Cryogenic mount for mirror and piezoelectric actuator

Cryogenic mount for mirror and piezoelectric actuator for an optical cavity A. N. Oliveira, L. S. Moreira, R. L. Sacramento, L. Kosulic, V. B. Brasil, W. Wolff, and C. L. Cesar

Citation: Review of Scientific Instruments 88, 063104 (2017); doi: 10.1063/1.4989404 View online: http://dx.doi.org/10.1063/1.4989404 View Table of Contents: http://aip.scitation.org/toc/rsi/88/6 Published by the American Institute of Physics

REVIEW OF SCIENTIFIC INSTRUMENTS 88, 063104 (2017)

Cryogenic mount for mirror and piezoelectric actuator for an optical cavity A. N. Oliveira,1,2 L. S. Moreira,1 R. L. Sacramento,1 L. Kosulic,3 V. B. Brasil,1 W. Wolff,1 and C. L. Cesar1

1 Instituto de F´ısica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ, Brazil 2 INMETRO, Av. Nossa Senhora das Grac ¸ as, 50, 25250-020 Duque de Caxias, RJ, Brazil 3 Massachusetts Institute of Technology, 77, Massachusetts Ave., Cambridge, Massachusetts 02138, USA

(Received 15 February 2017; accepted 7 June 2017; published online 21 June 2017) We present the development of a mount that accommodates a mirror and a piezoelectric actuator with emphasis on physical needs for low temperature operation. The design uses a monolithic construction with flexure features that allow it to steadily hold the mirror and the piezoelectric actuator without glue and accommodate differential thermal contraction. The mount is small and lightweight, adding little heat capacity and inertia. It provides a pre-loading of the piezoelectric actuator as well as a good thermal connection to the mirror and a thermal short across the piezoelectric actuator. The performance of the assemblies has been tested by thermally cycling from room temperature down to 3 K more than a dozen times and over one hundred times to 77 K, without showing any derating. Such mounts are proposed for the cryogenic optical enhancement cavities of the ALPHA experiment at CERN for laser spectroscopy of antihydrogen and for hydrogen spectroscopy in our laboratory at UFRJ. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4989404]

I. INTRODUCTION

Optical cavities are the basis for many experiments such as the detection of gravitational waves by Laser Interferometer Gravitational-wave Observatory (LIGO)1 that uses a Michelson interferometer with a high finesse Fabry-Perot cavity in each arm. The enhancement factor of the high finesse cavity results in an effective increase in length of the arm. A similar idea is present in cavity ring-down time spectroscopy2 where the many round-trips of the photons improve the sensitivity for spectroscopic detection of dilute atomic or molecular species. Enhancement cavities are regularly employed in continuous-wave (CW) harmonic generations since the nonlinear processes become more efficient with higher intensities. Enhancement cavities are most times essential for two—or higher order—photon spectroscopy. For example, in the case of Doppler-free two-photon spectroscopy, a cavity serves the purpose of enhancing the laser intensity as well as providing two balanced counterpropagating beams. As such, they are used for spectroscopy of positronium where intracavity CW power levels of 2.5 kW at 486 nm have been used.3 The precision spectroscopy of hydrogen in the 1s-2s transition4 also benefits from an enhancement cavity at 243 nm for the same reason. While the experiments above have been done with a cavity at room temperature, there are experiments planned and being done at low temperatures. In particular, we are setting up a cold hydrogen spectroscopy system5 at UFRJ, and the ALPHA collaboration at CERN is performing spectroscopy on trapped antihydrogen atoms.6 In both experimental setups, there are advantages of using a cryogenic enhancement cavity. Motivated by these experiments and previous experience with optics in cryogenic systems, we 0034-6748/2017/88(6)/063104/6/$30.00

designed a mirror–piezo mount that we now describe in detail.

II. DESIGN

In designing the cryogenic mount, we were guided by a series of requirements and desired properties. The assembly needs to withstand repeated thermal cycling between ambient temperature and 4 K. Joining different materials in cryogenic systems requires accounting for the differential thermal contraction, especially when one is dealing with optical substrates. For vacuum sealed optical windows, for instance, it is sometimes possible to use soft joining materials such as indium o-rings or thin metallic tubes to which windows can be glued, and the metal is so thin that it is not able to break the windows.7 But incorporating a strong movement driven by a piezoelectric almost rules out the use of thin metallic joints. The construction has to be compact. It should incorporate a piezo pre-loading, as recommended by the manufacturers.8 It has to be lightweight and stiff so as not to significantly decrease the piezo resonance affecting the dynamical response of the system. It would preferably provide for a good thermal conductance since most of these systems might end up being used in a high power configuration at low temperatures. It should respect and maintain the optical alignment. Based on the design criteria outlined above and our previous experience, we developed the mount shown in Fig. 1. The piezo-mirror mount is a monolithic piece of aeronautical aluminum (machined9 from the alloy AA7050). The top crown was designed for a 12.70 mm diameter and 6 mm thick mirror. The drawing asks for a 12.65 mm diameter at the fingers

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FIG. 1. Drawings of two slightly different monolithic aluminum piezo-mirror mounts: top (a) and bottom (b). The top crown is where the mirror is accommodated. The space beneath—surrounded by the flexure springs—is to be taken by the piezoelectric actuator under preload. The typical clearance for the mirror was 50 µm in diameter, while for the piezo it was of the order of 100 µm in height (the negative values mean that both the mirror and the piezo are put under tension).

so that the mirror can be accommodated under tension in its side, away from its face. The height of the crown fingers is 0.5 mm over the mirror thickness so that the mirror surface is protected in case the mount is set upside down on a flat surface. For easy introduction of the mirror—which should have a wedge itself—the holding fingers on the crown are also wedged at 45◦ . They are 1 mm thick from their base upwards until the place where they hold the mirror. This way the mirror is not compressed by the mount in the base where the differential thermal contraction could fissure the mirror. And the thin long fingers easily accommodate for the differential thermal contraction while exerting a steady grasp to the mirror. Finally, the place where the fingers tighten the mirror is 0.5 mm away from its face. This crown construction can easily accommodate slightly smaller or larger substrates out of tolerance, requiring some manual tightening (in a vise) or opening (with a wedged tool) of the aperture prior to inserting the optics. The piezo region was designed for a tube actuator,10 one [Fig. 1(a)] with a 5 mm inner diameter aperture, 10 mm outer diameter, and 9 mm of height and another with [Fig. 1(b)] with a 8 mm inner diameter aperture, 15 mm outer diameter, and 9 mm of height. A good height for the piezo aperture was 8.90 mm, stressing the flexure springs by about 100 µm once the piezo is inserted. For ease of manufacturing, the flexure springs have radial cuts rather than azimuthal cuts. Care was taken to achieve symmetry in the flexure springs, with the same number of turns to one side as to the opposite. The mounts have through holes for the laser beam, a 5 mm aperture in one case and an 8 mm in the other. Threaded holes are present both on the top crown and in the base for assembling and final attachment. Simple jigs were made whereby the bottom and the top part could be pulled apart. Opening up the spring in a controlled manner, the piezo can be inserted without having to resort to applying negative voltage to it. The insertion of the piezo—with the mounting jig—and the final assembly can be seen in Fig. 2.

FIG. 2. Photos of the assemblies. (Top left) Insertion of the piezo using the mounting jig for the piece in Fig. 1(b). The nuts are slowly adjusted to pull apart the piezo space stressing the flexure springs until the piezo can be fitted in and centered, and then released back. The assembled system with a test mirror inserted is shown just below it. (Bottom left) Mirror mounts attached to mounting plates ready to go in the Fabry-Perot cavity shown in the right. In the case shown, only one of the mounts has a piezo.

III. CALCULATIONS, SIMULATIONS, AND THERMAL CONDUCTION

In order to get a better handle on the spring constants, we have used the program COMSOL Multiphysics11 to simulate the flexure springs’ expansion. The simulation provided a spring constant around 3 N/µm, constant if the elastic regime is not exceeded. Both designs shown above [Figs. 1(a) and 1(b)] have the same flexure springs with external widths of 3 mm × 3 mm. In this case, using the nominal values for the height of the mount and the piezo, with the displacement of ∼ 100 µm to fit the piezo, we have a pre-stress of 300 N on the piezo (see Fig. 3). This value turned out to be about 10% of the maximum block force of the piezos. As we discuss below, this force is enough to pull the top mass with acceleration high enough to keep the piezo under tension in typical use. The program also allows us to obtain a maximum expansion

FIG. 3. Simulation of the flexure properties of the aluminum mount (alloy 7050). The left figure shows the displacement field for an applied force of 300 N with the bottom part mechanically anchored. The right figure shows the von Mises stress distribution in the piece as it is stretched by this force.

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of the flexure springs before it enters the inelastic (∼200 µm) and later rupture range. These values are within the experimental assembling procedure. In Fig. 3, the flexure properties as simulated are shown. Although there is a small expected radial motion of the piezoelectric actuator as it is expanding or contracting, we did not consider or study it in this work. Another important issue to simulate is the thermal conductance across the assembly—including the conductance across the mirror, across the aluminum mount, and the thermal contact between the mirror and the crown fingers. The latter cannot be obtained with accuracy from the simulation as it depends strongly on the actual pressure exerted and the surfaces’ finishes. In order to have knowledge of the magnitude of this thermal contact, we glued two chip resistors (which acted as a heating resistor and temperature sensor) on opposite sides of the mirror—not touching the aluminum fingers—and performed a calorimetric measurement of this conductance. We obtained for the tested mount the value 1.3 mW/K. Guided by typical experimental numbers, we performed a simulation of a cavity with 1 W of circulating power and a mirror absorption of 0.0024. The simulation was performed with the following conditions: laser beam diameter of 0.4 mm (supposing uniform intensity), fused silica substrate with a thermal conductivity curve from Ref. 12, and quartz substrate supposing a constant thermal conductivity from Ref. 13 of 500 W m 1 K 1 . They yield the temperature graphs shown in Fig. 4. A contrast of the thermal conductance of this mount could be made against a common design where the piezo would be glued to the mirror and then to a base plate. In this case, the thermal conductance across the piezo is the limiting factor. Considering the data in Ref. 14, if one scales their piezo cross section and length to our case and further suppose the same intrinsic thermal conductivity of the piezoelectric material itself, one would obtain a value of 0.02 mW/K. This difference of almost two orders of magnitude shows the relevance of providing a thermal short across the piezo for laser cavities at low temperature operating at high powers. This could be accomplished in the traditional design—with the mirror glued

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to the piezo—by a glued copper sheet thermal link between the mirror and the base. Another important characteristic to compute and measure is the first resonance of the assembly as it will usually limit the bandwidth of a servo system to lock the cavity to a laser. For the mount in Fig. 1(a), the piezoelectric actuator used has a specified (auto) resonance fpzt ≈ 40 kHz if mechanically disconnected. When it is held on one side, the resonance goes down by a factor of 2. In order to calculate the expected resonance frequency, we need to know all the masses involved. The mass of the piezo was measured mpzt ≈ 3.9 g. The mass of the aluminum flexure springs is negligible at 0.35 g, as estimated from the design program.15 In both these cases, the mass is distributed along the length and it can be considered as a lumped effective mass of 1/3 of these values at the end of the “massless” spring. The mass of the top aluminum crown was estimated from the design as mcrown ≈ 3.63 g (measured in a similar sacrificed piece to be 3.77 g) and the mass of the mirror as mmirror ≈ 2 g. We can then estimate the resonance by the following equation: s fpzt mpzt /3 ≈ 8.7 kHz. fres = 2 mpzt /3 + mmirror + mcrown For the other mount [Fig. 1(b)] with a more massive piezo at 8 g but stiffer with fpzt ≈ 50 kHz and a top crown mass of 4 g, the predicted value is 13.8 kHz. A relevant issue to assure is whether the mount would stay together even when the piezo is driven strongly. The nominal tension force on the aluminum crown and mirror masses, of ∼300 N, results in an acceleration under contraction of amirror+crown = 300 N/(mmirror + mcrown ) ≈ 52 000 m·s 2 . Considering the piezoelectric actuator by itself driven at its autoresonance of 50 kHz at 1 µm of peak-to-peak displacement, one obtains a peak acceleration of apiezo = (2πfpzt )2 0.5 µm ≈ 49 000 m·s 2 . Thus, the piezo should not disconnect—even momentarily—from the aluminum mount as long as it is not driven this intensely (1 µm peak-to-peak displacement at 50 kHz). IV. EXPERIMENTAL SETUP AND RESULTS

FIG. 4. Simulation of the thermal properties of the system. A 1 W laser beam deposits 2.4 mW on a surface spot of 0.4 mm of diameter in a mirror at low temperature. In the left, a fused silica mirror substrate—with its poor thermal conductivity12 —is used, while in the right a quartz mirror substrate—with its good thermal conductivity13 —is employed. Using a measured thermal conductance of the contact between the mirror and aluminum crown fingers and typical values for thermal conductivity of aluminum, one can map the temperature distribution in the system. The bottom plate is thermally anchored at 4 K. In the absence of the aluminum flexure springs thermally shorting the piezo, the temperature at the mirror surface could reach much higher values. See details in the text.

The mounted piezo-mirror systems were attached to plates and assembled in a Fabry-Perot cavity made of aluminum with a distance between mirrors of around 150 mm as shown in Fig. 2. In one case, we had only one mirror with the piezo, on one side, and a fixed mirror on the other side. In another case, we had both mirrors with piezos. The Fabry-Perot cavity was checked in an optical table and then attached to the cold head of a closed-cycle cryostat 16,17 where it was cooled to 3 K. The assemblies were thermally cycled a dozen times in total, and no breaking or derating was observed. In order to fully characterize the system, we measured the excursion of the piezo mount as a function of temperature, its resonant frequency at low temperature, and the thermal conductance between the mirror and the aluminum fingers at the top crown, as reported in Sec. III. For the purpose of measuring the excursion of the piezo, we used the setup shown in Fig. 5. A homemade extended cavity diode laser at 670 nm is scanned at 3 GHz, modulated at 100 Hz, as detected by the

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FIG. 5. Experimental setup composed of an extended cavity laser diode which is frequency scanned by its piezo actuator, a reference Fabry-Perot—internal to the laser box—whose transmission is detected in a photodiode (PDref ) and registered the laser scan, and the external Fabry-Perot placed in the closed-cycle cryostat whose reflection is detected by a second photodiode (PDtest ).

reference Fabry-Perot interferometer. The laser is coupled to a single-mode fiber going to the optical breadboard under the cold head. The laser is mode-matched to the cryogenic FabryPerot interferometer—containing the piezo-mirror mount— whose reflection is monitored by another photodiode. A slow ramp (at 10 to 100 mHz) is used to scan the cryogenic piezo with voltages from 30 to 200 V, applied through a Hamamatsu C9619-51 used as a dc-dc converter/amplifier with a ripple/noise quoted below 60 mV. The spectral structures of the two Fabry-Perot interferometers are analysed by the software, and the relative phase of the cryogenic Fabry-Perot with

respect to the stable Fabry-Perot is calculated and recorded as a function of temperature and applied voltage. From this, we can measure both the excursion response of the piezoelectric system as a function of temperature and the thermal contraction or expansion of the whole Fabry-Perot cavity attached to the cryohead as a function of temperature. A typical raw data acquisition is shown in Fig. 6. A piezoelectric actuator response as a function of temperature is shown in Fig. 7. One assembly [Fig. 1(a)] went from a response of 7.3 nm/V at room temperature to 2.4 nm/V at 3 K while another [Fig. 1(b)] went from 5.7 nm/V to

FIG. 6. Data acquired showing the laser scan voltage (green), the laser reference Fabry-Perot transmission signal (blue), the cryogenic Fabry-Perot (device under test) reflection signal (red), and the cryogenic piezo voltage (black) in the top graph. The computer records the relative phase of the Fabry-Perot interferometers as a function of time in the bottom graph: (in blue) phase of the reference Fabry-Perot, (in red) phase of the cryogenic Fabry-Perot, and (in black) the modulation on the cryogenic piezo.

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FIG. 7. Piezoelectric actuator response as a function of temperature taken while the cryostat slowly warms up.

1.8 nm/V for the same temperature range. This level of actuation loss (∼70%) is actually lower than that quoted by manufacturers who predict that the piezo retain only 10% to 20% of its excursion at low temperature compared to room temperature. We also measured the resonance frequency of the system by parking the laser frequency in the side of the reflection fringe from the cold Fabry-Perot cavity and applying a small modulation in the piezo and measuring the resulting amplitude oscillation in the reflected signal using a network analyzer. Since the laser was reasonably stable, we could manually keep its frequency controlled in a stable position on the fringe side,

rather than employing a low-bandwidth control system. The measured resonance, for the design of Fig. 1(a), came out at 7.8 kHz (see Fig. 8), rather than the expected value of 8.7 kHz calculated above. In the case of the other mount [Fig. 1(b)], the discrepancy was significant: we measured ∼9 kHz while the predicted value is 13.8 kHz. We do not know whether this discrepancy comes from the plate mounting to the Fabry-Perot cavity or whether some subtleties in the mount are playing a role. As the systems were cooled down to 4 K, the measured resonant frequency in both systems increased by about 7% showing an increase in the stiffness of the whole system.

FIG. 8. Bode plots [amplitude (a) and phase (b)] of the piezo response at room temperature. As described in the text, the laser was manually controlled in the fringe side while a network analyzer (Agilent 4395A) performed the scan. The structure is rich but the first resonance can be seen in the plots at 7.8 kHz. At 4 K, this resonance increases to 8.3 kHz.

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In order to further investigate fatigue of the material or departure from the linear regime, we subjected one of the assemblies [Fig. 1(a)] to further endurance tests. It was put inside a balloon with nitrogen gas and was dumped into liquid nitrogen—until thermalization at 77 K—and taken out to room temperature. This procedure was repeated over one hundred times and then it was remounted in the Fabry-Perot cavity where its resonance frequency was remeasured without showing discrepancy from the original value. Furthermore, an extra piece, similar to this one, without the mirror and the piezo was also mechanically tested with Instron ElectroPuls E3000 in Laborat´orio de Mecˆanica da Fratura at UFRJ. The actual value for the spring constant turned out to be a factor 2 below the value predicted by the modeling program (see Fig. 3) while the expansion of ∼270 µm was the limit of linear behavior. The assembly was sacrificed on purpose and broke apart only after ∼3 mm of stretching. These measurements show the feasibility and robustness of the assembly. V. CONCLUSION AND PROSPECTS

The designed assemblies for holding a piezoelectric actuator and a mirror were characterized and successfully passed many tests. The design is robust to thermal cycles between room temperature and 3 K. Using three different pieces and performing a dozen thermal cycles showed no episode of mirror, piezo, or mount breaking or getting loose. This is to be contrasted with traditional systems using epoxy directly between the piezo and the mirror. Even with care to match thermal contraction using intermediate matching elements, it can still result in damage and, even when tested successfully, carries uncertainties because of the aging of the cured epoxy. Also, a totally epoxy-free mount has other appeals as far as UHV is concerned. One assembly was also subjected to an endurance test with over one hundred abrupt thermal cycles between room temperature and 77 K. It kept the same structural response, as evidenced by the resonance frequency. The thermal conductance presented by the aluminum crown fingers to the mirror is appropriate and much better than a thermal link through the piezo alone. The assembly presents some cost in resonance frequency, as compared to a mount where the mirror would be directly glued to the piezo, since the aluminum crown adds extra mass. On the other hand, besides the robustness issue, this design allows for a change of the mirror or piezo. Of course the strategies adopted in this design can be modified and expanded. We are implementing an even more compact design using a ring piezoelectric actuator directly in contact with the mirror to improve substantially the resonance frequency. The basic rule to follow for a successful cryogenic operation is that one should allow flexibility between the

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different parts so as not to induce damage from the differential thermal contraction.

ACKNOWLEDGMENTS

This work is partially supported by the Brazilian institutions CNPq, FAPERJ, and RENAFAE. We acknowledge the help from Bruno X. R. Alves in the measurements with one of the piezoelectric systems and from Professor Enrique M. Castrodeza from Laborat´orio de Mecˆanica da Fratura at UFRJ for the tension test providing the measurements of the spring constant and plastic regime of one piece. 1 B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration),

“Observation of gravitational waves from a binary black hole merger,” Phys. Rev. Lett. 116, 061102 (2016); B. P. Abbott et al., “Detector description and performance for the first coincidence observations between LIGO and GEO,” Nucl. Instrum. Methods Phys. Res., Sect. A 517, 154 (2004). 2 D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. 23, 1238 (1984); A. O’Keefe and D. A. G. Deacon, “Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources,” Rev. Sci. Instrum. 59, 2544 (1988). 3 S. Chu, A. P. Mills, and J. L. Hall, “Measurement of the positronium 13 S 1 23 S 1 interval by Doppler-free two-photon spectroscopy,” Phys. Rev. Lett. 52, 1689 (1984). 4 Ch. G. Parthey et al., “Improved measurement of the hydrogen 1S-2S transition frequency,” Phys. Rev. Lett. 107, 203001 (2011); T. W. Hansch, “Passion for precision,” Rev. Mod. Phys. 78, 1297 (2006). 5 R. L. Sacramento et al., “Matrix isolation sublimation: An apparatus for producing cryogenic beams of atoms and molecules,” Rev. Sci. Instrum. 86, 073109 (2015). 6 M. Ahmadi et al., “Observation of the 1S–2S transition in trapped antihydrogen,” Nature 541, 506 (2017). 7 C. de Carvalho Rodegheri, “Proposta para uma nova t´ ecnica de carregamento de armadilhas magn´eticas—A fonte de a´ tomos criogˆenicos,” M.S. thesis, Universidade Federal do Rio de Janeiro, 2006. 8 See http://www.piezo.ws/piezoelectric actuator tutorial/Piezo Design part 3.php for Piezo design: Forces and stiffnes in piezoelectric actuation. 9 Equitecs–Inovac ¸ a˜ o e Tecnologia em Equipamentos, R. Georg Ptak, 715Jardim S˜ao Paulo, S˜ao Carlos-SP 13570-420, Brazil. 10 Piezo actuators: HPSt 500/10–5/7 and HPSt 1000/15-8/7 from Piezosystem Jena GmbH, Stockholmer Str. 12, 07747 Jena, Germany. These are commercially available but we asked for one with minimal external diameter within specified tolerance. 11 See www.comsol.com for COMSOL, Inc. 12 R. Br¨ uckner, “Properties and structure of vitreous silica I,” J. Non-Cryst. Solids 5, 123 (1970). 13 M. Hofacker and H. V. L¨ ohneysen, “Low temperature thermal properties of crystalline quartz after electron irradiation,” Z. Phys. B: Condens. Matter 42, 291 (1981). 14 M. Fouaidy et al., “Full characterization at low temperature of piezoelectric actuators used for SRF cavities active tuning,” in Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee, 2005, https://cds.cern.ch/record/928679/files/care-conf-05-054.pdf. 15 See www.autodesk.com for Autodesk Fusion-360. 16 See www.cryoindustries.com for Cryo Industries of America, Inc. 17 Sumitomo Closed Cycle (GM) Cryogenic Refrigerator System Model SRDK 408D.