Further author information: (Send correspondence to T.G.) E-mail:
<EMAIL_ADDRESS>
# Development of the Low Frequency Telescope focal plane detector arrays for
LiteBIRD

Tommaso Ghigna  QUP (WPI), KEK, Tsukuba, Ibaraki 305-0801, Japan  Aritoki
Suzuki  LBNL, Berkeley, California 94720, USA  Benjamin Westbrook  UC
Berkeley, Berkeley, California 94720, USA  Christopher Raum  UC Berkeley,
Berkeley, California 94720, USA  Hiroki Akamatsu  QUP (WPI), KEK, Tsukuba,
Ibaraki 305-0801, Japan  Shawn Beckman  UC Berkeley, Berkeley, California
94720, USA  Nicole Farias  UC Berkeley, Berkeley, California 94720, USA
Tijmen de Haan  QUP (WPI), KEK, Tsukuba, Ibaraki 305-0801, Japan  Nils
Halverson  CASA, University of Colorado, Boulder, Colorado 80309, USA  Masashi
Hazumi  QUP (WPI), KEK, Tsukuba, Ibaraki 305-0801, Japan  Kavli IPMU (WPI),
UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan  JAXA, ISAS,
Sagamihara, Kanagawa 252-5210, Japan  SOKENDAI, Miura District, Kanagawa
240-0115, Hayama, Japan  IPNS, KEK, Tsukuba, Ibaraki 305-0801, Japan  Johannes
Hubmayr  NIST, Boulder, Colorado 80305, USA  Greg Jaehnig  CASA, University of
Colorado, Boulder, Colorado 80309, USA  Adrian T. Lee  UC Berkeley, Berkeley,
California 94720, USA  LBNL, Berkeley, California 94720, USA  QUP (WPI), KEK,
Tsukuba, Ibaraki 305-0801, Japan  Samantha L. Stever  Okayama University,
Department of Physics, Okayama 700-8530, Japan  Yu Zhou  QUP (WPI), KEK,
Tsukuba, Ibaraki 305-0801, Japan  for the LiteBIRD Collaboration

###### Abstract

LiteBIRD, a forthcoming JAXA mission, aims to accurately study the microwave
sky within the 40-400 GHz frequency range divided into 15 distinct nominal
bands. The primary objective is to constrain the CMB inflationary signal,
specifically the primordial B-modes. LiteBIRD targets the CMB B-mode signal on
large angular scales, where the primordial inflationary signal is expected to
dominate, with the goal of reaching a tensor-to-scalar ratio sensitivity of
$\sigma_{r}\sim 0.001$. LiteBIRD frequency bands will be split among three
telescopes, with some overlap between telescopes for better control of
systematic effects. Here we report on the development status of the detector
arrays for the Low Frequency Telescope (LFT), which spans the 34-161 GHz
range, with 12 bands subdivided between four types of trichroic pixels
consisting of lenslet-coupled sinuous antennas. The signal from the antenna is
bandpass filtered and sensed by AlMn Transition-Edge Sensors (TES). We provide
an update on the status of the design and development of LiteBIRD’s LFT LF1
(40-60-78 GHz), LF2 (50-68-89 GHz) pixels. We discuss design choices motivated
by LiteBIRD scientific goals. In particular we focus on the details of the
optimization of the design parameters of the sinuous antenna, on-chip bandpass
filters, cross-under and impedance transformers and all the RF components that
define the LF1 and LF2 pixel detection chain. We present this work in the
context of the technical challenges and physical constraints imposed by the
finite size of the instrument.

###### keywords:

CMB, Bolometer, Transition Edge Sensor

##  1 INTRODUCTION

Studying the primordial CMB (Cosmic Microwave Background) B-mode signal stands
out as a primary objective in modern cosmology. While still an unanswered
question, existing theories predict a rapid and extensive inflationary
expansion of the Universe. The most effective tool at our disposal for
investigating inflation is to measure the polarized CMB signal [1, 2]. When
observing large angular scales ($\ell\lesssim 200$), it is expected that the
dominant constituent of the polarized B-mode signal is a primordial
inflationary component, given a tensor-to-scalar ratio $r\gtrsim 0.01$, or
even $r\gtrsim 0.001$ for $\ell<10$.

Detecting the primordial B-mode signal and constraining inflation are the main
goals of the LiteBIRD space mission [3] as well as several other ongoing and
planned CMB experiments [4, 5, 6]. A common feature of most CMB experiments is
the use of Transition-Edge Sensor (TES) bolometers to detect the incoming
radiation [7]. This technology has undergone intense development in the last
two decades.

Figure 1: A summary of LFT FPU (focal plane unit). A total of 180 lenslet-
coupled sinuous antenna pixels are arranged in a rectangular focal plane
divided among 8 FPSAs (focal plane sub-assemblies): 4 LF12 FPSAs (LF1 and LF2
pixels) at the edges of the FPU and 4 LF34[8] FPSAs (LF3 and LF4 pixels) at
the center of the FPU. The CAD rendering of LFT focal plane is adapted from 3.
Figure 2: Left: A summary of the LFT FPU layout showing the total number of
detector wafers and type (LF12 and LF34). Pixel types are highlighted in red
for LF1, yellow for LF2, green for LF3 and blue for LF4. Right: The layout of
a LF12 wafer showing 6 LF1 pixels (bottom 2 rows) and 3 LF2 pixels (top row).
The LFT focal plane layout on the left is adapted from 3.

In order to be used for millimetre-wave detection, a common technique in
modern experiment consists in coupling TES detectors to an antenna to collect
the incoming radiation. At present a handful of technologies are being used
for CMB observations. Among them we can find lenslet-coupled dual-polarised
sinuous antenna [4, 9] and horn-coupled OMTs [10] (orthomode transducer).
LiteBIRD will implement both technologies in three separate telescopes mounted
on the satellite payload: Low Frequency Telescope (LFT - 34-161 GHz), Mid
Frequency Telescope (MFT - 89-225 GHz) and High Frequency Telescope (HFT -
166-448 GHz)[11]. Sinuous antennas will be used for the lower frequency range
(LFT and MFT), while horns antenna will cover the highest frequencies
(HFT)[12]. Aside for the different antenna types, the two technologies share
many common features. Detector arrays are microfabricated on silicon wafers
and the signal collected by each antenna is routed to the detector by means of
microstrip (or coplanar) transmission lines. The signal is filtered by on-chip
band defining filters and dissipated on the TES island by a resistor matched
to the transmission line.

Figure 3: Left: A zoom-in on a LF12 wafer layout around one of the sinuous
pixels. The main components of the detector chain can be seen: the sinuous
antenna, the triplexer that defines the three frequency bands, impedance
transformers, cross-under structures and the TES bolometers. The light-green
area shows the extent of the silicon lenslet, while the dark-green area shows
the negative of the palladium deposited on the sky-side of the detector wafer.
Right: A side view of a HFSS model of the pixel structure, showing (from top
to bottom) the silicon lenslet with a 3-layer AR coating, the seating wafer,
the detector wafer and the metal backshort. The sinuous antenna is located on
the niobium surface that crosses the origin of the reference system. The
surface in purple above indicates the location of the palladium layer, while
the one below in pink indicates the backshort.

In this paper we describe the design of the lowest frequency pixels of
LiteBIRD Low Frequency Telescope (LFT): LF1 (40-60-78 GHz) and LF2 (50-68-89
GHz).

##  2 Low Frequency Telescope Focal Plane Unit

LiteBIRD LFT is a reflective Cross-Dragone telescope [11] and houses a
rectangular $\sim 420\times 210$ mm focal plane unit (FPU) to optimize the use
of the double mirror optical configuration. The focal plane unit is made of
eight $\sim 110\times 110$ mm focal plane sub-assemblies (FPSAs). The size of
the FPSA is primarily determined by the dimensions of the detector arrays
($101\times 101$ mm) which are fabricated on 6-inch silicon wafers (see Figure
2).

As shown in Figure 1, LFT spans the frequency range 34-161 GHz, from the
galactic synchrotron dominated low-end of the spectrum to the main CMB science
portion around 100 GHz.

LFT implements arrays of trichroic dual-polarization pixels by employing
lenslet-coupled sinuous antennas. The broad band observed by the antenna is
filtered using microstrip on-chip distributed filters (microfabricated on the
same silicon wafer that houses the sinuous antenna and TES detectors). From
each antenna we obtain three contiguous but separate 23-30% bands cantered at
the frequencies listed in Figure 1.

We implement four different pixel types (as shown in Figures 1 and 2): LF1
(40-60-78 GHz), LF2 (50-68-89 GHz), LF3 (68-89-119 GHz) and LF4 (78-100-140
GHz) for a total of 9 separate (but overlapping bands), with some bands
present in two different pixel types (12 total frequency channels).

In Figure 2 we can see that LF1 (red) and LF2 (yellow) pixels (lowest
frequency range of LFT) are placed in the 4 wafers (LF12) at the edge of the
focal plane unit. While LF3 (green) and LF4 (blue) are placed in the 4 wafers
(LF34) at the center of the focal plane unit.

Since in this paper we focus on the design of LF1 and LF2 pixels, in Figure 2
we only report the layout of a LF12 wafer, showing a total of 9 sinuous pixels
(6 LF1 and 3 LF2). In this plot we highlight the total size of the wafer and
the pixel pitch (in light green), corresponding to the size (32 mm) of the
silicon lenslet that is employed to boost the directivity of the antenna. LF34
wafers have the same total dimension of LF12 wafers but fit 36 pixels (18 LF3
and 18 LF4) with a pixel pitch of 16 mm.

As reported in Figure 1, with the aforementioned wafer layout and number of
wafers, LFT FPU will house a total of 180 dual-polarization trichroic sinuous
pixels for a total of 1080 optical TES bolometers.

Figure 4: Comparison of the beam function at 60 GHz for $\phi=0^{\circ}$ for
the LF1 pixel for three cases: baseline (black line), baseline without
palladium layer (green dashed line) and baseline without metal backshort (red
dashed line). We show this to highlight that the backshort significantly
reduces the back-lobe pickup as can be seen for $\theta>90^{\circ}$, and the
palladium layer interfere minimally with the antenna (and only away from the
main lobe as can be visibly seen in the range $60^{\circ}<\theta<90^{\circ}$)
when a 20 mm diameter hole in the palladium layer is aligned with the antenna
to let the radiation reach the antenna.

##  3 PIXEL STRUCTURE

Lenslet-coupled sinuous antennas are quite well known in the radio astronomy
community because of their dual polarization properties and broad-band nature.
Because of these two properties and the race to characterize CMB polarization,
the POLARBEAR/Simons Array [4, 9] and SPT[13] collaborations pioneered their
use for CMB observations.

After its use in Simons Array, SPT and more recently Simons Observatory, we
have decide to implement the same technology to leverage the decade long
experience developing this type of pixels and to use them in their full
potential by packing the largest possible amount of detectors given the
constraints in size and mass due to the nature of a space mission.

In Figure 3 we show the structure of the detector chain. On the left side we
highlight all the components that are part of the device wafer and are
microfabricated on 6-inch silicon wafers. While on the right side we show a
side view of the full pixel structure, composed of an anti-reflection (AR)
coated hemispherical silicon lenslet, a silicon seating wafer to extend the
lenslet and mimic an elliptical lens and enhance directivity, the detector
wafer (the wafer supports the sinuous antenna and all the other components of
the detector chain) and a metal backshort to suppress the a residual antenna
back-lobe.

Details of each component, design choices and simulated performance are going
to be explained in the following sections.

##  4 LENSLET-COUPLED SINUOUS ANTENNA

The first element of the detection chain is the lenslet-coupled sinuous
antenna. All the relevant components are shown in Figure 3. The key component
is the sinuous antenna which collects the radiation from the microwave sky. We
tuned the antenna dimensions to maximize its efficiency in the range of
interest for LF1 and LF2 pixels frequencies 34-99 GHz. After some trade-off
studies we settled on an antenna with a 24 $\rm{\mu}$m inner radius, expansion
factor $\tau=1.3$ and 21
cells111$R_{\mathrm{out}}=R_{\mathrm{in}}\tau^{n_{\mathrm{cell}}}$. In this
formula $R_{\mathrm{in}}$ is the radius of the innermost cell that defines the
sinuous antenna, $n_{\mathrm{cell}}$ is the total number of cells, $\tau$ is
the expansion factor defined as $R_{\mathrm{i+1}}/R_{\mathrm{i}}$ and
$R_{\mathrm{out}}$ is the outer radius of the sinuous antenna. The inner and
outer radius define respectively the highest and lowest frequency cut-offs of
the antenna. While $\tau$ defines how packed are the arms of the antenna..
With these parameters we obtain an outer radius of $\sim 6$ mm.

(a)

(b)

Figure 5: Left: HFSS simulation of the frequency-dependent full-width at half-
maximum of the beam function for LF1 and LF2. Right: Beam ellipticity and
average value for LF1 and LF2. In both plots the vertical blue and red bars
highlight the nominal bands of pixel LF1 and LF2 respectively.

For the trade-off study we looked predominantly at two factors: the complex
impedance of the antenna in free space and the minimum dimensions of the arms
of the sinuous antenna. From the theory[9, 14, 15] we expect that the complex
impedance of a sinuous antenna in free-space should be stable in the frequency
range of interest. In particular we want the impedance to be real with a value
of $\sim 250~{}\Omega$. Therefore in the first step of our optimization we
simulated (HFSS222https://www.ansys.com/products/electronics/ansys-hfss) the
smallest $R_{\mathrm{in}}$ and $R_{\mathrm{out}}$ that achieve the best in-
band performance in terms of complex impedance in free-space. While it is
known that smaller values of $\tau$ can achieve better stability in band, the
minimum dimensions of the arm of the antenna for $\tau<1.3$ become too small
to support the microstrip line efficiently, in fact the width of the arms of
the sinuous antenna (which define the ground plane of the microstrip
structure) for $\tau<1.3$, close to the center, become comparable to the width
of the microstrip line trace ($\sim 1~{}\mathrm{\mu m}$). In this
configuration the ground plane can not be assumed to be infinite anymore and
the loss of the transmission line increases.

As discussed in 9 a hemispherical silicon lenslet and a silicon wafer can be
used to boost the directivity of the antenna toward the sky. An elliptical
lenslet would be ideal but due to difficulties in procuring and handling
elliptical silicon lenslets, a stack with a hemispherical lenslet and a
silicon wafer that mimics the effect of an ellipse as been used successfully
in the past. From our analysis we find that a seating wafer with a thickness
$L\sim 0.37\times R_{\mathrm{lens}}$ achieves the best gain in the LF1 and LF2
frequency range and the pixel geometry described above. Given that for LF1 and
LF2 $R_{\mathrm{lens}}\sim 16$ mm, we find that this would require a very
thick and difficult to machine with standard techniques silicon wafer,
therefore we are currently exploring the possibility of building the extension
into the lenslet itself. This solution is still being studied and evaluated by
our team.

A second change compared to previous generations of this technology is the
anti-reflection coating on the surface of the lenslet. An anti-reflection
coating is required to minimize losses due to reflections at the boundary
between free-space and silicon, due to the difference in refractive index
($n\sim 3.4$ for silicon). A common technique that has been used in the past
in the CMB community for silicon or similar materials (e.g. sapphire and
alumina) to smooth the transition consists in coating the surface of the
lenslet with one or more layer of epoxy. By tuning the thickness of each layer
and choosing properly the refractive index of each layer it is possible to
reach efficiencies well above 90% across a broad frequency range. However an
important shortcoming of this technique comes from differential thermal
contractions and expansions due to the use of different materials which can
cause significant problems for cryogenic applications. In order to avoid this
issue, we have been developing an alternative approach where the surface of
the silicon lenslet is laser-machined to ablate part of the silicon creating a
sub-wavelength periodic structure[16]. Starting from the top of the lenslet
the filling factor of silicon increases towards the bulk of the lenslet
achieving a layer with a smooth refractive index transition from that of free-
space ($n=1$) to that of silicon. This technique is not completely new in the
community, however it was mostly employed on flat surfaces[17].

Figure 6: An example of an on-chip filter for the 40 GHz channel of LF1. Each
filter is a combination of a distributed three-pole Chebyshev bandpass filter
(BPF) and a distributed five-pole Chebyshev lowpass filter (LPF) to suppress
high-order harmonics. The lowpass cut-off is $\sim 2\times f_{c}$, where
$f_{c}$ is the central frequency of the bandpass filter. Figure 7: Comparison
of the response of the filter in Figure 6 in red and the bandpass filter alone
in blue. We can notice a significant suppression of a high-order harmonic
around 190 GHz because of the lowpass filter.

Due to memory limitations it is very challenging to include the geometry of
the anti-reflection coating in EM simulations, therefore we approximate this
by calculating the effective refractive index from the AR coating structure
filling factor and create a multi-layer coating in the HFSS model (see Figure
3).

There are two more differences between the LiteBIRD LFT pixel design and
earlier iterations of this technology: a reflective (metal) backshort placed
at $\lambda/4$ distance behind the sinuous antenna and a layer of palladium
deposited on the sky-side surface of the detector wafer. The former has been
introduced to mitigate the back-lobe of the antenna. This can be easily
noticed in Figure 4 where our baseline design in black (the geometry explained
above with both the backshort and palladium layer) is compared to a design
without the reflective backshort in red (dashed). We can easily notice how the
back-lobe ($90^{\circ}<\theta<180^{\circ}$) is suppressed by up to a few tens
of dBs in the baseline case.

The second difference is the addition of a palladium layer on the sky-side
surface of the detector wafer (in contact with the seating wafer). The reason
for this change is twofold: palladium has a large heat capacity that can be
leveraged to stabilize the temperature of the wafer during operation and to
reduce the impact of stray light or direct absorption on the TES bolometers.
However, in order to allow the signal from the sky to reach the antenna, after
deposition of the palladium layer, the palladium needs to be patterned by
removing it from the optical path. After some trade-off studies we found that
a circular opening of 20 mm diameter aligned with the sinuous antenna and
lenslet achieve the best compromise of protecting the TES bolometer (as can be
seen in Figure 3) and not-interfering with the antenna. We show this in Figure
4 where the baseline design in black is compared to a design without the
palladium layer (with the 20 mm hole) in green (dashed). We can see that the
main-lobe is unaffected by the presence of the palladium layer and only a
small discrepancy between the two cases can be noticed in the range
$60^{\circ}<\theta<90^{\circ}$.

(a)

(b)

Figure 8: Left: Simulated transmission of the LF1 pixel triplexer. Right:
Simulated response of the LF2 pixel triplexer (one more design iteration is
required to improve the response of the 89 GHz bandpass filter).

(a)

(b)

Figure 9: Left: Simulated response of the cross-under structure showing good
transmission and isolation of opposite ports in the LF1 and LF2 frequency
range. Right: Transmission and return loss of tapered 6.8 to 12.7 $\Omega$
impedance transformers in the LF1 and LF2 frequency range. In both plots the
vertical blue and red bars highlight the nominal bands of pixel LF1 and LF2
respectively.

In Figure 5 we show the simulated (HFSS) full-width at half-maximum (FWHM) and
ellipticity for the baseline case for LF1 and LF2.

##  5 RF STRUCTURES

The sinuous antenna is fabricated on a niobium layer deposited on the 6-inch
wafer (above a layer of silicon-nitride that is required as the structural
membrane of the TES bolometer). When the broad-band signal is collected by the
antenna, it needs to be filtered and routed to the TES bolometer. This step is
achieved with standard microwave engineering techniques, namely by employing a
microtrip line that channels the signal from the center of the antenna to the
edge where TES bolometers are fabricated.

Using microstrip line is particularly suited to this technology as the niobium
layer deposited for the antenna can be used to define the ground-plane of the
microstrip line. A layer of silicon-nitride of 1 $\mu$m thickness is deposited
above the ground plane to form the dielectric of the microstrip line.

Before reaching the detectors, the signal is filtered by a triplexer that
splits the broad-band signal from the antenna in narrower bands (23-30%
bandwidth). After a trade-off study of performance versus manufacturing errors
we decided to implement the filters with 6.8 $\Omega$ impedance microstrip
lines. This requires lowering the impedance from $\sim 50~{}\Omega$ at the
center of the antenna to the edge using a tapered impedance transformer.

The triplexer combines three separate filters with each filter defining a band
with 23-30% bandwidth. Each filter is a combination of a distributed three-
pole Chebyshev bandpass filter (BPF) and a distributed five-pole Chebyshev
lowpass filter (LPF) to suppress high-order harmonics. The lowpass cut-off is
$\sim 2\times f_{c}$, where $f_{c}$ is the central frequency of the bandpass
filter. An example for the 40 GHz LF1 filter can be seen in Figure 6. A
comparison of the behaviour of the bandpass filter alone and the bandpass
filter followed by the lowpass filter can be seen in Figure 7. We can notice a
significant suppression of a high-order harminic at $\sim 190$ GHz.

| LF1 | LF2
---|---|---
Band Center [GHz] | 40 | 60 | 78 | 50 | 68 | 89
Bandwidth [%] | 30 | 23 | 23 | 30 | 23 | 23
Optical Power [pW] | 0.2918 | 0.2419 | 0.2686 | 0.306 | 0.2709 | 0.2958
Table 1: LiteBIRD LFT LF1 and LF2 pixel design parameters for each frequency
band. The fractional bandwidth (ratio between bandwidth and the central
frequency) is reported. Details of the expected optical power calculation per
detector can be found in 18 and 19.

(a)

(b)

Figure 10: TES bolometers thermal conductance and heat capacity target values
for typical values of the thermal conductance index as a function of the
transition temperature Tc of the superconductive AlMn film. The shaded area is
for saturation powers $P_{\mathrm{sat}}$ in the range $2-3\times
P_{\mathrm{opt}}$. Typical value of 0.3 pW and 33 ms have been assumed for the
optical power and fundamental time-constant.

The total response of the LF1 and LF2 triplexer (simulated with
Sonnet333https://www.sonnetsoftware.com) can be seen in Figure 8. We are aware
that the response of the 89 GHz band of LF2 can be further improved in future
design iterations.

Given that 6 detectors are necessary to complete the detection chain for this
type of pixel, one more RF structure is necessary to avoid mixing the signal
between channels: a cross-under structure. This is a four-port devices where
the signal for one channel travels from port 1 to port 3 and from port 2 to
port 4 for a second channel. Hence, the requirement is to maximise
transmission between port 1 (2) and port 3 (4) while maintaining low return
loss and good isolation between ports belonging to different channels. After
some study we found better performances for a cross-under with 12.7 $\Omega$
impedance compared to the 6.8 $\Omega$ case that would match the impedance of
the triplexer. We opted for the former (12.7 $\Omega$) as it also matches the
impedance of the titanium load resistor on the TES island. The performance of
the cross-under can be seen on the left panel of Figure 9, while on the right
side the performance of tapered 6.8 to 12.7 $\Omega$ impedance transformers
are reported. These are necessary to minimize losses in the transition from
the low impedance triplexer to the higher impedance cross-under. The impedance
transformers used here are all $\sim 10$ mm long; we found that we obtained
the lowest $S_{11}$ (return loss) values for a linear taper design. In Figure
9 we can observe that $S_{11}<-30$ dB across the LF1 and LF2 bands. Other
design tested (stepped impedance and single quarter wave transformers) can
achieve better performances in certain frequency ranges but not across the
whole range.

##  6 TES BOLOMETERS

The final component of the detection chain are the superconducting TES
(transition-edge sensor) bolometers. The signal collected by the antenna after
being channeled and filtered by the RF circuit described above, is dissipated
on a silicon-nitride (SiN) island suspended by four thin silicon-nitride legs.
The microstrip line travels along two of the legs and it is terminated by a
titanium load resistor matched to the transmission line. The titanium resistor
is tightly coupled to a superconductive aluminum-manganese film (AlMn) that is
voltage-biased in its superconductive transition through niobium bias lines.

The response and properties of the TES are determined by its thermal
conductance G (primarily determined by the geometry of the silicon-nitride
legs) and heat capacity C (a palladium thermal ballast is deposited on the TES
island to tune its value). In Table 1 we report the expected optical power
loading each detector type for the LF1 and LF2 pixels. Details of this
calculation and assumptions can be found in 18 and 19. From these values and
assuming a target saturation power $P_{\mathrm{sat}}$ in the range $2-3\times
P_{\mathrm{opt}}$ (optical power) and target time-constant $\tau_{0}\sim 33$
ms, from standard bolometer equations[7] we can find the target thermal
conductance and heat capacity values as a function of the TES critical
temperature $T_{c}$ as reported in Figure 10. For the first fabrication
iteration of these devices we have included multiple TES designs with
different leg and thermal ballast geometries to test the thermal conductance
and heat capacity dependence from design choices. This will help us narrow
down the best design and incorporate changes in future fabrication iterations
to quickly converge to the desired properties for LF1 and LF2 detectors.

##  7 CONCLUSIONS

In this work we have provided an update on the status of the design and
development of LiteBIRD’s LFT thricroic pixels LF1 (40-60-78 GHz) and LF2
(50-68-89 GHz). We have discussed design choices motivated by LiteBIRD
scientific goals. In particular we focused on the details of the optimization
of the design parameters of the sinuous antenna, on-chip bandpass filters,
cross-under and impedance transformers and all the RF components that define
the LF1 and LF2 pixel detection chain. We have presented this work in the
context of the technical challenges and physical constraints of a space
mission.

While this design is rapidly maturing, compared to what has been presented in
the past for these low frequency pixels, we foresee that some design-
fabrication-characterization iterations are going to be needed before
converging to a definitive design and fabrication process that meets the
stringent requirements of a space mission.

The first fabrication iteration for the devices presented in this work is
ongoing right now (as of May 2024), this first batch of detectors will be used
to test our design and the outcome of these tests will be used to update both
the RF design presented in Sections 3, 4 and 5 as well as the TES bolometer
design discussed in Section 6.

###### Acknowledgements.

This work is supported by the World Premier International Research Center
Initiative (WPI), MEXT, Japan. TG acknowledges the support of JSPS KAKENHI
Grant Number 22K14054.

## References

  * [1] Zaldarriaga, M. and Seljak, U. c. v., “All-sky analysis of polarization in the microwave background,” Phys. Rev. D 55, 1830–1840 (Feb 1997).
  * [2] Kamionkowski, M., Kosowsky, A., and Stebbins, A., “A probe of primordial gravity waves and vorticity,” Phys. Rev. Lett. 78, 2058–2061 (Mar 1997).
  * [3] LiteBIRD Collaboration, “Probing cosmic inflation with the LiteBIRD cosmic microwave background polarization survey,” Progress of Theoretical and Experimental Physics 2023, 042F01 (Apr. 2023).
  * [4] Suzuki, A., Ade, P., Akiba, Y., Aleman, C., Arnold, K., Baccigalupi, C., Barch, B., Barron, D., Bender, A., Boettger, D., Borrill, J., Chapman, S., Chinone, Y., Cukierman, A., Dobbs, M., Ducout, A., Dunner, R., Elleflot, T., Errard, J., Fabbian, G., Feeney, S., Feng, C., Fujino, T., Fuller, G., Gilbert, A., Goeckner-Wald, N., Groh, J., Haan, T. D., Hall, G., Halverson, N., Hamada, T., Hasegawa, M., Hattori, K., Hazumi, M., Hill, C., Holzapfel, W., Hori, Y., Howe, L., Inoue, Y., Irie, F., Jaehnig, G., Jaffe, A., Jeong, O., Katayama, N., Kaufman, J., Kazemzadeh, K., Keating, B., Kermish, Z., Keskitalo, R., Kisner, T., Kusaka, A., Jeune, M. L., Lee, A., Leon, D., Linder, E., Lowry, L., Matsuda, F., Matsumura, T., Miller, N., Mizukami, K., Montgomery, J., Navaroli, M., Nishino, H., Peloton, J., Poletti, D., Puglisi, G., Rebeiz, G., Raum, C., Reichardt, C., Richards, P., Ross, C., Rotermund, K., Segawa, Y., Sherwin, B., Shirley, I., Siritanasak, P., Stebor, N., Stompor, R., Suzuki, J., Tajima, O., Takada, S., Takakura, S., Takatori, S., Tikhomirov, A., Tomaru, T., Westbrook, B., Whitehorn, N., Yamashita, T., Zahn, A., and Zahn, O., “The Polarbear-2 and the Simons Array Experiments,” Journal of Low Temperature Physics 184, 805–810 (Aug. 2016).
  * [5] Ade, P. et al., “The Simons Observatory: science goals and forecasts,” JCAP 2019, 056 (Feb. 2019).
  * [6] Abazajian, K. et al., “CMB-S4: Forecasting Constraints on Primordial Gravitational Waves,” ApJ 926, 54 (Feb. 2022).
  * [7] Irwin, K. D. and Hilton, G. C., “Transition-Edge Sensors,” in [Cryogenic Particle Detection ], Enss, C., ed., 99, 63 (2005).
  * [8] Raum, C., Westbrook, B., Beckman, S., Elleflot, T., Farias, N., Ghigna, T., Halverson, N., Hubmayr, J., Hazumi, M., Jaehnig, G., Lee, A., and Suzuki, A., “Fabrication Process Control to Realize High Yield, Uniform, Repeatable Low-Frequency Detector Arrays for the LiteBIRD CMB Experiment,” Journal of Low Temperature Physics (May 2024).
  * [9] Suzuki, A., Multichroic Bolometric Detector Architecture for Cosmic Microwave Background Polarimetry Experiments, PhD thesis, University of California, Berkeley (Jan. 2013).
  * [10] Hubmayr, J., Ade, P. A. R., Adler, A., Allys, E., Alonso, D., Arnold, K., Auguste, D., Aumont, J., Aurlien, R., Austermann, J. E., Azzoni, S., Baccigalupi, C., Banday, A. J., Banerji, R., Barreiro, R. B., Bartolo, N., Basak, S., Battistelli, E., Bautista, L., Beall, J. A., Beck, D., Beckman, S., Benabed, K., Bermejo-Ballesteros, J., Bersanelli, M., Bonis, J., Borrill, J., Bouchet, F., Boulanger, F., Bounissou, S., Brilenkov, M., Brown, M. L., Bucher, M., Calabrese, E., Calvo, M., Campeti, P., Carones, A., Casas, F. J., Catalano, A., Challinor, A., Chan, V., Cheung, K., Chinone, Y., Chiocchetta, C., Clark, S. E., Clermont, L., Clesse, S., Cliche, J., Columbro, F., Connors, J. A., Coppolecchia, A., Coulton, W., Cubas, J., Cukierman, A., Curtis, D., Cuttaia, F., D’Alessandro, G., Dachlythra, K., de Bernardis, P., de Haan, T., de la Hoz, E., De Petris, M., Della Torre, S., Daz Garca, J. J., Dickinson, C., Diego-Palazuelos, P., Dobbs, M., Dotani, T., Douillet, D., Doumayrou, E., Duband, L., Ducout, A., Duff, S. M., Duval, J. M., Ebisawa, K., Elleflot, T., Eriksen, H. K., Errard, J., Essinger-Hileman, T., Farrens, S., Finelli, F., Flauger, R., Fleury-Frenette, K., Franceschet, C., Fuskeland, U., Galli, L., Galli, S., Galloway, M., Ganga, K., Gao, J. R., Genova-Santos, R. T., Georges, M., Gerbino, M., Gervasi, M., Ghigna, T., Giardiello, S., Gjerlw, E., Gonzles, R. G., Gradziel, M. L., Grain, J., Grandsire, L., Grupp, F., Gruppuso, A., Gudmundsson, J. E., Halverson, N. W., Hamilton, J., Hargrave, P., Hasebe, T., Hasegawa, M., Hattori, M., Hazumi, M., Henrot-Versill, S., Hensley, B., Herman, D., Herranz, D., Hilton, G. C., Hivon, E., Hlozek, R. A., Hoang, D., Hornsby, A. L., Hoshino, Y., Ichiki, K., Iida, T., Ikemoto, T., Imada, H., Ishimura, K., Ishino, H., Jaehnig, G., Jones, M., Kaga, T., Kashima, S., Katayama, N., Kato, A., Kawasaki, T., Keskitalo, R., Kintziger, C., Kisner, T., Kobayashi, Y., Kogiso, N., Kogut, A., Kohri, K., Komatsu, E., Komatsu, K., Konishi, K., Krachmalnicoff, N., Kreykenbohm, I., Kuo, C. L., Kushino, A., Lamagna, L., Lanen, J. V., Laquaniello, G., Lattanzi, M., Lee, A. T., Leloup, C., Levrier, F., Linder, E., Link, M. J., Lonappan, A. I., Louis, T., Luzzi, G., Macias-Perez, J., Maciaszek, T., Maffei, B., Maino, D., Maki, M., Mandelli, S., Maris, M., Marquet, B., Martnez-Gonzlez, E., Martire, F. A., Masi, S., Massa, M., Masuzawa, M., Matarrese, S., Matsuda, F. T., Matsumura, T., Mele, L., Mennella, A., Migliaccio, M., Minami, Y., Mitsuda, K., Moggi, A., Monelli, M., Monfardini, A., Montgomery, J., Montier, L., Morgante, G., Mot, B., Murata, Y., Murphy, J. A., Nagai, M., Nagano, Y., Nagasaki, T., Nagata, R., Nakamura, S., Nakano, R., Namikawa, T., Nati, F., Natoli, P., Nerval, S., Neto Godry Farias, N., Nishibori, T., Nishino, H., Noviello, F., O’Neil, G. C., O’Sullivan, C., Odagiri, K., Ochi, H., Ogawa, H., Ogawa, H., Oguri, S., Ohsaki, H., Ohta, I. S., Okada, N., Pagano, L., Paiella, A., Paoletti, D., Pascual Cisneros, G., Passerini, A., Patanchon, G., Pelgrim, V., Peloton, J., Pettorino, V., Piacentini, F., Piat, M., Piccirilli, G., Pinsard, F., Pisano, G., Plesseria, J., Polenta, G., Poletti, D., Prouv, T., Puglisi, G., Rambaud, D., Raum, C., Realini, S., Reinecke, M., Reintsema, C. D., Remazeilles, M., Ritacco, A., Rosier, P., Roudil, G., Rubino-Martin, J., Russell, M., Sakurai, H., Sakurai, Y., Sandri, M., Sasaki, M., Savini, G., Scott, D., Seibert, J., Sekimoto, Y., Sherwin, B., Shinozaki, K., Shiraishi, M., Shirron, P., Shitvov, A., Signorelli, G., Smecher, G., Spinella, F., Starck, J., Stever, S., Stompor, R., Sudiwala, R., Sugiyama, S., Sullivan, R., Suzuki, A., Suzuki, J., Suzuki, T., Svalheim, T. L., Switzer, E., Takaku, R., Takakura, H., Takakura, S., Takase, Y., Takeda, Y., Tartari, A., Tavagnacco, D., Taylor, A., Taylor, E., Terao, Y., Terenzi, L., Thermeau, J., Thommesen, H., Thompson, K. L., Thorne, B., Toda, T., Tomasi, M., Tominaga, M., Trappe, N., Tristram, M., Tsuji, M., Tsujimoto, M., Tucker, C., Ueki, R., Ullom, J. N., Umemori, K., Vacher, L., Van Lanen, J., Vermeulen, G., Vielva, P., Villa, F., Vissers, M. R., Vittorio, N., Wandelt, B., Wang, W., Wehus, I. K., Weller, J., Westbrook, B., Weymann-Despres, G., Wilms, J., Winter, B., Wollack, E. J., Yamasaki, N. Y., Yoshida, T., Yumoto, J., Watanuki, K., Zacchei, A., Zannoni, M., and Zonca, A., “Optical Characterization of OMT-Coupled TES Bolometers for LiteBIRD,” Journal of Low Temperature Physics 209, 396–408 (Nov. 2022).
  * [11] LiteBIRD Collaboration, Allys, E., et al., “Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey,” arXiv e-prints , arXiv:2202.02773 (Feb. 2022).
  * [12] Hubmayr, J., Austermann, J. E., Beall, J. A., Becker, D. T., Dober, B., Duff, S. M., Gao, J., Hilton, G. C., McKenney, C. M., Ullom, J. N., Van Lanen, J., and Vissers, M. R., “Low-Temperature Detectors for CMB Imaging Arrays,” Journal of Low Temperature Physics 193, 633–647 (Nov. 2018).
  * [13] Sobrin, J. A., Anderson, A. J., Bender, A. N., Benson, B. A., Dutcher, D., Foster, A., Goeckner-Wald, N., Montgomery, J., Nadolski, A., Rahlin, A., Ade, P. A. R., Ahmed, Z., Anderes, E., Archipley, M., Austermann, J. E., Avva, J. S., Aylor, K., Balkenhol, L., Barry, P. S., Thakur, R. B., Benabed, K., Bianchini, F., Bleem, L. E., Bouchet, F. R., Bryant, L., Byrum, K., Carlstrom, J. E., Carter, F. W., Cecil, T. W., Chang, C. L., Chaubal, P., Chen, G., Cho, H. M., Chou, T. L., Cliche, J. F., Crawford, T. M., Cukierman, A., Daley, C., de Haan, T., Denison, E. V., Dibert, K., Ding, J., Dobbs, M. A., Everett, W., Feng, C., Ferguson, K. R., Fu, J., Galli, S., Gambrel, A. E., Gardner, R. W., Gualtieri, R., Guns, S., Gupta, N., Guyser, R., Halverson, N. W., Harke-Hosemann, A. H., Harrington, N. L., Henning, J. W., Hilton, G. C., Hivon, E., Holder, G. P., Holzapfel, W. L., Hood, J. C., Howe, D., Huang, N., Irwin, K. D., Jeong, O. B., Jonas, M., Jones, A., Khaire, T. S., Knox, L., Kofman, A. M., Korman, M., Kubik, D. L., Kuhlmann, S., Kuo, C. L., Lee, A. T., Leitch, E. M., Lowitz, A. E., Lu, C., Meyer, S. S., Michalik, D., Millea, M., Natoli, T., Nguyen, H., Noble, G. I., Novosad, V., Omori, Y., Padin, S., Pan, Z., Paschos, P., Pearson, J., Posada, C. M., Prabhu, K., Quan, W., Reichardt, C. L., Riebel, D., Riedel, B., Rouble, M., Ruhl, J. E., Saliwanchik, B., Sayre, J. T., Schiappucci, E., Shirokoff, E., Smecher, G., Stark, A. A., Stephen, J., Story, K. T., Suzuki, A., Tandoi, C., Thompson, K. L., Thorne, B., Tucker, C., Umilta, C., Vale, L. R., Vanderlinde, K., Vieira, J. D., Wang, G., Whitehorn, N., Wu, W. L. K., Yefremenko, V., Yoon, K. W., and Young, M. R., “The Design and Integrated Performance of SPT-3G,” ApJ 258, 42 (Feb. 2022).
  * [14] Suzuki, A., Arnold, K., Edwards, J., Engargiola, G., Ghribi, A., Holzapfel, W., Lee, A., Meng, X., Myers, M., O’Brient, R., Quealy, E., Rebeiz, G., and Richards, P., “Multi-chroic Dual-Polarization Bolometric Focal Plane for Studies of the Cosmic Microwave Background,” Journal of Low Temperature Physics 167, 852–858 (June 2012).
  * [15] Edwards, J. M., O’Brient, R., Lee, A. T., and Rebeiz, G. M., “Dual-Polarized Sinuous Antennas on Extended Hemispherical Silicon Lenses,” IEEE Transactions on Antennas and Propagation 60, 4082–4091 (Sept. 2012).
  * [16] Beckman, S., Advancements in Microwave Optics for Measuring Polarization Anisotropies in the Cosmic Microwave Background, PhD thesis, University of California, Berkeley (2023).
  * [17] Takaku, R., Wen, Q., Cray, S., Devlin, M., Dicker, S., Hanany, S., Hasebe, T., Iida, T., Katayama, N., Konishi, K., Kuwata-Gonokami, M., Matsumura, T., Mio, N., Sakurai, H., Sakurai, Y., Yamada, R., and Yumoto, J., “Large diameter millimeter-wave low-pass filter made of alumina with laser ablated anti-reflection coating,” Opt. Express 29, 41745–41765 (Dec 2021).
  * [18] Westbrook, B. et al., “Development of the Low Frequency Telescope Focal Plane Detector Arrays for LiteBIRD,” in preparation (2022).
  * [19] Hasebe, T., Ade, P. A. R., Adler, A., Allys, E., Alonso, D., Arnold, K., Auguste, D., Aumont, J., Aurlien, R., Austermann, J., Azzoni, S., Baccigalupi, C., Banday, A. J., Banerji, R., Barreiro, R. B., Bartolo, N., Basak, S., Battistelli, E., Bautista, L., Beall, J., Beck, D., Beckman, S., Benabed, K., Bermejo-Ballesteros, J., Bersanelli, M., Bonis, J., Borrill, J., Bouchet, F., Boulanger, F., Bounissou, S., Brilenkov, M., Brown, M. L., Bucher, M., Calabrese, E., Calvo, M., Campeti, P., Carones, A., Casas, F. J., Catalano, A., Challinor, A., Chan, V., Cheung, K., Chinone, Y., Cliche, J., Columbro, F., Coulton, W., Cubas, J., Cukierman, A., Curtis, D., D’Alessandro, G., Dachlythra, K., de Bernardis, P., de Haan, T., de la Hoz, E., De Petris, M., Torre, S. D., Dickinson, C., Diego-Palazuelos, P., Dobbs, M., Dotani, T., Douillet, D., Duband, L., Ducout, A., Duff, S., Duval, J. M., Ebisawa, K., Elleflot, T., Eriksen, H. K., Errard, J., Essinger-Hileman, T., Finelli, F., Flauger, R., Franceschet, C., Fuskeland, U., Galli, S., Galloway, M., Ganga, K., Gao, J. R., Genova-Santos, R. T., Gerbino, M., Gervasi, M., Ghigna, T., Giardiello, S., Gjerløw, E., Gradziel, M. L., Grain, J., Grandsire, L., Grupp, F., Gruppuso, A., Gudmundsson, J. E., Halverson, N. W., Hamilton, J., Hargrave, P., Hasegawa, M., Hattori, M., Hazumi, M., Henrot-Versillé, S., Hergt, L. T., Herman, D., Herranz, D., Hill, C. A., Hilton, G., Hivon, E., Hlozek, R. A., Hoang, T. D., Hornsby, A. L., Hoshino, Y., Hubmayr, J., Ichiki, K., Iida, T., Imada, H., Ishimura, K., Ishino, H., Jaehnig, G., Jones, M., Kaga, T., Kashima, S., Katayama, N., Kato, A., Kawasaki, T., Keskitalo, R., Kisner, T., Kobayashi, Y., Kogiso, N., Kogut, A., Kohri, K., Komatsu, E., Komatsu, K., Konishi, K., Krachmalnicoff, N., Kreykenbohm, I., Kuo, C. L., Kushino, A., Lamagna, L., Lanen, J. V., Laquaniello, G., Lattanzi, M., Lee, A. T., Leloup, C., Levrier, F., Linder, E., Louis, T., Luzzi, G., Macias-Perez, J., Maciaszek, T., Maffei, B., Maino, D., Maki, M., Mandelli, S., Maris, M., Martínez-González, E., Masi, S., Massa, M., Matarrese, S., Matsuda, F. T., Matsumura, T., Mele, L., Mennella, A., Migliaccio, M., Minami, Y., Mitsuda, K., Moggi, A., Monfardini, A., Montgomery, J., Montier, L., Morgante, G., Mot, B., Murata, Y., Murphy, J. A., Nagai, M., Nagano, Y., Nagasaki, T., Nagata, R., Nakamura, S., Nakano, R., Namikawa, T., Nati, F., Natoli, P., Nerval, S., Nishibori, T., Nishino, H., Noviello, F., O’Sullivan, C., Odagiri, K., Ogawa, H., Ogawa, H., Oguri, S., Ohsaki, H., Ohta, I. S., Okada, N., Okada, N., Pagano, L., Paiella, A., Paoletti, D., Passerini, A., Patanchon, G., Pelgrim, V., Peloton, J., Piacentini, F., Piat, M., Pisano, G., Polenta, G., Poletti, D., Prouvé, T., Puglisi, G., Rambaud, D., Raum, C., Realini, S., Reinecke, M., Remazeilles, M., Ritacco, A., Roudil, G., Rubino-Martin, J., Russell, M., Sakurai, H., Sakurai, Y., Sandri, M., Sasaki, M., Savini, G., Scott, D., Seibert, J., Sekimoto, Y., Sherwin, B., Shinozaki, K., Shiraishi, M., Shirron, P., Signorelli, G., Smecher, G., Spinella, F., Stever, S., Stompor, R., Sugiyama, S., Sullivan, R., Suzuki, A., Suzuki, J., Svalheim, T. L., Switzer, E., Takaku, R., Takakura, H., Takakura, S., Takase, Y., Takeda, Y., Tartari, A., Tavagnacco, D., Taylor, A., Taylor, E., Terao, Y., Thermeau, J., Thommesen, H., Thompson, K. L., Thorne, B., Toda, T., Tomasi, M., Tominaga, M., Trappe, N., Tristram, M., Tsuji, M., Tsujimoto, M., Tucker, C., Ullom, J., Vacher, L., Vermeulen, G., Vielva, P., Villa, F., Vissers, M., Vittorio, N., Wandelt, B., Wang, W., Watanuki, K., Wehus, I. K., Weller, J., Westbrook, B., Wilms, J., Winter, B., Wollack, E. J., Yamasaki, N. Y., Yoshida, T., Yumoto, J., Zacchei, A., Zannoni, M., Zonca, A., and LiteBIRD Collaboration, “Sensitivity Modeling for LiteBIRD,” Journal of Low Temperature Physics 211, 384–397 (June 2023).