Optimized Cross-Polarized LEKIDs for W-Band Using Sawtooth Inductors

Lumped-element kinetic inductance detectors (LEKIDs) based on sawtooth inductors for <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-band are presented in this article. A careful analysis is carried out for the cross-polarization in the inductor geometry, which brings out the absorption of the nondesired <inline-formula> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula>-field component of an incident wave plane. The proposed inductor geometry with sawtooth sections demonstrates improved cross-polarization. The analytical results are verified by comparison with 3-D electromagnetic (EM) simulations. As the first proof of concept, <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula>-band optical response is demonstrated through quasioptical characterization at room temperature of an aluminum LEKID array. Moreover, a LEKID array based on bilayer superconducting titanium/aluminum (Ti/Al) thin film is developed for evaluating the performance at millikelvin temperatures. Darkness characterization confirms the high-quality factor of the fabricated detectors and the low-frequency design reliability. In addition, cryogenic optical experiments are performed for spectroscopic and detector sensitivity characterization. The proposed geometry opens the possibility of developing large-format polarimetric cameras based on on-chip LEKID structures for future astronomical experiments.


I. INTRODUCTION
S PACE-or ground-based experiments increasingly require improved detectors, in terms of responsivity or noise performance, to reach new scientific milestones.In this regard, applications such as radio astronomy in the investigation of the origin of the Universe or the detection of dark matter [1] are continuously demanding state-of-the-art detectors able to distinguish extremely low-power signals.However, there is also a great interest in detecting the polarization of the incoming radiation.Particularly, the characterization of the polarization of the cosmic microwave background (CMB) radiation is considered to bring crucial information about the early stages of the Universe such as the epoch of reionization and the inflation time [2], [3], [4].
In the last years, low-temperature detectors have significantly evolved, providing significant roles in scientific applications at subKelvin temperatures [5], [6].These detectors employ superconducting materials to substantially improve detection limits and they have demonstrated significant results in terms of sensitivity within millimeter-wave bands [7], [8].Among superconducting detectors, kinetic inductance detectors (KIDs) are of particular interest since they are inherently multiplexable in the frequency domain, which enables the use of thousands of detectors over a single readout line [9].
KIDs are being employed in many radio astronomy instruments for millimeter and submillimeter-wave applications with thousands of multiplexed detectors [10], [11], [12], [13], [14].Two main types of KIDs are defined depending on how they absorb the radiation: antenna-coupled microwave KIDs (MKIDs) [15] and lumped-element KIDs (LEKIDs) [16].LEKIDs consist of a discrete meandered inductor in series with an interdigital capacitance coupled to a single transmission line.In comparison with MKIDs that use quarter-wavelength resonators, LEKIDs are more sensitive as a high and constant current density distribution is achieved in the lumped element inductor at resonance conditions.
Applications such as CMB experiments have pushed forward the development of new LEKID designs, focused on improving their sensitivity at lower-frequency bands, such as the W -band, and simultaneously developing dual-polarization designs [17], [18], [19].Furthermore, LEKID designs based on Hilbert fractal structures were implemented to evaluate polarization sensitivity, taking advantage of the use of a single layer for absorbing both orthogonal polarizations [13].However, this option requires duplicating the number of arrays and using an external polarizer.Other experiments proposed the detection of polarization by using KIDs together with an orthomode transducer (OMT), which separates orthogonal components of the polarized signal [20], [21].LEKIDs have demonstrated significant results in being able to absorb orthogonal polarizations, but at higher-frequency bands [12], [22].However, this performance has not been demonstrated at the W -band yet.
Aja et al. [23] proposed a W -band on-chip polarimeter based on two LEKIDs that consist of a series capacitor-inductor resonator coupled to a single 50-coplanar waveguide (CPW) transmission line.They are stacked one on top of the other and placed in orthogonal directions.This proposal is of particular interest since a minimum value of the foreground contamination is reached in this frequency range, thus a great effort is being made in the development of suitable W -band detectors [2].However, de Ory et al. [24] showed an extra cross-polarization that prevents its good performance as a polarimeter.Hence, in this work, we aim to minimize this cross-polarization.A new design is proposed based on sawtooth inductors to enhance LEKIDs performance in a single polarization to develop an optimized on-chip polarimeter for the W -band.
The article is organized as follows.After the Introduction, Section II describes high-and low-frequency designs of the LEKIDs for operation at the W -band. Section III deals with the tuning of the cut-off frequency of the superconductor based on titanium/aluminum (Ti/Al), describing the proposed methodology and fabrication.Section IV presents experimental set-ups to perform room temperature and cryogenic tests, describing the prototype assemblies.Test results at room and cryogenic temperatures are detailed in Section V. Finally, Section VI presents conclusions summarizing this article.

II. W -BAND LEKID DESIGN
The detector's design involves two steps: on the one side, the inductor improvement, in which geometry and impedance determine the absorption efficiency and responsivity; on the other side, the low-frequency design, including capacitor dimensions and electrical coupling, which determines its quality factor and resonant frequency, critical parameters for the LEKIDs readout.In Sections II-A and II-B, both steps are described.

A. W -Band Coupling Design
In LEKIDs, the inductor acts as the sensitive part of the detector, so a careful analysis of its geometry is critical for obtaining optical impedance matching and, therefore, optimizing the optical response.The traditional LEKID design, as described in [25] and shown in Fig. 1(a), is composed of long vertical strips that are addressed for providing the maximum absorption for a vertical E-field.These vertical inductor sections are joined by short horizontal lines, required to build the necessary inductance for the low-frequency resonator and to allow current flow.As a consequence of their orthogonal direction to the desired E-field radiation, these short lines have a nonnegligible impact and cause a nondesired absorption of the orthogonal E-field component, which produces a crosspolarization effect.
To reduce the cross-polarization effect, the sensitivity to the orthogonal E-field needs to be minimized.This can be done by modifying the horizontal section's impedance, diminishing the absorption of the undesired polarization.A circuit model is developed for analyzing the impedance of different geometries, to understand the origin of this undesired absorption.Although more accurate results are obtained through 3-D electromagnetic (EM) simulations, this previous development of the equivalent circuit models is very useful for optimizing the LEKID design and its response.
Several types of sections, such as wiggled sections [12], triangular shapes, or sawtooth shape lines, are analyzed in terms of the input impedance of a periodic array.An improved structure based on a sawtooth shape is proposed, where small vertical lines joined by angled ones replace the short horizontal sections [see Fig. 1(b)].The smaller angle with shorter distances between vertical short sections provides a higher reflection coefficient in the structure, minimizing the absorption of the orthogonal incident E-field.The best results, compatible with the nanofabrication process, are obtained for the sawtooth shape with short vertical strips joined with lines at 15 • angle.An additional advantage of this modification is that it also increases the inductor volume and, then, the dynamic range of the detector [12].
To understand the optical matching of this configuration, an incident wave with vertical E-field (TEM V ) referred to the position of the LEKID in Fig. 1 is considered.Because the long sections in both Fig. 1(a) and (b) have the same geometry (2a, g), they present the same impedance, with a resistive part and an inductive reactance.The impedance for this parallel metal strip grating is obtained based on equations in [26], [27], which are valid for spacing between strips shorter than λ.On the other hand, the short sections of the meandered line cause a capacitive reactance.The calculation of the impedance for these short horizontal sections is performed using a In both cases, metal strips have an inductive behavior for an electrical field parallel to them, Y stripsL , and a capacitive behavior for an orthogonal electrical field, Y stripsC .This capacitive effect is very small and practically negligible for the transmission of a so-oriented EM wave component.
The proposed circuit based on transmission lines is shown in Fig. 2(a), where η 0 is 377 , ε r Si = 11.9, and η Si = η 0 /(ε r Si ) 1/2 is 109.29 .This circuit also includes the silicon wafer whose thickness is chosen to be ∼λ/2 (482.8 µm) at 90 GHz (ℓ 2 = 480 µm in Fig. 2).The LEKID dimensions a, g, h, h s , and b in Fig. 1 provide the admittances, Y stripsL and Y stripsC , related to inductive and capacitive effects, respectively, of the equivalent circuit model in Fig. 2(a).The strip width 2a and spacing g are chosen to provide the broadest bandwidth around 90 GHz with Re(Y stripsL ) = 1/η 0 .The admittance of the short sections is obtained for two cases, strip width 2a and spacing h [Fig.1(a)] and strip width b and spacing h s [Fig.1(b)].The susceptance of the equivalent admittance (Y strips = Y stripsL +Y stripsC ) is compensated with a capacitive effect through an air gap (ℓ 1 = 970 µm, ∼0.29λ at 90 GHz in Fig. 2) ending in a backshort to be optically matched to the free space, maximizing the absorption and bandwidth.The cross section of the structure is shown in Fig. 2(b), where ε rAir is 1.
For simulation purposes, a nominal Ti/Al sheet resistance of 1.27 /sq is used; however, it is worth noting that this value may differ between the different experiments due to nanofabrication tolerances.With this value, the dimensions for the LEKIDs in Fig. 1 to match the air impedance are a = 1.5 µm and g = 443 µm.The calculated impedance of the long strips (1/Y stripsL ) at 90 GHz has an equivalent circuit composed of a 187.5-resistance in series with a 403-pH inductor, whereas the equivalent circuit for the short section of the meandered line (1/Y stripsC ) is a capacitor of 0.0049 fF for the shape shown in Fig. 1(a) and 6 fF for the sawtooth shape [Fig.1(b)].
For the analysis of an incident plane wave with horizontal E-field (TEM H ) referred to the position of the LEKID in Fig. 1, the different geometries of the short horizontal sections in Fig. 1(a) and (b) are taken into account.The impedance of the LEKID in Fig. 1(a) is calculated for strips of 2a width and spacing h of 3083 µm.On the other hand, for the sawtooth short sections, shown in Fig. 1(b), with sections of 15 • angle separated by 30 µm, at the W -band, the impedance can be calculated like uniform strips of width b of 103.5 µm and spacing h s of 2949 µm.Both impedances are obtained based on equations in [26] and [27] and the equivalent circuit of the calculated impedance for these short sections (1/Y stripsL ) at 90 GHz is a 1300-resistance in series with a 4.42-nH inductor for the LEKID of Fig. 1(a), whereas for the sawtooth shape LEKID in Fig. 1(b), it is a 36resistance with a 1.97-nH inductor.The short sections with a less resistive impedance result in a structure with a greater free space mismatching and, therefore, in a lower absorption.The capacitive effect of the long strips (1/Y stripsC ) in both cases for this incident wave is 0.332 fF.
Subsequently, using these values for the equivalent circuit as a starting point, the optimization of the LEKID is obtained through 3-D EM simulations.They are carried out at the W -band for an infinite array of LEKIDs on 480-µm-thick silicon and the backshort with 970-µm air using unit cell analysis and a Floquet port with HFSS in Ansys Electronics Desktop [28].Driven option Modal is selected as solution type for the analysis in HFSS, to compute incident plane waves.The initial mesh is smaller than 0.333λ and the maximum error is set to 0.01 for adaptive solution.From these 3-D EM simulations, it is found that the short parts of the inductive meander line are responsible for the absorption in the crosspolarization, which is calculated for each E-field polarization as 1−|S 11 | 2 .Fig. 3 shows LEKID absorption results for HFSS simulation and circuit model simulation without an interdigital capacitor.The circuit models agree with the HFSS simulation results.A maximum absorption around 99% is predicted at 91 GHz depicted in Fig. 3(a), whereas an improvement for the cross-polarization with the sawtooth LEKID is obtained as shown in Fig. 3(b).

B. Low-Frequency Resonator Design
The proposed LEKID based on a series capacitor-inductor resonator is coupled to a 50-CPW transmission line.The inductor geometry is fixed for the optical absorption, while other parameters such as capacitance and coupling need to be optimized.Momentum (Keysight Technologies) [29] and Sonnet [30] simulators are employed for this purpose.
First, an interdigitated capacitor of 0.7 pF is employed for fixing the readout resonant frequencies around 650 MHz and its value is swept from pixel to pixel by changing the length of one of its fingers for readout purposes.
Then, an accurate design of the coupling factor is critical for the dynamic range optimization of the detector under millimeter-wave radiation [31].The loaded quality factor of the resonator, Q, is given by 1 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where the internal quality factor, Q i , refers to the internal losses of the resonator, and the coupling quality factor, Q c , describes the strength of the coupling to the transmission line.In our case, the expected Q i under illumination is of the order of 10 5 .A coupling factor Q c ≈ 10 4 is chosen to avoid the undercoupling regime (Q i < Q c ), where the detector visibility (depth in the transmission scattering parameter, S 21 ) is degraded [4].For this purpose, an inductive coupling of the LEKID to the CPW is made through one of the long sections of the meandered line and the distance between the LEKID and the ground plane (s 1 ) as well as the inner ground plane width (m) are optimized.These parameters of the LEKID design are depicted in Fig. 1, where m = 40 µm and s 1 = 109 µm.

III. LEKID FABRICATION
The prototypes are fabricated by means of confocal sputtering following the technological process detailed in [25].

A. Tuning Cut-Off Frequency
The absorption capacity of a superconductor is limited by the energy required to break Cooper pairs, twice the superconducting gap, leading to a cut-off frequency, f cut .The superconducting gap, , is proportional to the critical temperature, T c , according to 2 ≈ 3.52 k B T c , where k B is the Boltzmann constant.In bulk aluminum, the critical temperature is 1.2 K that prevents the use of this material for detection in the W -band.However, the critical temperature can be reduced using the well-known superconducting proximity effect with a lower T c superconductor, such as titanium (with a bulk critical temperature of 0.38 K), resulting in a bilayer film [32].
Superconducting critical temperature is characterized for several Ti/Al bilayers by cryogenic transport measurements.The Al thickness is fixed to 15 nm, whereas the Ti thickness is varied from 25 to 10 nm.As can be seen in Fig. 4, even though the aluminum layer has a critical temperature of 1.3 K, by increasing the Ti layer thickness in the bilayer film, it can be reduced down to 700 mK.This dependence on Ti thickness demonstrates that the larger the thickness of the Ti layer, the lower the effective T c of the bilayer is [17].Considering the bilayer film as a pure superconductor, this is directly translated into a cut-off frequency smaller than 60 GHz, making the superconducting resonators suitable for the W -band (75-110 GHz).

B. LEKID Demonstrators Nanofabrication
For the cryogenic characterization, a nine-element array demonstrator with the sawtooth strip is fabricated in a 15-nm Ti/15-nm Al bilayer on a high-resistive silicon 480-µm-thick wafer with a measured T c of 785 mK.A photograph of the fabricated device is shown in Fig. 5.
Two dedicated prototypes for each LEKID design are fabricated to measure their absorption at room temperature using the quasi-optical setup described in [23].These measurements allow us to validate the design and extrapolate the absorption to low-temperature conditions.All of them are based on a

A. Room-Temperature Test System
For the room-temperature characterization, a quasi-optical system based on a free-space measurement is used.The system consists of two horn antennas, two dielectric lenses to collimate the beam at the measurement plane, and a vector network analyzer as explained in [23].The feed antenna shows wide bandwidth and excellent cross-polarization, allowing an almost perfect plane wave with only one polarization.Rectangular waveguide antennas, model QSH-SL-75-110-F-20 from Steatite, are employed, providing around 20-dBi gain with dimensions a × b = 14.8 × 11 mm at the aperture.The calculated output beam waist radius, at the reference plane of the array under measurement, is 16.87 mm, which establishes the size of the array's samples under measurement to a minimum diameter of around 34 mm for its correct characterization as an infinite array [23].

B. Cryogenic Test System
For the cryogenic characterization, a dilution He3/He4 refrigerator (Bluefors LD-250) is employed.The cryogenic harness is composed of CuNi and NbTi radio-frequency lines, attenuators, dc blocks, and a low-noise amplifier in the 4-K stage.The readout setup is based on LNA and a vector network analyzer E5071C (VNA).Further information is included in [23].
A dedicated holder, shown in Fig. 7, is designed to anchor the LEKID demonstrator to the 10-mK cold plate and assembles the required stack of optical elements to properly configure the experiments.The main chassis consists of a copper box where a 30 × 30 mm 2 area is drilled in the center of the package to place the demonstrator.It enables the connection of the chip with the cryogenic harness through circuit printed boards and SMA connectors.On top of it, there is an aperture lid that limits the incoming radiation to the center pixel, and two supports hold a 110-GHz cut-off frequency low-pass filter and a linear polarizer.On the rear part, a copper backshort is placed at 970-µm distance from the sample backside for optical matching.An absorber material suitable for the W -band based on Stycast 2850 FT is used to cover the inner metal parts of the holder.For responsitivity analysis, a blackbody load, provided with a temperature controller, is installed at the 4-K stage.
In addition, a spectroscopic cryogenic characterization of a single pixel is performed.The measurement setup consists of an SMB100A signal generator together with an SMZ110 frequency multiplier, both from Rohde&Schwarz that generate the W -band signal, and a W -band antenna (model 27240-20 from Flann Microwave) that defines the orientation of the E-field at room temperature and it is used to illuminate the array.Teflon-based lenses, infrared filters, and a 110-GHz low-pass filter are assembled in the different cryostat stages.Further details of the employed system are explained in [33].

A. Room-Temperature Measurements
First, the room-temperature prototypes based on the complete LEKIDs (with capacitors and inductors), described in Section III-B are characterized for the two orthogonal linearly polarized waves in the 75-110-GHz frequency range with the quasi-optical test bench.Fig. 8 shows the simulated and measured absorption of the LEKIDs for a linearly polarized incident wave parallel and perpendicular to the LEKID inductor at room temperature.
For both prototypes, the response to the vertical illumination (TEM V ) demonstrates a maximum absorption of around 94% at 92 GHz.The absorption in the frequency band can be affected by several issues, such as the thickness of the wafer, the air gap, and the thickness or sheet resistance of the bilayer.A sensitivity analysis, starting at nominal values for all these parameters, is carried out considering the fabrication tolerances, shown in Fig. 8.The parameters taken into account in the analysis are silicon thickness 480 ± 10 µm, the air gap to the backshort 970 ± 10 µm, and the film thickness 39 ± 3 nm (R s = 1.16−0.99/sq).Taking into account these tolerances, a good agreement between measurements and simulations for a TEM V wave is obtained.However, the absorption for the TEM H wave results in an undesired high reflection coefficient in both cases.As obtained from the circuit model and the 3-D simulations, this is mainly due to the interdigital capacitors.In this case, slight discrepancies between simulation and measurement are obtained which can be attributed to a small misalignment of the array in the quasioptical measurement setup, or even edge effects.
To demonstrate the cross-polarization improvement for the new sawtooth design, the second manufactured arrays including just inductors are characterized.The comparison between both designs, shown in Fig. 9, confirms the reduction of the undesired component using the new sawtooth topology and the effect caused by the capacitor depicted in Fig. 8 is removed.Moreover, for all fabricated prototypes the measured absorption versus frequency for the TEM V shows almost the same response.It is worth noting that at cryogenics conditions, the absorption in the capacitor has no impact since photons hitting the capacitor will not be detected as no change in the kinetic inductance (L k ) will be produced [34].

B. Cryogenic Temperature Measurements
The previously presented single-polarization array of nine LEKIDs with the sawtooth inductor is characterized at cryogenic conditions using the setup shown in Section IV-B.
1) Dark Characterization: The holder is fully enclosed using a copper lid and aluminum foil, to avoid any undesired radiation exciting the LEKIDs.Using the VNA, a frequency sweep is performed to individually characterize the resonant frequency and the quality factor of each resonator.A transmission response calibration is performed to set the reference plane of the measurement, correcting the input and output paths up to the LEKIDs plane.This procedure is done at 700 mK, just below the superconducting transition where LEKIDs are still not visible [31].Fig. 10 shows the obtained forward scattering parameter (S 21 ) amplitude at 10 mK with an input power P in = −105 dBm in the detector, setting the VNA with a power of P = −75 dBm, a frequency range from 670.5 to 691.0 MHz, and a frequency step of 1.025 kHz.Nine dips are observed, corresponding to each one of the nine fabricated LEKIDs.By varying the capacitance, the resonators are designed for having resonant frequencies  3 MHz step.However, the obtained resonant frequencies are nonhomogeneously spaced due to fabrication tolerances.From the obtained resonant frequency, the kinetic inductance L k and kinetic inductance fraction, α, are estimated as follows.First, the LEKID made of a lossless metal and L k = 0 is simulated using the Sonnet EM simulator, obtaining the values for the geometrical inductance (L g = 36 nH) and capacitance (C ≈ 0.7 pF).From these values and the experimental resonant frequency ( f res = 1/(2π((L g +L k )C) 1/2 )), the kinetic inductance is extracted and the kinetic fraction is calculated as α = (L k /L g + L k ), obtaining L k = 2.86 pH/sq and α = 0.53 [16].
Fig. 11 shows the quality factor of each resonator obtained by following the procedure detailed in [35].Coupling quality factors around 2 • 10 4 are obtained, which match reasonably  well to the designed values.In addition, internal quality factors greater than 6 • 10 5 demonstrate the good quality of the fabricated films.
2) Responsivity Characterization: For optical characterization, the holder faces the blackbody load, and the lid of the holder is replaced by the aperture lid, filter, and polarizer, presented in Section IV-B.The polarizer is aligned with the inductor lines to fix the polarization of the incoming radiation.The blackbody temperature (T bb ) is swept from 4.5 to 10.5 K, increasing the optical power.The results are shown in Fig. 12 where the shift to lower frequency and the decrease in the quality factor confirm the response to the incoming radiation.
The fractional frequency shift is defined as  where f 0 and f are the initial measured frequency and the measured frequencies, respectively.In Fig. 13, this frequency shift is plotted as a function of the blackbody temperature.A linear relationship is observed, corresponding to the slope, ∂x/∂T bb , to the detector responsivity which is 2.58 ppm/K, agreeing with previous experiments [12].
3) Spectroscopic Characterization: The spectral responsivity of the detectors is characterized using the external W -band setup previously explained in Section IV-B and consists in the study of the relative shift of the resonant frequency of the LEKID normalized to its maximum value, given by where f off is the resonant frequency in dark conditions and f illum is the measured resonant frequencies as a function of the frequency of the incoming radiated signal.Fig. 14 shows the obtained results which confirm the response within the W -band using the Ti/Al technology and the optical design.A maximum shift in the resonant frequency is observed around 90 GHz demonstrating the high-frequency quasioptical design and agrees with the room-temperature results.

VI. CONCLUSION
In this work, we present an improved state-of-the-art design of superconducting LEKIDs for future astronomical experiments in the W -band.In LEKIDs, the inductor, which acts as the sensing area of the detector, consists of parallel vertical lines joined by short horizontal sections that cause a nondesired orthogonal absorption and, hence, induce crosspolarization.Based on equivalent circuits and 3-D EM simulations, we demonstrate that this undesired cross-polarization absorption can be reduced by engineering the short horizontal section admittances.A sawtooth-based structure LEKID is proposed for reducing the sensitivity in the undesired direction.Room-temperature optical characterization shows a reduction of the cross-polarization when compared with traditional LEKIDs.A nine-pixel prototype is tested at cryogenic temperature, demonstrating sensitivity in the W -band.This design pushes forward the previous efforts for developing onchip polarimeters based on LEKIDs and opens the possibility of its use in polarimetric astronomical experiments in the W -band.

Fig. 1 .
Fig. 1.Structure of LEKIDs.A meander inductor with strips of width 2a and spacing g.Coupling separation (s 1 and m) between the resonator and the readout 50-CPW feedline.(a) Inductor with straight short horizontal stripes [24].(b) Inductor with sawtooth horizontal strips.

Fig. 2 .
Fig. 2. (a) Equivalent circuit with transmission lines of an LEKID with the structure to be optically matched to the free space.(b) Cross section of a single-polarization LEKID.

Fig. 3 .
Fig. 3. LEKID absorption results for HFSS simulation and circuit model simulation without the interdigital capacitor.(a) Vertical E-field (TEM V ) referred to the position of the LEKIDs in Fig. 1.(b) Horizontal E-field (TEM H ) referred to the position of the LEKIDs in Fig. 1.

Fig. 4 .
Fig. 4. Dependence of the critical temperature and cut-off frequency of the bilayer film with the titanium thickness over a 15-nm aluminum layer.

Fig. 6 .
Fig. 6.Fabricated array of 11 × 11 LEKIDs with sawtooth inductor on a 480-µm silicon wafer.(a) LEKID array assembly to be characterized at room temperature with size 40 × 40 mm.(b) Detail of the first prototype (LEKIDs with an inductor and a capacitor).(c) Detail of the second prototype (LEKIDs without capacitor).

Fig. 7 .
Fig. 7. Cryogenic experimental setup for the optical characterization.(a) W -band low-pass filter.(b) Assembly of the holder in the millikelvin stage with the polarizer on top.(c) Details of the aperture lid placed over the center LEKID.

Fig. 9 .
Fig. 9. Simulated and measured absorption at room temperature for the LEKID prototypes without capacitors.Linearly polarized incident wave for orthogonal polarizations.

Fig. 10 .
Fig. 10.Resonant frequencies for the fabricated 3 × 3 LEKID array with the sawtooth strip, under dark conditions at T = 10 mK, with an input power at the detector of P in = −105 dBm and a frequency step 1.025 kHz.

Fig. 11 .
Fig. 11.Quality factors for the nine fabricated pixels under dark conditions at T = 10 mK.Q is the loaded quality factor, Q i the internal quality factor, and Q c the coupled quality factor.Values obtained from the frequency sweep in Fig. 10.

Fig. 12 .
Fig. 12. Transmission measurement corresponding to the illuminated LEKID as a function of blackbody temperature (T bb ).The radiation linear polarization is parallel to the inductor lines.

Fig. 14 .
Fig. 14.Frequency shift of the resonant frequency with respect to the one in darkness condition (f off ) normalized to its maximum value (f off −f illum ) as a function of the input radiation frequency within the W -band.