1. J Low Temp Phys
DOI 10.1007/s10909-015-1386-7
The Broadband Anti-reflection Coated Extended
Hemispherical Silicon Lenses for POLARBEAR-2
Experiment
P. Siritanasak1 · C. Aleman1 · K. Arnold2 · A. Cukierman3 ·
M. Hazumi4 · K. Kazemzadeh1 · B. Keating1 · T. Matsumura5 ·
A. T. Lee3 · C. Lee1 · E. Quealy3 · D. Rosen3 · N. Stebor1 · A. Suzuki6,7
Received: 30 September 2015 / Accepted: 19 November 2015
© Springer Science+Business Media New York 2015
Abstract Polarbear- 2(PB-2)isanext-generationreceiverthatispartoftheSimons
Array cosmic microwave background (CMB) polarization experiment which is located
in the Atacama desert in Northern Chile. The primary scientific goals of the Simons
Array are a deep search for the CMB B-mode signature of gravitational waves from
inflation and the characterization of large-scale structure using its effect on CMB
polarization. The PB-2 receiver will deploy with 1897 dual-polarization sinuous
antenna-coupled pixels, each with a directly contacting extended hemispherical sili-
con lens. Every pixel has dual polarization sensitivity in two spectral bands centered
at 95 and 150GHz, for a total of 7588 transition edge sensor bolometers operating at
270mK. To achieve the PB-2 detector requirements, we developed a broadband anti-
reflection (AR) coating for the extended hemispherical lenses that uses two molds to
apply two layers of epoxy, Stycast 1090 and Stycast 2850FT. Our measurements of the
absorption loss from the AR coating on a flat surface at cryogenic temperatures show
less than 1% absorption, and the coating has survived multiple thermal cycles. We
can control the diameter of the coating within 25 µm and translation errors are within
B P. Siritanasak
psiritan@physics.ucsd.edu
1 Department of Physics, University of California, San Diego, CA 92093-0424, USA
2 Department of Physics, University of Wisconsin-Madison, Madison, WI, USA
3 Department of Physics, University of California, Berkeley, CA 94720, USA
4 High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
5 Institute of Space and Astronautical Studies (ISAS), Japan Aerospace Exploration Agency
(JAXA), Sagamihara, Kanagawa 252-5210, Japan
6 Department of Physics, University of California, Berkeley, CA 94720, USA
7 Radio Astronomy Laboratory, University of California, Berkeley, CA 94720, USA
123

2. J Low Temp Phys
25 µm in all directions, which results in less than 1% decrease in transmittance. We
also find the performance of the AR-coated lens matches very well with simulations.
Keywords Polarbear- 2 · Anti-reflection coating · Extended hemispherical
silicon lenses
1 Introduction
Polarbear is a cosmic microwave background (CMB) polarization experiment which
islocatedattheJamesAxObservatoryonCerroTocointheAtacamadesertinNorthern
Chile at an altitude of 5200m. The Polarbear-1 receiver is installed on the the
3.5m Huan Tran Telescope and observation started in 2012. The primary goal of
the Polarbear experiment is to detect small scale B-mode signal from gravitational
lensing as well as a large-scale B-mode signal from inflationary gravitational waves[1].
Polarbear- 2 (PB-2) is an upgraded receiver that will be installed on a new 3.5m
telescope as a part of the Simons Array which is an expansion of the Polarbear
experiment [2,3]. The PB-2 receiver design uses multi-chroic detectors and extended
hemispherical lens antenna-coupled detector technology. In order to increase the direc-
tivity and focusing power to the antenna, we use silicon as the lens material because it
has a high dielectric constant ( = 11.7) [4,5]. However, the reflection loss that would
occurbetweenvacuumandsiliconsurfacesisabout R = [(ns − 1)/(ns + 1)]2 ≈ 30 %
per surface [6–8]. An anti-reflection (AR) coating is used to suppress the loss at the
boundary surface. There are various AR-coating methods [9], but it can be challenging
to apply on a highly curved surface such as the PB-2 hemispherical lens (diameter =
5.346mm). The AR coating needs to be broadband over the observing frequencies,
and mass-produceable because each pixel requires an individually AR-coated lens.
In this paper, we will discuss the methodology to fabricate the AR coatings on the
hemispherical lens, simulations, and the test results. Further details about PB-2 can be
found in the accompanying papers in this proceeding on the Polarbear- 2 and the
Simons Array[10].
2 Methodology
For PB-2, a two-layer coating with dielectric constants of 2 and 5 is applied. To have
sufficient bandwidth to cover 95 and 150GHz bands, a Tlayer = λ0/(4
√
) thickness
coating is applied, where λ0 = wavelength at center frequency at 120GHz. With a
design AR coating, we can suppress the reflection loss from 30% per surface down
to about 0.6% at 95GHz and 0.2% at 150GHz. We used two types of epoxies: Sty-
cast 1090 and Stycast 2850FT [11], which have dielectric constants well-matched to
our application at 2.05 and 4.95, respectively [7,8]. By using epoxies as the coating
material, we were able to mold it to proper thickness for AR-coating layers.
In order to make a precise coat on the hemispherical lens, we machined a mold
using a computerized numerical control (CNC) milling machine and a high precision
ball-ended mill which has a tolerance of 12.5 µm. The radius of the ball-ended mill
is R = Rlens + Tlayer, which forms a layer of thickness Tlayer over the hemispherical
123

3. J Low Temp Phys
lens. Combining the machining tolerance and the tolerance from the ball-ended mill,
we were able to achieve a coating tolerance of 25 µm. The epoxy filled the cavity and
the exact amount was controlled by measuring its weight. The lens was placed on the
seat which mates concentrically to the cavity. Then we inserted the lens, which was on
the seat, into the cavity. We also applied the adhesion enhancer LORD AP-134 [12]
on the surface of the lens before applying the coating. The process was repeated with
the other layer with a different mold cavity radius.
3 Simulations
We used a PB-2 detector design coupled to a sinuous antenna mated to an extended
silicon hemispherical lens with a two-layer AR coating using HFSS [13]. The HFSS
model also included the silicon extension layer under the hemispherical silicon lens
with a thickness L = 0.46R = 1.230 mm. We ran the simulation with a frequency
sweep from 70 to 120GHz with 2GHz spacing for the 95GHz band and from 120 to
170GHz with 2GHz spacing for the 150GHz band. We integrated all the beam profiles
from each frequency using design PB-2 frequency bands. The beams were fitted to
2D Gaussian functions to calculate the width and the ellipticity. We then compared
the results between the simulations and the beam map measurement, which will be
described in Sect. 4.4.
4 Testing
4.1 Transmission Testing
To test the broadband AR-coating performance, we applied a 2-layer AR coating
with Stycast 1090 and Stycast 2850FT using a PB-2 design thickness on both sides
of a 5.08-cm-diameter flat alumina disk, which has a dielectric constant of 9.6. The
sample was cooled down to 140K, and we measured a transmission spectrum using
a Fourier transform spectrometer. The reflection was measured to be below 10%
over 92% fractional bandwidth for the 2-layer AR coating. Cooling down the sample
reduced the band-integrated absorption loss from 15 to less than 1%. Further details
and discussions were presented in Rosen et al. [8].
4.2 Roundness Testing
A misalignment of an AR coating on hemispherical lens or an incorrect shape of the
AR coating can lead to a beam systematic error [14]. In order to control the systematic
error to acceptable levels, we inspected the quality of the AR coatings by taking side
photographs of the coating on the hemispherical lens, as shown in Fig. 1a. Then we did
a circular fit to the surface of the coating and hemispherical lens. Using this method,
we were able to verify that the accuracy of the radius of the coating was within 25
µm and the translation error from the design position was within 25 µm. Within the
tolerance, this would result in an approximately 10% of a single-layer thickness, which
corresponded to a decreasing in transmittance less than 1%.
123

4. J Low Temp Phys
Fig. 1 Left a Picture of a single layer AR coating under the microscope. We used these photographs to
inspect the shape of the AR coating. Solid red line indicates a fit to the AR coating and solid white line
indicates a fit to the hemispherical lens. Middle b The mold for one layer of coating is shown in cross section.
The hemispherical lens which is placed on the seat, is also shown in the drawing. Right c A photograph of
the fully populated broadband AR-coated hemispherical lenses on the wafer (Color figure online)
Fig. 2 A photograph of the milliKelvin stage setup in IR lab dewar used for testing. We placed 14 broadband
AR-coated hemispherical lenses on top of the seating wafer which helped us align each pixels the sinuous
antenna and its hemispherical lens. We placed the copper can with Eccsorb inside on the backside of the
detector to terminate the backside lobe. The 3He fridge is on the left of the dewar and it is connected directly
to wafer holder clip. The DC SQUID from Quantum Design Inc is on front side of the dewar. The SQUIDs
used for readout of the current from TES bolometer (Color figure online)
123

5. J Low Temp Phys
Fig. 3 Beam maps results compared between HFSS and measurement. Top left 95GHz band beam map
result from HFSS simulation, Top right 95GHz band beam map measured, bottom left 150GHz band beam
map result from HFSS simulation, and bottom right 150GHz band beam map measured. The FWHM of
measured beam maps agree with HFSS simulations to within 7% (Color figure online)
4.3 Thermal Cycling Testing
To test the cryogenic adhesion properties of the AR coating, we made ten 2-layer-
coated silicon lenses. Because of more than 90% of a thermal contraction occurs
from room temperature to 77 [15], we thermally cycled the AR-coated lenses from
room temperature to 77K with liquid nitrogen. We repeated the thermal cycling 25
times. The lens coating on only one lens failed after 13 dunks. The other nine samples
survived all thermal cycles. We concluded that the adhesion performance meets the
PB-2 requirement.
4.4 Beam Performance
We tested a prototype of PB-2 detector with AR coating lens in an IR Lab dewar.
For infrared filters, we used two layers of 0.3175cm thickness expanded Teflon and
a metal mesh low pass filter with 18cm−1 cut-off mounted to 77K shield. Two metal
mesh low pass filters with cut offs at 14 and 12cm−1 were mounted to the 4K shield.
We placed 14 two-layer AR-coated hemispherical lenses on the seating wafer. Then
we used an invar clip to attach the detector wafer to the back side of the seating wafer
123

6. J Low Temp Phys
(see Fig. 2). The detector wafer was cooled to 0.8K using a 3He absorption fridge.
Commercial DC SQUIDs from Quantum Design Inc. were used to readout the output
current from the bolometer.
We produced beam maps by raster scanning 6.35 by 6.35cm with step size of
0.3175cm with a 1.27-cm-diameter source modulated between room temperature
Eccosorb [16] and 77 K temperature Eccosorb.
We fit the beam maps to a 2D-Gaussian function and then calculated the ellipticity
from = (a − b)/(a + b) where a and b are the major axes and minor axes of the
ellipse, respectively. The beam maps are shown in Fig. 3. Ellipticities were 2.07%
for 95GHz band and 1.93% for 150GHz band. The full width at half maximum of
measured beam maps agrees with HFSS simulations to within 7%.
5 Conclusion
The broadband AR coating on the hemispherical lens is one of the keys to making
the multi-chroic technology viable. By using a precise molding method, we were
able to make two-layer AR coatings on highly curved surface with high precision.
We successfully tested the performance of the two-layer AR coating on extended
hemispherical lens and our result meets PB-2’s requirement. We also demonstrated
this method can be scaled to the mass-production levels required for next-generation
CMB experiments.
Acknowledgments POLARBEAR and POLARBEAR-2 are funded by the NSF under Grants AST-
1212230 and AST-0618398. Antenna-coupled bolometer development is also funded by NASA under
Grant NNG06GJ08G. The Simons Array is funded by the Simons Foundation. PS was supported by a
Royal Thai Government fellowship.
References
1. Z. Kermish et al., Proc. SPIE (2012). doi:10.1117/12.926354
2. T. Tomaru et al., Proc. SPIE (2012). doi:10.1117/12.926158
3. K. Arnold et al., Proc. SPIE (2014). doi:10.1117/12.2057332
4. D.F. Filipovic, S.S. Gearhart, G.M. Rebeiz, IEEE Trans. Microw. Theory Tech. 41, 1738–1749 (1993).
doi:10.1109/22.247919
5. J.M. Edwards et al., IEEE Trans. Antennas Propag. 60, 389–392 (2012). doi:10.1109/TAP.2012.
2207048
6. J. Lau et al., Appl. Opt. 45, 3746 (2006). doi:10.1364/AO.45.003746
7. A. Suzuki et al., Proc. SPIE (2012), doi:10.1117/12.924869
8. D. Rosen et al., Appl. Opt. 52, 8102 (2013). doi:10.1364/AO.52.008102
9. E. Quealy, The POLARBEAR cosmic microwave background polarization experiment and anti-
reflection coatings for millimeter wave observations. Ph.D. thesis, University of California, Berkeley,
2012
10. A. Suzuki et al., J. Low Temp. Phys., this Special Issue
11. Stycast, Henkel Corporation, Rocky Hill
12. LORD Chemlok AP-134 primer, LORD cooperation, Cary
13. ANSYS HFSS, ANSYS, Inc., 2600 ANSYS Drive, Canonsburg
14. M. Shimon et al., Phys. Rev. D 77, 083003 (2008). doi:10.1103/PhysRevD.77.083003
15. G. Ventura, L. Risegari, The Art of Cryogenics: Low-Temperature Experimental Techniques (Elsevier,
Amsterdam, 2008)
16. Eccsorb, Emerson & Cuming Microwave Products, Inc., Randolph
123