreflectivity, but low thermal noise, alternative to conventional coatings forgravitational wave detector test mass mirrors. Grating waveguide (GWG)coatings can show a reflectivity of up to 100% with an overall thickness of lessthan a wavelength. We theoretically investigate GWG coatings for 1064 nmbased on tantala (Ta2O5) on a silica substrate focusing on broad spectralresponse and low thickness.PACS numbers: 04.80.Nn, 42.79.Gn, 42.79.Dj1. IntroductionDedicated research during the last few years has revealed that thermally driven motion of thetest masses, the so-called thermal noise [1], is larger than foreseen in future gravitational wavedetectors. A major, but previously underestimated, contribution is given by the multilayerdielectric coating stacks of the high reflectivity test mass mirrors [2, 3]. This currently limitsthe design sensitivity of the advanced LIGO detector [4]. In conventional schemes, up to 40layers of Ta2O5 and SiO2 with an optical thickness of a quarter wavelength are needed to reachhigh reflectivities sufficiently close to 100%. The thermal noise of the coating is due to themechanical loss of the layers with a dominant contribution from Ta2O5. New concepts arerequired that have less loss but still achieve the required high reflectivity. One approach beingpursued is to design an alternative multilayer system deviating from the classical quarter wavedesign and containing less Ta2O5 [5]. Doping of Ta2O5 with TiO2 has also been investigatedand a reduction of the loss by a factor of 1.5 was observed [6]. Another approach is toavoid high reflection coatings at all by the use of corner reflectors which employ total internalreflection instead of multiple interference at different layers to reach high reflectivity [7].However, in this case thermo-refractive noise which results from a temperature-dependent0264-9381/06/247297+07$30.00 © 2006 IOP Publishing Ltd Printed in the UK 72977298 A Bunkowski et alSubstrateWaveguideGratingsdαgnLnHIncident rayr0T0R1TTotal internalreflectionDestructiveinterferenceConstructiveinterference1T*0R*1R*Figure 1. Schematic of a grating waveguide structure in a simplified ray picture. For clarity, anon-zero angle of incidence and only one first-order transmission are shown.refractive index and also thermal lensing are increased due to the large optical path length inthe substrate material.Grating waveguide structures [8] provide another possibility of constructing highreflectivity devices. The interest of earlier work on grating waveguides lay mainly in narrow-band (highly resonant) devices for applications in optical filtering [9] and optical switching[10]. However, grating waveguide structures can also provide broadband (weakly resonant)reflectors. This makes them interesting candidates for test mass coatings in gravitational wavedetectors, because only a very small amount of dielectric coating material is required whichresults in a considerable reduction in coating thermal noise.2. Resonant grating waveguide structuresThe remarkable property of a grating waveguide (GWG) is that it can show a reflectivity of100% for a given optical wavelength λ despite its thickness of typically less than a micron.For an extensive overview of grating waveguides we refer to [11]. In the simplest case, aGWG consists of a substrate material with low refractive index nL followed by a waveguidelayer with high refractive index nH which has periodic corrugation with period d as shown infigure 1. A simplified ray picture [8] can be used to understand its behaviour. The structurecan be designed such that light incident onto the grating will only produce one diffractionorder in reflection (0R) but three diffraction orders in transmission (0T and ±1T). (For clarity,the −1 T order has been omitted in figure 1.)The first-order beams are coupled into a layer of high refractive material where they arestored due to total internal reflection. Light inside the waveguide is also coupled out via thegrating. For a proper choice of grating parameters and incident angle, the light coupled outfrom the layer (1R*) interferes destructively with the zero-order transmitted beam (0T) andthe device is a perfect reflector.The possible parameter range for the period d depends on the angle of incidence α, the(vacuum) laser wavelength λ (λ0), and the refractive indices nL and nH and can be calculatedHigh reflectivity grating waveguide coatings for 1064 nm 7299from the grating equationsin α + sin βm = mλ/d, (1)where βm is the angle of the mth diffraction order. For test mass mirrors in gravitational wavedetector Michelson interferometers, the angle of incidence is typically restricted to α = 0. Toensure that only the m = 0 order is allowed in reflection,d < λ0 (2)has to hold. Another condition is that only |m|  1 orders in transmission exist from whichfollows that1 < dnHλ0< 2. (3)Total internal reflection of the first order at the boundary of the waveguide and the substratematerial is ensured ifd < λ0/nL. (4)A resonant grating waveguide structure has analogous behaviour to a Fabry–Perotresonator: with decreasing coupling to the waveguide the finesse of the structure increases[8]. For high reflectors in GW detectors high finesse structures are disadvantageous, becausesmall deviations from the design parameter would dramatically decrease the reflectivity forthe desired wavelength λ0. Additionally, the power build-up inside a high finesse waveguidecould be a problem for high-power laser interferometers. Accordingly, a broadband resonanceis desired for the high reflector.3. Spectral response of waveguide coatingsUsing Rigorous-Coupled-Wave (RCW) analysis [12] it is possible to calculate the opticalproperties of the structure. Design considerations for binary gratings must include groovedepth g, waveguide thickness s and ridge width r, see figure 1, in addition to the above-mentioned period d and refractive indices nL and nH. The goal is to design a broadbandreflection being less sensitive to fabrication tolerances and avoiding the problem of strong lightpower build-up in the waveguide. Here, we restrict ourselves to nH = 2.04 and nL = 1.45.This corresponds to tantala and fused silica which are the favourite high index coating materialand test mass material, respectively [2].According to (2)–(4) the following constraints apply to the period when one assumes thecommonly used Nd:YAG laser wavelength of λ0 = 1064 nm:521 nm < d < 734 nm. (5)For a broadband response, the calculated coupling to the waveguide which corresponds to thediffraction efficiency of the ±1T ray should be maximized. It only depends on the gratingproperties g and r/d but not on the thickness s of the waveguiding layer. Figure 2 shows howthe coupling depends on the groove depth g and fill factor (r/d) for selected values of d forTM (magnetic field vector is parallel to the grooves) illumination. The plots indicate that themaximum coupling increases with increasing period d. This is illustrated in figure 3 where weplotted the maximum values of the coupling obtained when g and r/d were varied accordingto figure 2 versus grating period d for TM and TE polarization. Hence, for the purpose of abroadband reflection peak large values for the grating period are favourable.The direct connection between coupling and spectral width of the resonance is illustratedin figure 4. The right-hand side of the figure again shows the coupling to the waveguide7300 A Bunkowski et alFigure 2. Coupling to the waveguide for each of the ±1 T rays (colour-coded) versus groove depthg and fill factor r/d for TM illumination and selected values of d.522 552 582 612 642 672 702 73205101520253035d [nm]maximal coupling [%] TMTEFigure 3. Maximum achievable coupling per diffraction order ±1 T for TM and TE polarizationversus grating period d. For each point the groove depth was varied between 0 and 1 µm and thefill factor between 0 and 1.[%]Figure 4. Right: TM coupling to the waveguide (colour-coded) versus groove depth and fill factor.Left: spectral response of three waveguide structures corresponding to the marked values in theright figure. From a deviation of greater than −20 nm inequality (4) is no longer fulfilled whichleads to the kinks in the curves.versus groove depth and fill factor for a specific grating period. For three selected values ofthe groove depth (marked with three asterisks) and fixed fill factor, we determined the optimalwaveguide thickness s0 for a resonance peak around λ0 = 1064 nm. On the left-hand side offigure 4, we show the calculated reflectivity versus the deviation from λ0 for the correspondingwaveguide coating.High reflectivity grating waveguide coatings for 1064 nm 7301Figure 5. Colour-coded TM reflectivity of a waveguide structure versus groove depth andwaveguide thickness s. The values for d, r/d and g correspond to the dotted line in figure 4(right). In this case, 100% reflectivity can be obtained for vanishing layer thickness at a groovedepth of g ≈ 0.39 µm.We note that for materials with higher refractive index than nH = 2.04 higher diffractionefficiencies (couplings to the waveguide) and therefore even broader reflection peaks arepossible [13, 14].4. Thickness of the coatingThe crucial factor for coating thermal noise in gravitational wave detector test masses is theoverall thickness of the high index coating material. To reach a reflectivity of 1 − R =10 ppm with a λ/4 stack of SiO2 and Ta2O5, typically 40 layers are needed, adding up to20λ/(4nH) ≈ 2.6 µm overall tantala thickness. In contrast to this, a grating waveguide mirrorcan get along with a tantala thickness of much less than a wavelength.In addition, if the total thickness of tantala in the waveguide structure is to be comparedwith a conventional mirror, one has to take into account that the grating region is not uniformlyfilled. Hence to first-order approximation one can assume that the coating thermal noise shouldbe proportional to an effective tantala thickness of s + g(r/d).The layer thickness s determines the phase of the light travelling in the waveguide andhence the resonance condition of the device. The thickness s0 for which a resonance occursvaries if the grating parameters g, r and d are changed as illustrated exemplary in figure 5,where the calculated power reflectivity is plotted versus the groove depth and the waveguidethickness. One can see a periodic behaviour of the reflectivity as s varies as expected. Moreinteresting to note is that for a certain value of g the 100% reflectivity resonance occurs ats = 0. Accordingly, the grating itself can provide perfect reflection and no waveguide layeris needed. This is extremely useful since the amount of the high index material can be greatlyreduced. For vanishing waveguide layer thickness, the explanation of the device via the raypicture presented in figure 1 seems to break down. However, the results are based on a RCWanalysis which is still valid for s = 0.An optimal design of a grating waveguide coating for gravitational wave detectors will bea trade-off between the broadest spectral response and the smallest effective tantala thickness.As an example, we consider the GWG corresponding to the dashed (green) curve on the left-hand side of figure 4 which still has λFWHM ≈ 22 nm. With g = 0.3 µm and s ≈ 0.06 µm,the effective tantala thickness is only about 0.24 µm. This suggests a thermal noise reductionby more than an order of magnitude compared to a conventional coating.7302 A Bunkowski et alFigure 6. (Colour-coded) Reflectivity plotted as 1-R versus the deviation from optimal wavelengthλ0 and deviation from optimal waveguide thickness s0 ≈ 239 nm. Other parameters for the grating:g = 0.6 µm; r/d = 0.52.5. Parameter tolerancesWhen designing diffractive structures one also has to consider how accurately gratingparameters and layer thicknesses can be manufactured by state-of-the-art procedures andhow strongly deviations from design values affect the performance of the waveguide coating.Here, we consider the fabrication errors in the waveguide thickness and how they can becompensated by tuning the laser wavelength. Figure 6 shows how the power reflectivity Rof a waveguide is affected when the thickness of the waveguide or the wavelength of thelaser deviates from their optimal values s0 and λ0, respectively. A typical power reflectivityrequirement for GW detectors is (1 − R) < 10 ppm. Typical production accuracies of thinfilms are on the order of 1 nm. The deviation from s0 could be compensated by tuning thelaser wavelength to a small fraction of a nanometre. Deviations in other grating parametersaffect the reflectivity by a similar way.6. ConclusionWe have proposed a high reflectivity grating waveguide coating for advanced gravitationalwave detectors which can provide perfect reflection despite the small amount of coatingmaterial that is needed. This has great potential to lower the coating thermal noise of highreflectivity mirrors. Focusing on a laser wavelength of λ0 = 1064 nm and tantala as the coatingmaterial we presented sample calculations of the spectral response of the coating as well asthe overall tantala thickness of the coating. Our analysis was based on RCW analysis andassumed plane wave inputs as well as infinite gratings. Future theoretical work will includeGaussian input beams and finite grating size effects. On top of that more sophisticated designsof grating waveguide structures such as double periodic structures [15] or double gratings [16]will also be investigated. Future experimental work will aim for a detailed characterizationof such devices as an alternative to conventional high reflectivity multilayer dielectric coatingstacks. An important issue will be the reduction of optical losses that may arise from writingerrors during grating fabrication.AcknowledgmentsThis work has been supported by Deutsche Forschungsgemeinschaft within theSonderforschungsbereich TR7. The authors would also like to thank T Clausnitzer, E-BKley and A Tu¨nnermann for fruitful discussions.High reflectivity grating waveguide coatings for 1064 nm 7303References[1] Braginsky V B et al 1999 Phys. Lett. A 264 1–10[2] Harry G M et al 2002 Class. Quantum Grav. 19 897–917[3] Fejer M M et al 2004 Phys. Rev. D 70 082003[4] www.ligo.caltech.edu/advLIGO[5] Agresti J et al 2006 Proc. SPIE Int. Soc. Opt. Eng. 6286[6] Harry G M et al 2006 Appl. Opt. 45 1569–74[7] Braginsky V B et al 2004 Phys. Lett. A 324 345–60[8] Sharon A et al 1997 J. Opt. Soc. Am. A 14 2985–93[9] Sharon A et al 1996 Appl. Phys. Lett. 69 4154–6[10] Sharon A et al 1996 Opt. Lett. 21 1564–6[11] Rosenblatt D et al 1997 IEEE J. Quantum Electron. 33 2038–59[12] Moharam M G et al 1982 J. Opt. Soc. Am. 72 1385–92[13] Mateus C F R et al 2004 IEEE Photon. Technol. Lett. 16 518–20[14] Mateus C F R et al 2004 IEEE Photon. Technol. Lett. 16 1676–8[15] Lemarchand F et al 1998 Opt. Lett. 23 1149–51[16] Kappel C et al 2004 J. Opt. Soc. Am. B 21 1127–36

High reflectivity grating waveguide coatings for 1064 nm

Crossref

Bunkowski, Alexander

Burmeister, Oliver

Friedrich, Daniel

Danzmann, Karsten

Schnabel, Roman

Max Planck Society eDoc Server

http://pubman.mpdl.mpg.de/pubman/item/escidoc:150418/component/escidoc:150417/cqg6_24_007.pdf

High reflectivity grating waveguide coatings for 1064nm

High reflectivity grating waveguide coatings for 1064nm

Abstract

Similar works

Full text

Available Versions

MPG.PuRe

Crossref

MPG.PuRe

Max Planck Society eDoc Server

Crossref