P Torne

J Macías-Pérez

B Ladjelate

A Ritacco

M Sánchez-Portal

S Berta

G Paubert

M Calvo

G Desvignes

R Karuppusamy

S Navarro

D John

S Sánchez

J Peñalver

M Kramer

K Schuster

Detection of the magnetar XTE J1810-197 at 150 and 260 GHz with the NIKA2 kinetic inductance detector camera

Keywords: magnetars -(Stars, ) pulsars, individual XTE J1810-197 -Instrumentation, detectors -Astronomical instrumentation, methods and techniques -Radiation mechanisms, non-thermal

Context. The investigation of pulsars between millimetre and optical wavelengths is challenging due to the faintness of the pulsar signals and the relative low sensitivity of the available facilities compared to 100-m class telescopes operating in the centimetre band. The kinetic inductance detector (KID) technology offers large instantaneous bandwidths and a high sensitivity that can help to increase the ability of existing observatories at short wavelengths substantially to detect pulsars and transient emission. Aims. To investigate whether pulsars can be detected with KIDs, we observed the anomalous X-ray pulsar XTE J1810-197 with the New IRAM KIDs Array-2 (NIKA2) camera installed at the IRAM 30m telescope in Spain. Methods. Several short observations of XTE J1810-197 were made on 2019 March 25 under good weather conditions to verify the stability of the KIDs and to try to detect the expected broadband pulsations from the neutron star. Results. We detected the pulsations from the pulsar with NIKA2 at its two operating frequency bands, 150 and 260 GHz (λ=2.0 and 1.15 mm, respectively). This is the first time that a pulsar is detected with a receiver based on KID technology in the millimetre band. In addition, this is the first report of short millimetre emission from XTE J1810-197 after its reactivation in December 2018, and it is the first time that the source is detected at 260 GHz, which gives us new insights into the radio emission process of the star. Conclusions. We demonstrate that KIDs can fulfil the technical requirements for detecting pulsed emission from neutron stars in the millimetre band. We show that the magnetar XTE J1810-197 is again emitting strong pulsations in the short millimetre band.

Introduction

Pulsars are rotating neutron stars that emit broadband-beamed emission that is detectable as pulses from Earth as their beams cross our line of sight. They act like cosmic clocks, and studying them enables high-precision astronomy (e.g. Kramer et al. 2006;Eatough et al. 2013;Cromartie et al. 2020). Nevertheless, the mechanism of their coherent radio emission is still unknown (for a review, see e.g. Melrose 2017).

One way to better understand the coherent and incoherent components of pulsar emission and aid constraining theoretical models is to measure the spectrum of pulsars in the poorly explored window between the radio and optical regimes (e.g. Michel 1978). However, pulsars in general are steep spectral sources in the radio band, which means that their emission is extremely weak above a few gigaherz (Maron et al. 2000). Ad-Main contact author, e-mail: torne@iram.es ditionally, with higher frequencies, the collecting areas and efficiency of the available telescopes tend to decrease, and instrumentation with a high enough time resolution to resolve the pulsations is rarely available. As a result, pulsar studies in the millimetre, infrared, and optical regimes are sparse and highly challenging.

To improve our ability to detect and study pulsars at short wavelengths, we need higher sensitivity. One solution is to use large-bandwidth and low-noise receivers. In recent years, a new technology based on kinetic inductance detectors (KIDs) has been used to fabricate sensitive large-array detectors (for a review, see Mauskopf 2018). KID arrays of thousands of pixels can be built and operated with the most advanced sensitivity [START_REF] Monfardini | kinetic inductance detectors for space applications[END_REF]Mazin et al. 2013;Catalano et al. 2014;Calvo et al. 2016;Perotto et al. 2020).

Furthermore, KIDs are fast detectors, with typical time constants of about 100 µs (Catalano et al. 2016;[START_REF] Monfardini | kinetic inductance detectors for space applications[END_REF], and they can be used at very high sampling rates up to few megaherz (Swenson et al. 2010;Bourrion et al. 2016;Fasano et al. 2020). This makes KIDs a promising tool for investigating pulsars in unexplored sections of their spectrum and test models of pulsar magnetospheres.

The KID-based NIKA2 camera installed at the IRAM 30m telescope (Adam et al. 2018) is a dual wide-band camera operating simultaneously at 150 and 260 GHz (λ=2.0 and 1.15 mm) with 45 GHz of bandwidth and a total of 2896 KIDs cooled down to about 150 mK (Calvo et al. 2016). NIKA2 offers an excellent performance with typical sensitivities per detector of 9 and 30 mJy s1/2 at 150 and 260 GHz, respectively (Perotto et al. 2020). In the future, NIKA2 will also offer polarisation measurements in the 260 GHz band [START_REF] Ritacco | Universe @ NIKA2 -Observing the mm Universe with the NIKA2 Camera[END_REF]. Currently, the maximum theoretical sampling frequency of NIKA2 is 500 Hz 1 .

The observations presented here focus on the anomalous X-ray pulsar XTE J1810-197. This pulsar was identified as a magnetar in 2003 after a sudden increase in its X-ray luminosity (Ibrahim et al. 2004). Magnetars are a small family of pulsars whose high-energy luminosity cannot be accounted for solely by the spin-down energy, and they are thought to be powered in addition by magnetic field decay (for a review on magnetar properties, see e.g. Kaspi & Beloborodov 2017). XTE J1810-197 was furthermore the first magnetar to exhibit radio emission (Halpern et al. 2005;Camilo et al. 2006), an uncommon property that only five of the known 23 known magnetars have shown to date. Interestingly, and in contrast to the majority of the pulsar population, radio magnetars share a tendency to maintain a flat or even inverted spectrum in the radio band (Levin et al. 2010;Camilo et al. 2007Camilo et al. , 2008;;Torne et al. 2015). Radio magnetars can therefore be very bright in the millimetre band (Torne et al. 2017).

XTE J1810-197 is highly variable, and its radio emission ceased about three years after the discovery of the radio pulsations (Camilo et al. 2016). However, radio emission from the neutron star was re-detected in December 2018 (Levin et al. 2019), and follow-up campaigns at several wavelengths including X-ray (Gotthelf et al. 2019) confirmed that the source entered a new period of intense radiative activity. Observations were also carried out with the Superconductor-Insulator-Superconductor (SIS) Eight Mixer Receiver (EMIR, Carter et al. 2012) at the IRAM 30m telescope, confirming that the source was also bright in the millimetre band. These observations will be presented elsewhere, but they confirmed that XTE J1810-197 was a good candidate for trying to observe it with NIKA2 and test whether the KIDs are able to detect broadband pulsations in the millimetre band.

Dataset and methods

Observations

XTE J1810-197 was observed on 2019 March 25 with the NIKA2 camera at the IRAM 30m telescope under good weather conditions (τ z 225 GHz = 0.29). The KID arrays were configured to sample at a standard frequency F s = 23.84 Hz, which is enough to obtain 132 data points across one rotational period of the pulsar (P ≈ 5.54 s). The observing mode was set to stare mode, in which the telescope continuously tracked the source at a fixed position on the three arrays of the camera.

The resonance frequency of each detector in NIKA2 is proportional to the input signal, and signal variations translate into resonance shifts. During the observations, we measure the signal via the amplitude and phase shift (transfer function) of a specific microwave test tone for each detector (Calvo et al. 2016). Prior to an observation, the detectors and readout are tuned to adapt the response to the input background signal from the sky. To ensure a coherent time series, the data were acquired continuously during each full scan and were recorded into a single data file.

In total, we recorded four scans of XTE J1810-197, the first two with 10 min duration each, and the last two with 15 min duration each. The maximum integration time per scan was set to ensure efficient and manageable data processing.

Data processing

The exact position of the magnetar on the KID arrays was a priori only known to a certain precision. To search for the exact pixels on which the source was centred, we wrote as 32 bit float time series the values of reconstructed signal (in resonance frequency units) from a number of pixels around the estimated position, corresponding to an area on sky of about 1 arcmin 2 . Because the pixel size and separation are different for the 2 and 1.15 mm arrays, time series from 45 pixels (slightly larger area) were extracted for the 2 mm array (called A2), and 77 and 84 pixels for the two arrays at 1.15 mm (called A1 and A3, respectively). The difference in the number of pixels for the two 1.15 mm arrays is due to a slightly larger number of non-valid pixels in array A3 (Perotto et al. 2020).

Next, we filtered the time series to subtract the atmospheric variations. We applied a running-fit filter consisting of a moving window of 4.5 s. As the window moves, a first-order polynomial is fit and subtracted from the data. Each filtered time series (i.e. from each extracted KID pixel) was then directly folded by the routine prepfold from the pulsar analysis suite PRESTO 2 . An ephemeris from Camilo et al. (2016), obtained from the pulsar database PSRCAT3 (Manchester et al. 2005), was used to predict the spin period at the observation epochs. The resulting pulsar candidate plots were manually inspected to identify the time series, and so the KID pixel of each array that contained the best signal in terms of signal-to-noise ratio at the spin period of XTE J1810-197. The KID pixels containing the highestsignificance pulsations were KH097, KC016, and KP018 for the A1, A2, and A3 array, respectively.

A running-fit (or running-median or mean) filtering tends to subtract part of the pulsar signal, which affects the intensity measurements. For this reason, we re-processed the data after the pixels that contained the magnetar signal were identified. In this re-processing, we used a so-called multi-pixel filter. This method exploits the advantage of having multiple beams on the sky and removes the atmospheric variations, but preserves the pulsations unchanged. For 150 GHz, we selected pixels pointed on the sky between 2 and 3 half-power beam widths (HPBW, θ 150 ≈17.7 arcsec) around the magnetar. Because the detectors are less sensitive and the atmospheric fluctuations stronger, we selected pixels at 260 GHz that pointed somewhat closer, between 1.25 and 2.5 HPBWs (θ 260 ≈11.2 arcsec). From this subset, the pixels showing residual pulsations at any signal-to-noise ratio (as found with the running-fit filter) were flagged and excluded from the analysis. For the remaining pixels (17 pixels for A2, 14 pixels for A1 and A3), a running median with a window of 1.5 s was applied, and the resulting running median vectors were averaged and subtracted from the time series centred on the magnetar. This was done separately for arrays A1, A2, and A3. The time series at 260 GHz still showed some residual slow fluctuations after this procedure. In these cases, a final smoothing by a running median of window 5 s was applied. This filtering method resulted in a clean average profile with a flat off-pulse region, and without the typical dips resulting from direct running median or running fit subtractions.

Finally, the time series cleaned with the multi-pixel filter were reformatted as SIGPROC4 filterbank-type files by adding a header containing the metadata of the observation. The binary formatting of the header was made with tools from SIG-PYPROC5 . To increase the total signal-to-noise ratio, the four individual scans were concatenated by letting prepfold pad the gaps in between scans. For the 260 GHz frequency, arrays A1 and A3 receive half of the total power each. Before concatenation and folding, the time series from the orthogonal linearly polarised pixels KH097 and KP018 were therefore combined to produce the total intensity output.

Calibration

To convert into flux density units, and prior to the analysis presented in Sec. 2.2, we scaled the time series by calibration factors obtained from observations of Uranus taken in September 2018 and March 2019 (see Perotto et al. 2020, for details of the NIKA2 calibration). These observations were also used to compute the relative sky position between detectors. A correction was applied to the intensity at 260 GHz to account for a slight misalignment of the beams from pixels KH097 and KP018 with respect to the position on sky of pixel KC016. The distance between the beams at 150 and 260 for the pixels we used was 4.5 arcsec. The correction includes a pointing offset of 2 arcsec from the magnetar position. The beam misalignment plus pointing offset result in an increase by a factor of two for the 260 GHz intensity. The uncertainties are derived from the noise statistics, combined with a 6 and 10% 1σ error for the 150 and 260 GHz bands, respectively, that originates from the scaling to Jansky factors (Perotto et al. 2020), combined with a 10% 1σ error for the correction due to the misalignment of the beams.

Results and discussion

The magnetar XTE J1810-197 was clearly detected in both bands of the NIKA2 camera at central frequencies 150 and 260 GHz (λ=2.0 and 1.15 mm), with peak significances of 124σ and 13σ, respectively. Figure 1 shows the average profiles and signal intensities as a function of integration time. At 150 GHz we detect individual pulsations in almost every rotation of the magnetar (see Fig. 2).

Table 1 presents the continuum-equivalent (or averaged) flux density (i.e. the area below the pulse divided by the rotational period) and derived spectral index. The spectrum and fit are shown in Figure 3. With S 150 = 11.7±0.7 mJy and S 260 = 6.4±1.0 mJy, the average spectral index is α = -1.1 ± 0.3 (for S ν ∝ ν α ). Because we have only a few data points and to better estimate the uncertainties, the spectral index was fit in a Markov chain Monte Carlo (MCMC) analysis using the Python package emcee6 (Foreman- [START_REF] Foreman-Mackey | emcee: The MCMC Hammer[END_REF].

The resulting spectrum is relatively flat, although much steeper than the inverted spectrum measured between 0.7-4.0 GHz (α ≈ +0.3, Dai et al. 2019). The millimetre flux density is about nine times higher than what can be estimated from the light curve reported by Maan et al. ( 2019) (≈1.0 mJy at 650 MHz). When we include this low-frequency value, the spectral fit would result in α ≈ +0.39 ± 0.02, consistent with the derived value at lower frequency. The difference in spectral index resulting from using the millimetre data alone might be related to a poor constraint of the fit with only two data points. However, interstellar scintillation (see the discussion in Lazaridis et al. 2008) and/or a frequency-dependent intrinsic variability of the magnetar emission may also play a role. We measured variations in the flux density of up to 50% peak to peak during our observations (in scales of tens of minutes), which supports the variability scenario. We should simultaneously consider that the spectrum of XTE J1810-197 may not always be well described over wide frequency ranges by a single power law. This is consistent with the spectral turnover reported by Dai et al. (2019) and has been observed for other radio magnetars (Camilo et al. 2008;Torne et al. 2017). A conclusive answer for the spectral shape between centimetre and millimetre wavelengths, which would enable testing the radio emission mechanism (e.g. revealing spectral turn-ups, Michel 1978), requires simultaneous multi-frequency observations.

The single pulsations at 150 GHz allow an estimation of the brightness temperature of the emission region, enabling us to test whether the millimetre emission is still coherent. For a distance to XTE J1810-197 of 3.5 ± 0.5 kpc (Minter et al. 2008) and a typical detected 0.75 Jy pulse, the brightness temperature at 150 GHz is T B > 10 17 K (see e.g. [START_REF] Lorimer | Handbook of Pulsar Astronomy Maan[END_REF]. We set the value as a lower limit because the pulses are not resolved, and narrower pulses correspond (following a light traveltime argument) to smaller emitting regions and higher brightness temperatures. Even at the lower limit, this high brightness temperature rules out incoherent mechanisms for the production of the pulses (e.g. [START_REF] Singal | [END_REF]). We therefore conclude that the underlying mechanism that causes the emission at 150 GHz must still maintain a level of coherency. Without detected single pulses, we cannot constrain the emission mechanism at 260 GHz. We hypothesise, however, that because the continuumequivalent flux density and pulse profile are so similar in the two frequency bands, the 260 GHz emission is probably caused by the same emission process. Additional observations with higher time-resolution are encouraged. They might help to further constrain the coherence of the emission mechanism by detecting narrower pulses7 , perhaps also at 1.15 mm or even shorter wavelengths.

A&A proofs: manuscript no. 38504corr_v3 While XTE J1810-197 was detected in the 2 mm band during its previous epoch of activity in 2006(at 144 GHz, λ=2.08 mm, Camilo et al. 2007), this is the first detection of the source at 260 GHz (λ=1.15 mm). The fact that we see again strong emission from XTE J1810-197 in the millimetre band, as in 2006, suggests that the radio emission process that has been reactivated now is the same as in the previous period of activity. In the 2 mm band, however, the emission is about ten times stronger than what was reported by Camilo et al. (2007).

IRAM 30m 150 GHz

IRAM 30m 260 GHz

The results presented here demonstrate that XTE J1810-197 produces strongly pulsed emission in the millimetre band after its reactivation in December 2018. The intrinsic variability of the source means that XTE J1810-197 opens a new opportunity of investigating the properties of pulsar emission at short millimetre wavelengths, where only another radio magnetar and two canonical pulsars have been detected above 50 GHz (Torne et al. 2015(Torne et al. , 2017;;Morris et al. 1997;Torne 2017;Liu et al. 2019). The current intensity and activity of this magnetar encourage observations at even shorter wavelengths, including submillimetre to optical bands.

Finally, we remark that this is the first time that KID technology as used in NIKA2 is successfully applied to detect broadband pulsations from neutron stars in the millimetre wavelength regime. In the future, the sampling frequency of NIKA2 may be increased, allowing for observations of faster-spinning pulsars or even burst emission of the kind of fast radio bursts (FRB, see e.g. Cordes & Chatterjee 2019).

Conclusions

The KID technology has the capability of detecting pulsations from neutron stars in the millimetre band, as demonstrated by these results for the magnetar XTE J1810-197 with the NIKA2 camera installed at the IRAM 30m telescope. Similarly, KIDs may be applied at even shorter wavelengths to observe pulsars and transient emission.

The detections of XTE J1810-197 at 150 and 260 GHz (λ=2.0 and 1.15 mm, respectively) are the first detections of the magnetar above 144 GHz, showing that the star is again emitting intense millimetre radiation after its reactivation in Decem- ber 2018. The spectrum in the millimetre band is relatively flat, but steeper than what was seen at centimetre wavelengths. The brightness temperature of the individual pulsations supports the hypothesis that a coherent mechanism is the source of the millimetre emission.

Fig. 1 .

 1 Fig. 1. Average profiles (shown twice for clarity) of the detection of XTE J1810-197 with NIKA2 at 150 GHz (left) and 260 GHz (right). Profiles have 128 bins, corresponding to a time resolution of ≈43 ms on the horizontal axis. The bottom panels show the signal intensity over time with 1.7 min resolution on the vertical axis. The white gap corresponds to the time when the telescope did not observe the source.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Single-pulse activity from XTE J1810-197 during our observations with NIKA2 on 2019 March 25. Only the last 10 min of the observation at 150 GHz are shown for clarity, but the activity is similar for the total 50 min on-source. No single pulses are detected at 260 GHz, which may be an effect of spectral index and instrumental sensitivity. The upper panels show a zoom (1.25 s around the peak) into a selection of six pulses, and they share the y-axis scale in Jansky units. The bottom panel shows the 10 min time series. The time resolution in all panels is ≈42 ms, limited by the sampling frequency set for the KID arrays. Many pulses show structure. Most pulses are unresolved.

Table 1 .

 1 XTE J1810-197 measured properties at the epoch of observation (2019 March 25): MJD epoch, barycentered spin period, continuum-equivalent flux density at 150 and 260 GHz, and spectral index. Uncertainties in parentheses indicate the 1σ error on the last significant quoted digit.

	Epoch	P	S 150	S 260	α
	(MJD)	(s)	(mJy)	(mJy)
	58567.23714 5.541396(3) 11.7(7) 6.4(10) -1.1(3)

This fast-sampling mode is pending commissioning.

https://www.cv.nrao.edu/~sransom/presto/

https://www.atnf.csiro.au/research/pulsar/psrcat/

http://sigproc.sourceforge.net

https://github.com/ewanbarr/sigpyproc

https://emcee.readthedocs.io/

Time scales for individual pulses at lower frequencies are 1 ms (Maan et al. 2019).

Acknowledgements. We thank the anonymous referee, Clemens Thum and Carsten Kramer for their constructive comments on the manuscript, and the NIKA2 team for supporting the observations. This work is based on observations carried out with the IRAM 30-m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). Financial support by the European Research Council for the ERC SynergyGrant BlackHoleCam (ERC-2013-SyG, Grant Agreement no. 610058) is gratefully acknowledged.


G Pisano

A Ritacco

A Monfardini

C Tucker

P A R Ade

A Shitvov

A Benoit

M Calvo

A Catalano

J Goupy

S Leclercq

J Macias-Perez

A Andrianasolo

N Ponthieu

Development and application of metamaterial-based Half-Wave Plates for the NIKA and NIKA2 polarimeters

Keywords:

come

Introduction

The polarization state of the radiation coming from astronomical sources carries important information about the astrophysical environments at the origin of the electromagnetic wave. Generally, only a small fraction of the total signal is polarized and this is embedded within a more intense signal arising from unpolarized light and radiation from other astrophysical sources. However, a linearly polarized signal can be modulated and lifted above the noise level by using a rotating Half-Wave Plate (HWP) operating directly on the incoming beam of the instrument. The rotation of the HWP at a frequency ω induces a rotation of the polarized signal at twice the mechanical angular rotation speed, 2ω. Detectors sensitive to orthogonal polarizations will eventually detect signals at a frequency 4ω [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF].

The New IRAM KIDs Array (NIKA) [START_REF] Monfardini | A DUAL-BAND MILLIMETER-WAVE KINETIC INDUCTANCE CAMERA FOR THE IRAM 30 m TELESCOPE[END_REF][START_REF] Catalano | Performance and calibration of the NIKA camera at the IRAM 30 m telescope[END_REF] instrument, operated at the IRAM 30-meter telescope in the period 2010-2015, has represented a scientific and technological pathfinder for instrumentation based on Kinetic Inductance Detectors (KIDs). The advantage of KIDs, when compared to the competing technology of bolometers, and in the context of polarization modulation, is the fast (i.e. 0.1 ∼ ms) response time. NIKA2 [START_REF] Adam | The NIKA2 large-field-ofview millimetre continuum camera for the 30 m IRAM telescope[END_REF] is the successor of NIKA and represents, with around 3k-pixels and three distinct arrays, the ultimate instrument for dual-band (150 and 260 GHz) imaging and polarimetry (260 GHz) at the 30-meter telescope. NIKA2 is a general purpose camera open to the astronomical community via periodic competitive calls. The NIKA2 collaboration is, however, independently pursuing five science objectives spanning from cosmology (e.g. observations of clusters of galaxies via the Sunyaev-Zel'dovich effect, deep integration on cosmological fields) to the study of the Interstellar Medium (ISM) in intensity and polarization (Mayet et al. 2020;Ruppin et al. 2020;[START_REF] Bracco | Probing changes of dust properties along a chain of solar-type prestellar and protostellar cores in Taurus with NIKA[END_REF]Peretto et al. 2020;Lestrade et al. 2020). Among the most innovative science projects is the polarization study of large galactic regions, to understand the role of magnetic fields in the fragmentation and evolution of star-forming filaments [START_REF] Arzoumanian | Characterizing the properties of nearby molecular filaments observed with Herschel[END_REF][START_REF] André | Probing the cold magnetised Universe with SPICA-POL (B-BOP)[END_REF]. Magnetic fields, still poorly explored, seem to play a crucial role in a large number of different astrophysical processes [START_REF] Crutcher | Magnetic Fields in Molecular Clouds[END_REF]. They can be traced via observations of dust polarization (Planck Collaboration: et al. 2015). The NIKA2 polarimeter, and previously the NIKA one, can fill the gap between high-resolution observations provided by interferometers like ALMA, NOEMA and low-resolution ones as cosmological experiments, e.g. Planck, WMAP and future LiteBird satellites. For this reason it was important to implement polarimetric capabilities in the instrument concept of NIKA2, taking advantage of the new HWP technology that is described in detail in the present paper.

At millimeter wavelengths, the quasi-optical modulation of linear polarization can be achieved using different types of HWPs. Diverse solutions have been developed in the past, ranging from birefringent multiplate designs [START_REF] Pancharatnam | Achromatic combinations of birefringent plates[END_REF][START_REF] Murray | High efficiency half-wave plates for submillimetre polarimetry[END_REF][START_REF] Hanany | Millimeter-wave achromatic half-wave plate[END_REF][START_REF] Pisano | Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: experimental characterization[END_REF][START_REF] Savini | Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: modeling and simulation[END_REF][START_REF] Savini | Recovering the frequency dependent modulation function of the achromatic half-wave plate for POL-2: the SCUBA-2 polarimeter[END_REF][START_REF] Moncelsi | Empirical modelling of the BLASTPol achromatic half-wave plate for precision submillimetre polarimetry[END_REF][START_REF] Komatsu | Demonstration of the broadband half-wave plate using the nine-layer sapphire for the cosmic microwave background polarization experiment[END_REF], artificial birefringent material based devices [START_REF] Glenn | A 1.2Millimeter BroadBand Polarimeter[END_REF][START_REF] Henderson | Advanced ACTPol Cryogenic Detector Arrays and Readout[END_REF]) and reflective-based solutions (Chuss et al. 2012a,b;[START_REF] Pisano | Multi-octave metamaterial reflective half-wave plate for millimeter and sub-millimeter wave applications[END_REF].

However, in this work we present the novel development of two large bandwidth metamaterial based HWPs, which have been installed and have successfully operated in the NIKA [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF][START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF] and NIKA2 [START_REF] Adam | The NIKA2 large-field-ofview millimetre continuum camera for the 30 m IRAM telescope[END_REF][START_REF] Ritacco | Observing with NIKA2Pol from the IRAM 30m telescope : Early results on the commissioning phase[END_REF] instruments. These devices have been developed using the well-established mesh-filter technology [START_REF] Ade | Millimeter and Submillimeter Detectors and Instrumentation for Astronomy III[END_REF][START_REF] Pisano | [END_REF]. Previous realizations of mesh-HWPs had either limited bandwidth, of the order of 30% [START_REF] Pisano | Metal-mesh achromatic half-wave plate for use at submillimeter wavelengths[END_REF][START_REF] Pisano | A broadband metal-mesh half-wave plate for millimetre wave linear polarisation rotation[END_REF], or non-ideal phase-delays [START_REF] Zhang | Polypropylene embedded metal mesh broadband achromatic half-wave plate for millimeter wavelengths[END_REF]. The goal of this work is to demonstrate high performance across bandwidths of the order of 90% (∼3:1), never achieved before with this technology.

The NIKA and NIKA2 instruments

In this section we briefly describe the NIKA (pathfinder) and NIKA2 (final instrument) optical designs and the requirements for the associated HWPs. We remind that both NIKA and NIKA2 are based on custom dilution cryostats, designed and realized in order to provide the needed base temperature of around 0.1∼K for the KID focal planes (filled arrays). At the same time, a part of the optics is cooled to cryogenics temperatures, contributing thus to reduce to negligible levels the influence of stray radiation. Both NIKA and NIKA2 are dual-band, mapping simultaneously the same portion of the Sky in the so-called 1mm and 2mm atmospheric windows. NIKA2 has been designed, since the beginning, with the polarisation mapping at 260 GHz in head. On the other hand, NIKA has been adapted a posteriori to measure the polarisation, despite in non-optimised conditions, at both 150 GHz and 260 GHz. For more details please refer to paragraphs 2.1 and 2.2.

As already mentioned, the KID detectors allow a fast, i.e. ≥10∼Hz, modulation of the incoming polarization. To achieve that, a mechanical rotational frequency of around 3 Hz is applied to the HWP modulator. The distinct advantage of a fast and continuous modulation is the ability of eliminating almost completely the influence of the atmospheric 1/f noise that is often limiting the sensitivity of the groundbased polarimeters operating at similar wavelengths.

NIKA optics

NIKA covered an instantaneous field-of-view of around 2 arc-minutes (diameter), mapped with angular resolution of 18 arc-sec (150 GHz) and 12 arcsec (260 GHz). The NIKA optics, schematically shown in Fig. 1, is split between a warm part entirely made by reflective elements (cabin optics) and a purely refractive (cryostat optics) section realised using anti-reflection-coated HDPE (High-Density Polyethylene) lenses. NIKA was not intrinsically designed for polarization measurements. For this reason, both the HWP modulator and the fixed wire-grid projection polarizer were located at room temperature, at the intersection of the cold and warm optics sections. This sub-optimal configuration has two unwanted effects: a) since only one polarization is transmitted into the cryostat, the overall quantum efficiency is reduced by a factor of two; b) a non-negligible background is added by the room-temperature wire-grid via reflections of the ambient radiation. Despite that, the polarization studies in NIKA have produced important science results and most importantly provided crucial lessons for the design of NIKA2.

The beam size at the HWP location, shown in Fig. 1, is of about 100 mm (diameter).

NIKA2 optics

NIKA2 features an instantaneous field-of-view of 6.5 arcminutes (diameter), mapped with angular resolution (at 260 GHz) of 11 arc-sec. The size of the primary image of the 30-meter telescope, for such a field-of-view, is of the order of 60 cm. This already gives an idea of the dimensions of the optical components that are needed to reform the image onto the 80 mm (diameter) focal planes (see Fig. 2). As was the case for NIKA, the NIKA2 optics is split between a warm part entirely made by reflective elements (cabin optics) and a cold section realised mixing mirrors and AR-coated HDPE lenses. Thanks to its low emissivity, the HWP polarization modulator can sit at room temperature, at the intersection between the two (warm and cold) optics sections. In order to minimize possible systematic, at the HWP location the NIKA2 beam exhibits a pupil; it is in other words completely defocused. The wire-grid projection polarizer is, in NIKA2, mounted at 45 degrees and at base temperature (0.1 K). It feeds two arrays sensitive to orthogonal polarizations, and does not add significant background. For these reasons, we consider that NIKA2 has been designed, since the beginning, also with polarimetric observations in mind.

The size of the beam at the HWP location, shown in Fig. 2, is of the order of 200 mm in diameter. Please refer to [START_REF] Adam | The NIKA2 large-field-ofview millimetre continuum camera for the 30 m IRAM telescope[END_REF]) for more details concerning the NIKA2 instrument. As shown in Fig. 3, the NIKA and NIKA2 spectral bands are similar, requiring a HWP with good performance between 120 and 300 GHz.

Mesh HWPs design, manufacture and laboratory characterization

3.1. Mesh-HWPs for NIKA and NIKA2

Different approaches, and associated technologies, can be employed to design quasi-optical HWPs operating at millimetre wavelengths [START_REF] Pisano | Development of large radii halfwave plates for CMB satellite missions[END_REF]. In this work we have pushed forward the development of the mesh-HWP technology, started with the air-gap version [START_REF] Pisano | Metal-mesh achromatic half-wave plate for use at submillimeter wavelengths[END_REF] which subsequently evolved into more sophisticated dielectrically embedded versions [START_REF] Pisano | A broadband metal-mesh half-wave plate for millimetre wave linear polarisation rotation[END_REF][START_REF] Zhang | Polypropylene embedded metal mesh broadband achromatic half-wave plate for millimeter wavelengths[END_REF]. The dual goal was to achieve both a high performance in terms of transmission and a differential phase-shift across large bandwidths (of the order of 90%, or 3:1) never achieved before with our technique.

A single HWP was required to operate simultaneously across the 1mm and 2mm channels of both the NIKA and NIKA2 instruments (Fig. 3).

The work was carried out between the last observational campaigns of the NIKA instrument and the deployment of the new NIKA2 polarimeter at the IRAM telescope. The staggered development phases comprised three mesh-HWPs: one for NIKA (M-HWP A ); one for further R&D (M-HWP B ); and one for NIKA2 (M-HWP C ). The knowledge and understanding gained during the manufacture and test of these waveplates allowed us to improve the design of the successive plates and to achieve increasingly better performances. Ultimately, this new design has met both the NIKA and NIKA2 instrument requirements.

Before describing the development details of the three HWPs we are going to summarize the design, manufacture and testing procedures which are common for all these devices.

Design of the mesh-HWPs

The simplest design for a HWP operating at millimetre wavelengths consists of a birefringent plate (usually Sapphire) with its thickness tuned to provide a phase-shift of 180 • (at a specific frequency) between the ordinary and extraordinary axes (Fig. 4 a ). In order to achieve large bandwidths it is possible to stack many plates together with different orientations following the well-known Pancharatnam designs [START_REF] Pancharatnam | Achromatic combinations of birefringent plates[END_REF]. The relatively large refractive index of the Sapphire plates (n∼3.1) needs to be matched to free-space by means of multi-layer anti-reflection coatings (ARCs) on both sides of the plate. The difficulties associated with the development of ARCs operating at cryogenic temperatures due to differential thermal contraction effects, the fragility of the device and the overall mass of the HWP pushed us to investigate alternative solutions based on the mesh-filter technology.

A mesh-HWP is a combination of two anisotropic mesh-filters interacting differently (and separately) with two orthogonal polarizations: a capacitive low-pass filter along one axis and an inductive high-pass filter along the orthogonal axis, both providing phase-shifts in opposite directions (Fig. 4b). These filter elements can be realized with thin copper grids embedded within polypropylene (n∼1.5). They must show high in-band transmission while keeping an almost frequency-independent differential phase-shift, close to 180 • . In order to operate across large bandwidths (∼90%) both the capacitive and the inductive filters should comprise at least six grids. The inductive grids resemble parallel lines whereas the capacitive grids look like parallel dashed-lines (see Fig. 5). The final mesh-HWP consists of a capacitive stack in series with an inductive stack but oriented in orthogonal directions. Ideally each stack should be transparent to in-band radiation in its orthogonal direction so as not to deteriorate the performance of the other stack. Finally, single layers of porous-PTFE (n∼1.25) applied on both sides of the plate can be used as efficient anti-reflection coatings.

The mesh-HWP design is carried out by means of a specifically developed propagation matrix code. The grids are treated like lumped elements in a transmission line circuit and their admittances are accurately calculated using finite-element analysis (Ansys HFSS www.ansys.com) along both polarization directions. Optimisation procedures are implemented to obtain high transmission and the required differential phase-shift within the required frequency ranges. The non-ideal behaviour of the grids, the multiple reflections within them, and the interactions between the stacks are inherently taken into account within the code. Details of these procedures have been reported elsewhere [START_REF] Pisano | A broadband metal-mesh half-wave plate for millimetre wave linear polarisation rotation[END_REF].

Manufacture of the mesh-HWPs

In summary, the design of the metal-mesh HWP involves a stack of capacitive low-pass elements (C) and a stack of inductive high pass elements (L), bonded together. Each stack consists of six grids, different in each of the three designs presented, aligned and stacked in a symmetrical arrangement, as shown in Fig. 5. Layers of anti-reflection coating (ARC) are eventually applied on both sides of the device.

The grids are made by photolithographically patterning high purity 400nm thick copper layers, which have been thermally evaporated onto polypropylene substrates. The lithography and wet-chemical etching are highly controlled, producing uniform, replicable patterns. However, to further improve device performance, the geometry of each grid is measured and fed back into the model code in order to optimize the device at the assembly stage.

Alignment of the grids over a large area is achieved with the aid of fiducial markers and back-lighting and takes the expertise of an experienced cleanroom process technician. Once aligned the individual C and L stacks are hotbonded together using a standard oven with a highly controlled pressure-temperature cycle over 3 days. These separate stacks are also spectrally characterised, using the setup described in section 3.4, and a further optimisation process performed. Then the C and L stacks are orthogonally aligned and hot-bonded. Finally, an ARC layer of porous-PTFE is applied to both surfaces and also hot-bonded in place.

Experimental setup for laboratory tests of the mesh-HWPs

The NIKA/NIKA2 HWP elements and final devices were all tested with a Martin-Puplett polarizing Fourier Transform Spectrometer (FTS). The FTS was configured for optimized performance in the 100 to 330 GHz range, using photolithographically-etched polarizers. The FTS output was coupled to a pumped 4He germanium bolometric detector allowing high sensitivity measurements in this FIR spectral regime. Data were taken at room temperature with 120-interferogram averages recorded and Fouriertransformed; these data are ratioed against background spectra from the FTS with no sample installed. The polarisation in the FTS was defined by a polarizer in front of the source. Two additional polarizers aligned with the first one were located at the output the FTS. The HWPs under test were positioned in between the output polarizers and could rotate around their optical axis (see Fig. 6). Three sets of measurements were performed for each HWP by aligning their C-and L-axis with the polarizers and at 45 • from these.

NIKA mesh-HWP first prototype (M-HWP A )

The target performance of the NIKA mesh-HWP was a transmission along the capacitive and inductive axes above 90%, i.e. T C ≥ 0.90 and T L ≥ 0.90, and a differential phaseshift between the axes ∆Φ C-L = 180 • ± 20 • averaged within the 1-mm band. These latter values would guarantee an averaged polarization modulation efficiency around 97%. Good performance of the HWP within the 2-mm band was desirable but not a requirement. However, as it will be discussed in Sec.7, polarization measurements on astronomical sources have been eventually performed in both bands. The optimization procedure of the propagation matrix code was set to minimize the phase-shift error and maximize the transmissions across the whole range of frequencies including the two bands, i.e. from 110 to 320 GHz. The result of this optimisation provided a 12-grid device, six capacitive and six inductive grids, with the geometries and the spacing reported in Fig. 7. The six inductive grids were all identical whereas three types of capacitive grids were required. All the evaporated grids had a copper thickness of 400nm. Single-layer anti-reflection coatings were added on both sides of the waveplate to ensure good matching to free space. The conductive losses of the copper grids and the dielectric losses of the polypropylene substrates were taken into account in the simulations. The polypropylene loss-tangent was extracted from previous measurements on planar slabs of material.

The twelve grids were manufactured, the capacitive and inductive stacks assembled, hot-pressed and AR-coated following the procedures described in Sec. 3.3. A picture of the M-HWP A device, during its operation in NIKA instrument, is shown in Fig. 8. The device had a diameter of 20 cm and a thickness of ∼2.5 mm. Laboratory FTS measurements were performed using the setup discussed in Sec. 3.4. The transmission measurements along both axes and the 45 • cross-polarization are reported, together with the model expectations in Fig. 9 and Fig. 10. The differential phase-shift can be extracted by combining the previous three measurements, as discussed elsewhere [START_REF] Pisano | Multi-octave metamaterial reflective half-wave plate for millimeter and sub-millimeter wave applications[END_REF]. The model and the results are reported in Fig. 11. The phase-shift jump around 180 • is due to the sign indeterminacy of the arc-cos function used to extract these values and to the FTS noise, creating a systematic offset from 180 • .

Although the resulting transmissions can be seen to be above 90% across the whole 1mm band, there is some disagreement between measurement and simulation. The expected ripples in the capacitive axis transmission are slightly out-of-phase with the measurements. The lowfrequency cut-off of the inductive stack is slightly shifted compared to the model (Fig. 9). The 45 • cross-polarization is a little bit higher than expected, implying a systematic deviation in the differential phase-shift (Fig. 10 and Fig. 11).

We want to note that the 45 • cross-polarization, which is a measure of the differential phase-shift error, is different from the cross-polarization leakage. The latter is the amount of signal leaking into the orthogonal direction when the signal polarization is aligned with one of the HWP axes. In mesh-HWPs this signal is theoretically null due to the symmetry of the design. However, small inaccuracies in the alignment of the grids during the manufacturing processes (at the level of ±1 • ) can lead to the appearance of crosspolarization leakages below the -30 dB level, which are much lower than the averaged 45 • cross-polarization measurements [MHWP].

The M-HWP A transmission along the axes and the differential phase-shifts integrated and weighted across the 1mm and 2-mm bands are reported in the data in Fig. 12. The performance of this first device met all the NIKA requirements, in terms of transmission and differential phaseshift. It was installed in the NIKA instrument and successfully used for astronomical polarimetry observations, as discussed in Sec. 7.

Although the device performed well within the 1-mm band, we wanted to investigate the origin of the discrepancies described earlier in order to predict them and improve the performance of the following prototypes. The roots of these deviations lie in the assumptions that we have made in our models, which were based on previously manufactured mesh-devices. For example, the models assumed the refractive index of the polypropylene to be n PP = 1.48 and an electrical conductivity of the copper grids being σ Cu = 4e7 S m -1 . The validity of these values, as well as those of other geometrical parameters, will be questioned and investigated in detail in the next two sections. We note that M-HWP A had also a 2% unbalance between the axes transmission within the 1-mm band, although it differed only by 1% across a 98% bandwidth . This was due to the ripples of the capacitive axis transmission (in the 1mm band) being outâ Ȃ Şof-phase with respect to the model (see Fig. 9). This kind of deviation will be also addressed in the design of the following prototypes.

NIKA mesh-HWP second prototype (M-HWP B )

Given the results achieved with the first prototype we manufactured the second waveplate, adopting a more rigorous step-by-step approach. We produced new grids using the same masks of the MHWP A device and took microscope pictures and measurements of the geometrical details of them all. The period of the grids was found to be as expected, within the measurement error, i.e. below 1µm. However, we noticed a general over-etching effect associated with the photolithographic processes. The widths and the lengths of the copper lines were systematically reduced by a few microns. The capacitive dash-lines were narrower and shorter respectively by ∼3% and ∼6%. The effect on the inductive lines was much larger given their nominal width of 9 µm and their actual realizations of ∼7 µm (22% narrower). Such a large relative change implied not only having less effective grids but also higher losses, due to the thin layer of copper (400nm). We note that, although similar effects were known in the production of mesh filters, in our case the ratio between the period of the grids and the line widths was much larger. This implied removing higher percentages of copper and different etching procedures.

The above effects implied that the grids were less reactive and so introduced individual phase-shifts smaller than expected. The impact on the capacitive-grid stack was limited to the shift in frequency of the transmission ripples seen in MHWP A , whereas the effect on the inductive-stack was more relevant because it implied the addition of higher losses due to their higher resistance.

In order to accurately take into account the above effects, each grid was simulated again with finite-element analysis using the actual measured values. The new and more realistic admittances were extracted and inserted in the propagation matrix code. A new optimisation was run to re-design the device with the appropriate corrected spacing between the 6-L and 6-C grids. However, the required performance in terms of phase-shift could not be achieved anymore, even by rearranging the grids, due to the reduced efficiency inductive grids. The differential phase-shift curve moved up by 20 degrees and its averaged values within the band were outside the requirement range.

There were two options to proceed further: i) produce new masks with wider lines to take into account the overetching effects; ii) add another inductive grid to the current design to compensate for the phase deficit. We decided to proceed with the latter option because this was an R&D phase and the device was not meant to be used in any instrument requiring high performance across both bands. What was required at that stage was to develop a technique that would allow us to reproduce the experimental data more accurately, regardless of the actual performance.

The new 6-C and 7-L recipe was similar to the one sketched in Fig. 7 but slightly thicker, ∼ 3.3 mm. The inductive stack was made of these lossy grids and the performance within the 2-mm band was expected to present a large unbalance in transmission between the two axes (of the order of 6%). The MHWP B modelled performance parameters, integrated and weighted within the NIKA bands, are reported in the data in Fig. 19.

The new capacitive and inductive stacks were assembled and hot-pressed as previously. This time, before the final assembly we wanted to check and test each stack individually. The hot-pressed capacitive and inductive stacks were thicker than expected by 9µm (0.7%) and 5µm (0.3%) respectively. These values are consistent with the tolerances associated with the large number of polypropylene films used for stacks of these thicknesses.

Both stacks were tested with the FTS. The measured transmissions along the reactive and transparent axes of each stack are reported in Fig. 13 and Fig. 14. In order to achieve agreement between the model and the measured data, an optimization was run by varying the only two parameters left that could still be different from the predictions: the refractive index of the polypropylene and the electrical conductivity of the copper grids. The best fit was achieved when these parameters were respectively n PP 1.512 and σ Cu = 3e7 S m -1 . The refractive index increase, from the nominal value 1.48, is believed to be a consequence of the hot-pressing process of the many thin polypropylene layers (of the order of 200) which then became a single plastic block. In fact, the bi-axially oriented polypropylene substrate material is known to contract during the hot-pressing process; whilst this is controlled to a certain extent, there is inevitably some slight increase in the material density over progressive pressings. The fitted copper conductivity is consistent with values expected by evaporation processes and measured previously with some mesh-filter devices. We note in Fig. 13 and Fig. 14 that the reactive C-and L-axis show the expected low-pass and high-pass cut-off while the transparent axes behave similarly to dielectric slabs.

Given the good agreement between data and fitted models, the two stacks were eventually bonded together and AR-coated. The final device had an overall thickness of ∼3.3 mm. Fig. 15 is a picture with details of this second prototype. The expected performance of the original design and the test results of the M-HWP B are shown in Fig. 16,Fig. 17 and Fig. 18. In order to better fit the experimental data, we left the refractive index to be a variable parameter which eventually transpired to be higher than those mea- sured for the individual stacks, i.e. n PP =1.535. This is attributable again to the further and final hot-bonding process. The model results obtained using this latter value, reported again in Figs. 16, 17 and 18, show good agreement between model and data. In particular, the transmissions cut-on and cut-off frequencies coincide now with those measured experimentally. The performance parameters within the NIKA bands are summarised in the data in Fig. 19. The transmissions are greater than 90% in both bands, there is a clear improvement of the 45 • cross-polarization and differential phase-shift on the 2-mm band but a deterioration in the 1-mm band. We note that the averaged cross-pol is below the -15 dB requirement across a 92% bandwidth (105-285 GHz).

Although the performance of this device was not meant to meet the requirements, the main achievement of this R&D phase was to understand which parameters could change during the various manufacturing processes. We have either evaluated or directly measured these parameters and assessed their variability range. We have built models with fitted parameters providing results very close to the experimental data, both for the single stacks and for the final assembled device. We conclude that, within the various parameters, the increase of the substrate refractive index and the change in the grid geometries play the major roles in the performance deviations of the manufactured device.

NIKA2 mesh-HWP (M-HWP C )

The results achieved through the development of the first two waveplates proved our ability to model the performance of the final devices with good accuracy. The NIKA2 requirements were similar to the NIKA ones (T C ≥ 0.90, T L ≥ 0.90 and ∆Φ C-L = 180 • ± 20 • ) but extended now to both bands. Some further improvement was required in terms of differential transmission because, in the previous realizations, we had a slight unbalance between the transmissions along the axes in the 2-mm band (see Figs. 12 and19). As mentioned, this was due to the larger losses introduced by the narrow inductive grids near their low frequency cutoffs, around 100 GHz. A solution was to move the cutoff frequency to lower frequencies. A way to achieve this was to relax some of the parameter constraints in the optimisation procedure. Given the narrow width of the two NIKA2 bands there was no need to achieve high performance across the whole 110-320 GHz frequency range. The optimisation procedure was then modified to maximise the transmissions and minimise the phase error only within the NIKA2 bands. This resulted in a dip in the inductive axis transmission around 200 GHz which had no impact on the overall performance because this region would be filtered out. The differential transmission was eventually kept within 1% in both bands (see Fig. 20). The 45 • crosspolarization had targeted minima within each of the bands, so forcing the differential phase-shift to cross the ideal 180 • within them.

We note that at the end of each design optimisation the output grid parameters need to be rounded to values which allow periodicity between grids. This is needed for Fig. 20. Originally modelled, measured and required performance parameters of the M-HWP C across the two NIKA2 bands. The labels and colours are the same as described in the data in Fig. 12. Note that this was the only plate designed to work across both bands. their finite-element computation which is based on periodic boundaries. The overall effect is a small deviation from the previously optimised performance.

The grids were manufactured using the processes described above, this time more accurately controlling the grid etching processes using a weaker etch solution and microscopic imaging of the grids. The widths of inductive lines were chosen to be at least 20 µm wide in order to reduce their losses and to minimise the over-etching effects on the performance faced earlier. The capacitive and inductive stacks (6-C and 6-L) were assembled and pressed separately and, as previously, were slightly thicker than expected, within the percent level. The transmission of both stacks was measured with the FTS along their reactive and transparent axes, as reported in Fig. 21 and Fig. 22.

For each stack, a parameter optimisation was run in order to determine the PP refractive index and the copper conductivity. The optimisation was run by minimising the difference between the modelled and the measured transmissions in a discrete number of frequency points. It was found that the stacks had slightly different refractive indices, n PP-C =1.517 and n PP-L =1.535, and conductivity σ Cu 3.00e7 Sm -1 . The over-etching in the C-stack ranged within 1-6 µm, while in the L-stack we actually observed 2-3 µm under-etching of the lines. As shown in Fig. 21 and Fig. 22, the above values provided very good agreement between data and models in all four transmission curves. The fitted-parameter models gave very good agreement with the measured data for both axes and 45 • crosspolarization (Fig. 24 and Fig. 25). In the same figures we have also reported the expected performance of the original design, i.e. the model results with the nominal values. The differential phase-shift, extracted from the data as before, is reported in Fig. 26 along with its fitted and original model. We note that the measured data is accurately reproduced by the fitted models in all the performance parameters. In addition, these curves are now very close to the original models with the nominal values.

The M-HWP C transmissions and differential phaseshift, weighted by the band transmission profiles, are reported in Fig. 20. The device met the 2-and 1-mm NIKA2 band requirements for all the parameters. We note that the differential transmission is now kept at 1% level in both bands, meaning that the unbalance evident in the previous devices has been successfully addressed and solved. We note that, given the noise level in the NIKA2 band transmissions (see Fig. 3), we have integrated the above values between 109-182 GHz and 221-304 GHz respectively for the 2-and 1-mm bands, i.e. within the ranges where the band transmission profiles are above their respective noise level ( 5% and 10%).

To conclude, as a representative example of all the M-HWPs discussed before, in Fig. 27 we report the results of a finite element simulation of M-HWP C . The simulation, run at 230 GHz, shows the interaction of an electromagnetic wave going through the mesh HWP and its dependence on the polarization alignment with respect to the capacitive or inductive axis.

Polarimetry with NIKA and NIKA2 instruments

Adopting the strategies described in Sec. 2, we have performed polarization observations with both NIKA [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF][START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF] and NIKA2 [START_REF] Ajeddig | Preliminary results on the instrumental polarization of NIKA2-Pol at the IRAM 30m telescope[END_REF][START_REF] Ritacco | Observing with NIKA2Pol from the IRAM 30m telescope : Early results on the commissioning phase[END_REF]) on compact and extended galactic and extra-galactic objects.

In order to show the performance of the NIKA and NIKA2 polarimeters we recall here the maps obtained on a supernova remnant, the Crab nebula. An extended study by using the NIKA polarization results as well as all existing polarization data at submm and mm wavelengths is reported in [START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF]. We anticipate that, thanks to the larger instantaneous field-of-view, better sensitivity and optimised configuration, the NIKA2 mapping speed in polarization will be more than an order of magnitude higher when compared to NIKA.

On sky observations

In polarimetric mode the signal received by NIKA/NIKA2 detectors is a combination of the three Stokes parameters I, Q, U; being the polarized signal in Q, U modulated at four times the mechanical rotation frequency ω of the HWP. In order to have the right compromise between the sampling rate, the telescope speed and to limit systematic effects the mechanical rotation frequency ω for both instruments is set to ∼ 2.98 Hz [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF]. The polarization data are calibrated using standard calibration procedures developed for total intensity observations [START_REF] Perotto | Calibration and Performance of the NIKA2 camera at the IRAM 30-meter Telescope[END_REF]).

In addition, in order to treat polarization data three major steps in the data analysis have to be considered: i) the HWP Synchronous Signal subtraction that appears as a spu- rious signal modulated at harmonics of ω; ii) the instrumental polarization characterization that shows up as a bipolar (NIKA) and quadrupolar pattern (NIKA2); iii) demodulation procedure to produce independent Stokes I, Q, U timelines to project onto final maps. [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF] present the data analysis pipeline specifically developed to treat these effects for NIKA, extended then to NIKA2. The commissioning of the NIKA2 polarimeter started in fall 2017 and it is still ongoing due to few technical issues. The first lights obtained are shown in [START_REF] Ajeddig | Preliminary results on the instrumental polarization of NIKA2-Pol at the IRAM 30m telescope[END_REF]; [START_REF] Ritacco | Observing with NIKA2Pol from the IRAM 30m telescope : Early results on the commissioning phase[END_REF].

NIKA/NIKA2 polarimeters on the sky

As an illustration we summarize here the results obtained on the Crab nebula with NIKA and NIKA2 polarimeters.

The Crab nebula is a supernova remnant that exhibits a synchrotron emission in a large range of frequency, from radio to X-ray. [START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF] demonstrated that the spectral index in polarization at submm and mm wavelengths is consistent with total intensity spectral index.

We therefore expect to have the same polarization in the two mm bands of interest. Fig. 28 shows the polarization maps in terms of Stokes Q and U obtained with NIKA at 150 GHz [START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF]) and NIKA2 at 260 GHz [START_REF] Ritacco | Observing with NIKA2Pol from the IRAM 30m telescope : Early results on the commissioning phase[END_REF]. Although the maps obtained with NIKA2 are only preliminary we can already notice the high consistency of the polarized signal observed on both maps between NIKA and NIKA2. Notice that for more or less the same time of observation it was not possible to get a sufficient SNR on the maps at 1mm with NIKA. A more detailed study on this comparison is beyond of the scope of this paper and will be reported by the end of the NIKA2 polarimeter commissioning.

Conclusions

The different challenges of modern astrophysics in the polarization field require high precision and control of systematics, which is possible with HWPs devices like the one used in NIKA and NIKA2. The NIKA and NIKA2 instruments are dual-band imaging instruments observing simultaneously in the 1mm and 2mm atmospheric windows. Polarization modulation can be implemented by using a single rotating HWP in front of these instruments. The HWP is required to have a large fractional bandwidth, of the order of 3:1.

For this purpose we have pushed further the development of half-wave plates based on the mesh-filter technology. Three different mesh-HWPs were designed, manufactured and tested. The first device, while showing some variations from the expected performance, met the NIKA single-band requirements. The second device was developed to understand, isolate and control the variations of the geometrical and physical parameters occuring during the manufacture of the waveplates. The knowledge acquired in developing the first two devices was successfully implemented in the third device, which had more challenging dual-band requirements set by the NIKA2 instrument.

The first mesh-HWP was installed in the NIKA instrument at IRAM providing high precision simultaneous observations at 150 GHz and 260 GHz of the polarization in different targets, from quasars to galaxies and star forming regions [START_REF] Ritacco | Polarimetry at millimeter wavelengths with the NIKA camera: calibration and performance[END_REF]. It has also provided the first polarization observation of the Crab nebula at 150 GHz with an angular resolution (FWHM ∼18 arcsec) [START_REF] Ritacco | NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution[END_REF], as well as presenting for the first time an in-depth study of the spectral dependence of its polarization at millimeter wavelenghts.

The third mesh-HWP was installed in the NIKA2 instrument and tested along the last two years while NIKA2 was already used for open-time observations in total intensity. Despite the expectations, the commissioning of the NIKA2 polarization system is taking longer than expected because of a number of technical challenges and adverse weather conditions. However, the first light results are already promising.

We note that mesh-HWPs, like mesh-filters, are very light and robust devices. Their anti-reflection coating, which is part of their structure, does not suffer delamination at cryogenic temperatures, as in Sapphire-based wavaplates. In addition, a Sapphire HWP operating across the NIKA2 bands would require a 3-plate Pancharatnam design with a total thickness of ∼6.3 mm and a weight of ∼780 g (assuming a diameter of 200 mm). The NIKA2 mesh-HWP is 3.9 mm thick and has a weight of ∼120 g, a factor 6.5 lighter. The final advantage of a large bandwidth mesh-HWP is the fact that the waveplate axes are uniquely defined by the metal grids and their orientation do not change with the frequency, as it happens in multiplate Pancharatnam devices.

Fig. 1 .

 1 Fig. 1. NIKA instrument optical layout.

Fig. 2 .

 2 Fig. 2. NIKA2 instrument optical layout.

Fig. 3 .

 3 Fig. 3. NIKA and NIKA2 instruments "1mm" and "2mm" spectral bands. The different profiles have been taken into account in the design of the different waveplates.

Fig. 4 .

 4 Fig. 4. a)Sketch of a birefringent (Sapphire) HWP. The ordinary and extraordinary axes lie across the waveplate. b) Sketch of a dielectrically embedded mesh-HWP. The ordinary and extraordinary axes are replaced by capacitive and inductive axes.

Fig. 5 .

 5 Fig. 5. CAD design example of a dielectrically embedded mesh-HWP. The cylindrical section drawn here has a diameter of 6mm.

Fig. 6 .

 6 Fig. 6. Martin-Puplett Fourier Transform Spectrometer setup used for the characterization of the mesh-HWPs.

Fig. 7 .

 7 Fig. 7. M-HWP A design details: sketch of the capacitive and inductive metal grid geometries and their symmetric arrangement. This device consists of 6 capacitive and 6 inductive grids embedded into polypropylene, with one layer of AR-coating bonded on its sides. The overall thickness is ∼2.5 mm.

Fig. 8 .

 8 Fig. 8. The NIKA M-HWP A first prototype.

Fig. 9 .

 9 Fig. 9. M-HWP A : Capacitive and inductive axes modelled and measured transmissions.

Fig. 10 .

 10 Fig. 10. M-HWP A : 45 • cross-polarization model and measurements.

Fig. 11 .

 11 Fig. 11. M-HWP A : Differential phase-shift model and measurements.

Fig. 12 .

 12 Fig. 12. Originally modelled, measured and required performance parameters of the M-HWP A across the two NIKA bands. The parameters are: the axes transmissions T C and T L ; the differential transmission ∆T CL ; the crosspolarization X-pol; and the differential phase-shift between the axes ∆Φ CL . The values are averaged and weighted using the NIKA band profiles. The background colours indicate: non-ideal performance (red); acceptable (yellow); and good performance (green). Note that this waveplate was designed to work only in the NIKA 1-mm band.

Fig. 13 .

 13 Fig. 13. M-HWP B : Capacitive stack fitted model and measured transmissions along the reactive and transparent axes. The reactive axis (C) is essentially a low-pass filter while the transparent one (L) is similar to a dielectric slab.

Fig. 14 .

 14 Fig. 14. M-HWP B : Inductive stack fitted model and measured transmissions along the reactive and transparent axes. The reactive axis (L) looks like a high-pass filter for polarization aligned with it, while the transparent axis (C) like a dielectric slab.

Fig. 15 .

 15 Fig. 15. Cross-section details of the second prototype M-HWP B . The white layers are the porous-PTFE antireflection coatings while the brown part is the polypropylene substrate hosting all the embedded copper grids.

Fig. 16 .

 16 Fig. 16. M-HWP B : Capacitive and inductive axes modelled and measured transmissions.

Fig. 17 .

 17 Fig. 17. M-HWP B : 45 • cross-polarization model results and measurements.

Fig. 18 .

 18 Fig. 18. M-HWP B : Differential phase-shift model results and measurements.

Fig. 19 .

 19 Fig. 19. Originally modelled, measured and required performance parameters of the M-HWP B across the two NIKA bands. The labels and colours are the same as described in the data in Fig. 12. Note that this plate was part of an R&D phase and not meant to work either in the NIKA or NIKA2 instrument.

Fig. 21 .

 21 Fig. 21. M-HWP C : Capacitive stack fitted model and measured transmissions along the reactive and transparent axes.

Fig. 22 .

 22 Fig. 22. M-HWP C : Inductive stack fitted model and measured transmissions along the reactive and transparent axes.

Fig. 23 .

 23 Fig. 23. M-HWP C device mounted in front of the NIKA2 istrument.

Fig. 24 .

 24 Fig. 24. M-HWP C : Capacitive and inductive axes original/fit model and measured transmissions.

Fig. 25 .

 25 Fig. 25. M-HWP C : 45 • cross-polarization original/fit model and measurements.

Fig. 26 .

 26 Fig. 26. M-HWP C : Differential phase-shift original/fit model and measurements.

Fig. 27 .

 27 Fig. 27. M-HWP C finite-element unit cell model and simulations, run at 230 GHz, showing the propagation of the orthogonal electric fields, aligned with the L and C grids. Note that, at those specific positions, the outgoing vectors are in-phase (E L ) and out-of-phase (E C ) with respect to the incoming ones, so showing the expected introduction of a 180 • phase-shift between the two polarization components.

Fig. 28 .

 28 Fig. 28. From left to right Stokes Q and U maps obtained with NIKA at 150 GHz (top) Ritacco, A. et al. (2018) and NIKA2 at 260 GHz (bottom)[START_REF] Ritacco | Observing with NIKA2Pol from the IRAM 30m telescope : Early results on the commissioning phase[END_REF]).

Acknowledgements. We would like to thank the IRAM staff for their support during the campaigns. The NIKA and NIKA2 dilution cryostats have been designed and built at the Institut Néel. We acknowledge the crucial contribution of the Cryogenics and Electronics Groups in Grenoble. This work has been partially funded by the Foundation Nanoscience Grenoble and the LabEx FOCUS ANR-11-LABX-0013. This work has been supported by the French National Research Agency under the contracts "MKIDS", "NIKA" and ANR-15-CE31-0017 and in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02). This work has benefited from the support of the European Research Council Advanced Grant ORISTARS under the European Unionś Seventh Framework Programme (Grant Agreement no. 291294).


Jimmy Armoogum

Barbara Christian

Christelle Paulo

Anne -Eole

Anne-Eole Meret-Conti

#146 -Comparison of Respondent's profile of Computer-Aided Web Interviewing and Computer-assisted personal interviewing: The case of Ile-de-France mobility Surveys

whether they are published or not. The documents may come

Comparison of Respondent's profile of Computer-Aided Web Interviewing and Computer-assisted personal interviewing: The case of Ile-de-France mobility Surveys

Introduction

Experimental description

Methodologies and results

Conclusions

Even adjusting the samples with response mechanism and variables of interest, we find large (and significant) discrepancies. The cause may depend on two factors:

A non-ignorable non-response => Find other variables (that are link with the interest variables) to weight the surveys Measurement errors => Improve the design in order to interest people to give full answers

We took this opportunity to test the administration of this survey by two media first a Computer-assisted personal interviewing (CAPI) and second a Computer-Aided Web Interviewing (CAWI) in order to study the effect of both media on the response mechanism.

For both media we compute a logit model to model the response mechanism.

Effect DL CAPI CAWI

Wald Chi-Square Pr > ChiSq Wald Chi-Square Pr > ChiSq

Calibration on Census

Calibration on Census Say they are more immobile (+46%) Underestimate : • the number of trips (-13%),

• the daily travel time (-8%) • the distance traveled daily (-23%)

The characteristics of people with the largest CAPI-CATI discrepancies are as follows: Immobility