Determination of the light exposure on the photodiodes of a new instrumented baffle for the Virgo input mode cleaner end-mirror
A. Romero, A. Allocca, A. Chiummo, M. Martinez, Ll.M. Mir, H. Yamamoto
DDetermination of the light exposure on thephotodiodes of a new instrumented baffle for theVirgo input mode cleaner end-mirror
A. Romero , A. Allocca , A. Chiummo , M. Mart´ınez , Ll.M.Mir , and H. Yamamoto Institut de F´ısica d’Altes Energies (IFAE), Barcelona Institute of Science andTechnology, Barcelona, Spain Universit`a di Napoli ‘Federico II’, Dipartimento di Fisica ‘Ettore Pancini’,Complesso Universitario Monte S. Angelo, Napoli, Italy European Gravitational Observatory (EGO), Cascina, Pisa, Italy Instituci Catalana de Recerca i Estudis Avanats (ICREA), Barcelona, Spain LIGO laboratory, California Institute of Technology (Caltech), Pasadena, CA, US
September 1, 2020
Abstract
As part of the upgrade program of the Advanced Virgo interferometer,the installation of new instrumented baffles surrounding the main testmasses is foreseen. As a demonstrator, and to validate the technology, theexisting baffle in the area of the input mode cleaner end-mirror will befirst replaced by a baffle equipped with photodiodes. This paper presentsdetailed simulations of the light distribution on the input mode cleanerbaffle, with the aim to determine the light exposure of the photodiodesunder different scenarios of the interferometer operation.
Advanced Virgo is a power-recycled Michelson interferometer with 3 km longFabry-Perot cavities in the two orthogonal arms [1]. Its next upgrade, namedAdvanced Virgo Plus (AdV+), will occur in two phases. The first phase, orPhase I, will take place between the O3 and O4 observation runs, while Phase IIwill take place between the O4 and O5 observation runs [2]. Among several otherimprovements, AdV+/Phase II foresees the installation of baffles instrumentedwith photosensors surrounding the main test masses. The information providedby these photosensors will improve the understanding of the stray light (SL)distribution at low angles in the interferometer, detect the appearance of excitedhigher order modes which show up as modified patterns in the SL detected bythe baffles, allow the monitoring of the contamination of the mirror surfaces thatleads to low-angle scattering, and facilitate a more efficient pre-alignment and1 a r X i v : . [ phy s i c s . i n s - d e t ] A ug ne-tuning of the parameters of the interferometer after shutdowns and duringoperations.As part of the Phase I upgrade, the replacement of the input mode cleaner(IMC) end-mirror and payload is being planned. This motivated the replace-ment of the current baffle by a new one instrumented with photodiodes (PDs),acting as a demonstrator of the selected technology. It will also serve to gainexperience on operating such a new device within Virgo.The IMC cavity is an in-vacuum triangular cavity with suspended optics,used for modal and frequency filtering of the laser beam before entering the in-terferometer. Figure 1 shows a schematic optical setup of the IMC, where MC2is the end-mirror and MC1 and MC3 are the input and output mirrors, respec-tively. The end-mirror has a radius of curvature of 187 m, whereas the input-and output- mirrors are flat. The half round trip length is approximately 143 m.Table 1 summarises the IMC optical parameters relevant for the calculations inthis paper. The complete information can be found in reference [1]. Figure 2shows a picture of the current IMC end-mirror area, with the suspended mirrorand the surrounding non-instrumented baffle [3]. LaserNd:YAG
MC2MC1 MC3 recycling mirror towards interferometer main arms
Input mode cleaner (length = 143 m)λ = 1064 nmP = 40 W Figure 1: Sketch of the IMC cavity geometry. The instrumented baffle will beplaced around the end-mirror (MC2).Parameter Symbol ValueFinesse F F SR . × MC1 transmissivity T in (cid:39) . × − MC3 reflectivity R out (cid:39) is used for a singlePD, which corresponds to its effective sensitive area. However, since the PDsare “hidden” behind holes of 0.4 cm of diameter, the power they will actuallybe exposed to will be in principle reduced by a factor of four. All the resultspresented in the following sections are obtained for a laser input power of 40 W.3 Input Mode Cleaner in Resonance
In this section we evaluate the amount of light that reaches the baffle whenthe IMC is in resonance, both under the assumption of perfect alignment andfor misalignments compatible with the resonance state. The software used isreferred to as Static Interferometer Simulation (SIS15) and is based on a fastFourier transform simulation tool that computes the field propagation in anyresonant cavity [5]. It makes use of user-defined high-reflective profiles of thetest masses, also known as surface maps. These surface maps are used to cal-culate the reflection of the fields on the test masses, and a paraxial diffractionkernel is employed to evaluate the propagation of the light in the cavity. Thestationary state of the field in the triangular cavity includes the backward scat-tering in the end mirror (see ref. [6]).In the implementation presented in this paper the baffle, with its physicalproperties, does not exist, it is simply a geometrical location surrounding theend mirror, where the field is evaluated. Although this is considered a crudeapproximation, the simulation still provides sensible results given the fact thatthe amount of light illuminating the baffle is very small.
We first consider the IMC locked and perfectly aligned. In this steady statecondition the laser beam hits the center of the end-mirror. The power lightdistribution in the ensemble mirror plus baffle can be seen in figure 4 left. Thetotal power reaching the mirror and the baffle, altogether, is of the order of1 . × W, as obtained integrating the differential distribution of the powerover the mirror and baffle areas. Figure 4 right shows the power reaching thebaffle surface only, which amounts to 0.21 W, a 1 . × − % of the total power.The region in the baffle with the maximum light exposure is of about 2 × − Wover an area of 3.1 cm . Expressed in terms of sensors, this implies that a PDlocated in that region would receive a maximum dose of about 3 . × − W,whereas a PD located in the outer part of the baffle, at a radius of 17 cm fromthe center of the mirror, would receive a power of the order of 3 . × − W.The very low dark current for the PDs in the baffle, at the level of 50 to 5000pA, will allow detecting light power at the level of 10 − W with more than threeorders of magnitude of margin in the signal over noise ratio.
We now consider a scenario in which the IMC is misaligned, but the misalign-ment is such that the cavity remains in resonance. The misalignment is imple-mented in the simulation via a tilt of the end-mirror with respect to its nominalposition. Figure 5 shows the power in the mirror plus baffle ensemble as afunction of the tilt angle α in the range 0 to 25 µ rad. As expected, the powerdecreases with increasing tilt.As an example, figure 6 left shows the power distribution in the case α =10 µ rad. The total power in the mirror and baffle ensemble becomes 1 . × W, where only 0 .
17 W (a 1 . × − % of the total power) illuminate thebaffle itself. Figure 6 right shows the power distribution in the baffle surfaceonly. The region in the baffle with the maximum exposure receives a total of4igure 4: 2-D map of the power distribution (in W / m ) in the ensemble mirrorplus baffle (left) and in the baffle surface only (right) for the cavity completelyaligned. The white line in the left plot indicates the inner radius of the baffle.Figure 5: Total power (in W) reaching the mirror plus baffle ensemble as afunction of the tilt applied to the end-mirror.8 . × − W, distributed in an area of 1.4 cm , which translates into a maximumexposure of a single PD of about 3 . × − W.Given that the mirror has not perfect circular symmetry, the radial distribu-tion of the power depends on the angle θ , depicted in figure 7. Figure 8 showsthe power as a function of the radius for different values of θ . As expected, thedistributions at θ = 0 and θ = π are not exactly equal, though quite similar.Similarly, the radial distribution of the power in the vertical axis is not identicalat θ = π and θ = π . 5igure 6: 2-D map of the power distribution (in W / m ) in the ensemble mirrorplus baffle (left) and in the baffle surface only (right) for the cavity on resonancebut with a misalignment α = 10 µ rad. The white line in the left plot indicatesthe inner radius of the baffle. θ Figure 7: Definition of θ and color code used in figure 8.Figure 8: Distribution of power (in W / m ) as a function of the distance fromthe center of the mirror at θ = 0 and θ = π (top) and θ = π/ θ = 3 π/ α = 10 µ rad. The vertical line indicates the inner radius of the baffle.6 Input Mode Cleaner out of Resonance
For a completely misaligned beam ( α > µ rad) the cavity loses its lock. Inorder to determine the level of exposure of a PD in such configuration, an an-alytical calculation is performed based on the transmissivities and reflectivitiesof the mirrors of the cavity [7]. For a beam size of 1 cm at MC2, the intensity, I MC , is evaluated as I MC = P in × T in × R out /A beam . (3.1)Using the values of T in and R out in table 1, I MC = 1 . × W / m .Assuming a Gaussian beam illuminating directly a PD, the maximum exposureit would receive becomes 2 . × − W. Laser-induced damage-threshold testsperformed at the laboratory indicate that the PDs have a light power toleranceat least two orders of magnitude larger than the light dose expected to reachthe sensors in each lock loss.
Finally, we have considered the scenario of a sudden cavity misalignment due totransient noise, which would lead to a mechanical drift that could potentiallyresult in exposing the PDs for a short period of time to the energy stored inthe cavity. The total energy stored in the cavity in nominal conditions can beexpressed as E cav = P in × g × τ [7], where P in is the input power, g is the gain ofthe cavity, defined in terms of its finesse F as g = Fπ , and τ is the decay timeof the cavity (average time that a photon stays in the cavity) defined in termsof its finesse and free spectral range F SR as τ = F π × F SR . Using the values intable 1, g ∼ τ = 153 µ s, and E cav = 3 . area, we estimate it would be exposed to a power of about 130 W during 10 ms,as obtained integrating the Gaussian shape of the power distribution over thearea of the PD. This is a rough estimation of the maximum value that couldreach a PD, since a much more detailed analysis would be required to fullyaddress this scenario.In the current long-arm Fabry-Perot cavities of AdV, the energy stored is ofthe order of 170 J , with a beam radius at the test masses of the order of 5 cm.This means that an average power not exceeding 170 J /
10 ms = 1 . × W, In a Fabry-Perot arm, the stored energy is calculated through the gain of the powerrecycling cavity RG and the beam splitter transmission BS t as follows: E cav = P in × RG × BS t × g × τ . Using the current AdV values, P in = 20 W, RG = 35, BS t = 0 . τ = 1 . g = 2 × /π = 286 . E cav (cid:39)
170 J. . × − m can potentially hit the baffles surroundingthe test masses, meaning an intensity of 2 . × W / m , much larger than thatin the IMC cavity. Laboratory characterization has shown the laser-induceddamage-threshold of these baffles to be roughly 0 . × W / m . Nonetheless,no damage has been noticed in them, suggesting that the above upper limit forthe IMC is very conservative. Table 4 summarizes the values of the power reaching the IMC end-mirror andbaffle ensemble, the power reaching the baffle, and the maximum power thatcould impinge on a PD, for the different scenarios discussed in the paper. Asexplained in the introduction, even if the PDs are partially hidden by the baffle,their total sensitive area has been used in the calculations. Thus, the quotedvalues are conservative. Moreover, neither the current IMC end-mirror bafflenor the baffles surrounding the test masses have ever been damaged by the laserbeam.
Scenarios Mirror plus baffle Baffle PDResonance 1 . · . · − Misaligned (10 µ rad) 1 . · . · − Completely misaligned – – 2 . · − Mechanical drift 390 – 130 (for 10 ms)
Table 2: Values (in W) for the total power reaching the mirror and baffle ensem-ble, the power reaching the baffle and the maximum power that could impingeon a PD, for the different scenarios discussed in the paper and an input laserpower of 40 W.Due to the simplicity of the model used to simulate the baffle, the valuesshown in Table 4 should be taken as a semi-quantitative estimate of the powerin the baffle area in the different scenarios. Therefore, the data obtained withthe instrumented baffle surrounding of the IMC end-mirror will be used notonly to determine the relevance of the PDs geometry in the baffles to be placedaround the test masses, but also, to calibrate the simulation.
Acknowledgements
The authors gratefully acknowledge the European Gravitational Observatory(EGO) and the Virgo Collaboration for providing access to the facilities. TheLIGO Observatories were constructed by the California Institute of Technol-ogy and Massachusetts Institute of Technology with funding from the NationalScience Foundation under cooperative agreement PHY-9210038. The LIGOLaboratory operates under cooperative agreement PHY-1764464. This workwas partially supported by the Spanish MINECO under the grants SEV-2016-0588 and PGC2018-101858-B-I00, some of which include ERDF funds from theEuropean Union. IFAE is partially funded by the CERCA program of the Gen-eralitat de Catalunya. 8 eferences [1] F. Acernese et al.,
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