Half-wave Plate Rotation Research Articles

CMB polarization signal demodulation with a rotating half-wave plate

ABSTRACT Several forthcoming Cosmic Microwave Background polarization experiments will employ a Continuously Rotating Half-Wave Plate (CRHWP), the primary purpose of which is to mitigate instrumental systematic effects. The use of a CRHWP necessitates demodulating the time-ordered data during the early stages of data processing. The standard approach is to “lock in” on the polarization signal using the known polarization modulation frequency and use Fourier techniques to filter out the remaining unwanted components. However, an alternative, less well-studied option is to incorporate the demodulation directly into the map-making step. Using simulations, we compare the performance of these two approaches to determine which is most effective for B-mode signal recovery. Testing the two techniques in multiple experimental scenarios, we find that the lock-in technique performs best over the full multipole range explored. However, for the recovery of the largest angular scales (multipoles, $\ell \lt 100$) we find essentially no difference in the recovery of the signal between the lock-in and map-making approaches, suggesting that a parallel analysis based on the latter approach could represent a powerful consistency check for primordial B-mode experiments employing a CRHWP. We also investigate the impact of a detector-differencing step, implemented prior to demodulation, finding that, in most scenarios, it makes no difference whether differencing is used or not. However, analysing detectors individually allows the point at which information from multiple detectors is combined to be moved to later stages in the analysis pipeline. This presents alternative options for dealing with additional instrumental systematic effects that are not mitigated by the CRHWP.

Effect of instrumental polarization with a half-wave plate on the B-mode signal: prediction and correction

We study the effect of incident unpolarized signal converted to polarized light produced by a realistic half-wave plate (HWP) and evaluate the impact of the effect in the measurement of Cosmic Microwave Background (CMB) B-mode polarization signal targeting to probe the tensor-to-scalar ratio r. The HWP is modeled with the Mueller formalism, and coefficients are decomposed for any incident angle into harmonics of the HWP rotation frequency due to azimuthal angle dependence. Although we use a general formalism, band-averaged matrix coefficients are calculated as an example for a 9-layer sapphire HWP using EM propagation simulations. We perform simulations of multi-detector observations in a band centered at 140 GHz using LiteBIRD instrumental configuration. We show both theoretically and with the simulations that most of the artefacts on Stokes parameter maps are produced by the dipole leakage on B-modes induced by the fourth harmonics MQI (4f) and MUI (4f). The resulting effect is strongly linked to the spin-2 focal plane scanning cross linking parameters. We develop a maximum likelihood-based method to correct the IP leakage by joint fitting of the Mueller matrix coefficients as well as the Stokes parameter maps. We show that the residual leakage after correction leads to an additional noise limited uncertainty on r of the order of 10-7, independently of the value of the Mueller matrix coefficients. We discuss the impact of the monopole signal and the potential coupling with other systematic effects such as gain variations and detector nonlinearities.

Dynamic control of hybrid grafted perfect vector vortex beams

Perfect vector vortex beams (PVVBs) have attracted considerable interest due to their peculiar optical features. PVVBs are typically generated through the superposition of perfect vortex beams, which suffer from the limited number of topological charges (TCs). Furthermore, dynamic control of PVVBs is desirable and has not been reported. We propose and experimentally demonstrate hybrid grafted perfect vector vortex beams (GPVVBs) and their dynamic control. Hybrid GPVVBs are generated through the superposition of grafted perfect vortex beams with a multifunctional metasurface. The generated hybrid GPVVBs possess spatially variant rates of polarization change due to the involvement of more TCs. Each hybrid GPVVB includes different GPVVBs in the same beam, adding more design flexibility. Moreover, these beams are dynamically controlled with a rotating half waveplate. The generated dynamic GPVVBs may find applications in the fields where dynamic control is in high demand, including optical encryption, dense data communication, and multiple particle manipulation.

Modeling TES Nonlinearity Induced by a Rotating HWP in a CMB Polarimeter

Most upcoming CMB experiments are planning to deploy between a few thousand and a few hundred thousand TES bolometers in order to drastically increase sensitivity and unveil the B-mode signal. Differential systematic effects and 1/f noise are two of the challenges that need to be overcome in order to achieve this result. In recent years, rotating half-wave plates have become increasingly more popular as a solution to mitigate these effects, especially for those experiments that are targeting the largest angular scales. However, other effects may appear when a rotating HWP is being employed. In this paper, we focus on HWP synchronous signals, which are due to intensity to polarization leakage induced by a rotating cryogenic multilayer sapphire HWP employed as the first optical element of the telescope system. We use LiteBIRD LFT as a case study and we analyze the interaction between these spurious signals and TES bolometers, to determine whether this signal can contaminate the bolometer response. We present the results of simulations for a few different TES model assumptions and different spurious signal amplitudes. Modeling these effects is fundamental to find what leakage level can be tolerated and minimize nonlinearity effects of the bolometer response.

Simultaneous measurement of phase retardation and fast axis azimuth of wave plate based on equivalent component and phase detection

Wave plates (WPs) are key components in optical polarization systems whose phase retardations and fast axis azimuths should be determined accurately. At present many measurement methods are based on light intensity detection which is inevitably affected by light intensity fluctuations so that the measurement accuracy is limited. What’s more, quite a few methods cannot measure WPs’ fast axis azimuths simultaneously. In this paper a method of simultaneously measuring the phase retardation and fast axis azimuth of arbitrary WP is proposed, which is based on equivalent component and phase detection. A rotatable half wave plate (HWP) and a retroreflector are used and its effect is equivalent to measuring an equivalent WP whose phase retardation is twice that of the measured wave plate, which is equivalent to doubling the measurement resolution. Phase detection is used to process the signals which means the measurement accuracy is better than that by usual light intensity detection. What’s more, the presented method eliminates the angle positioning errors of birefringent components in principle which exists in many present WP measurement methods. Finally, the measurement system setup is simple as well as the measurement process. The measurement formulae are deduced and corresponding WP measuring system is established. The error analysis shows that the system measurement uncertainty is about 3.9′ for the phase retardation and 5” for the fast axis azimuth. Experiment results and comparisons of quarter WPs and HWPs show that the presented method is in good agreement with other method. The phase retardation measurement repeatability is also good with a standard deviation about 2′.

QUBIC III: Laboratory characterization

We report on an extensive test campaign of a prototype version of theQUBIC (Q & U Bolometric Interferometer for Cosmology) instrument,carried out at Astroparticle Physics and Cosmology (APC) inParis. Exploiting the novel concept called bolometric interferometry,QUBIC is designed to measure the CMB polarization at 150 and 220 GHzfrom a high altitude site at Alto Chorillo, Argentina. The prototypemodel called QUBIC Technological Demonstrator (QUBIC-TD) operates in asingle frequency band (150 GHz) and with a reduced number ofbaselines, but it contains all the elements of the QUBIC instrument inits final configuration. The test campaign included measurements ofthe synthesized beam and of the polarization performance, as well as averification of the interference fringe pattern. A modulated,frequency-tunable millimetre-wave source was placed in the telescopefar-field and was used to simulate a point source. The QUBIC-TD fieldof view was scanned across the source to produce beam maps. Ourmeasurements confirm the frequency-dependent behaviour of the beamprofile, which gives QUBIC the possibility to do spectral imaging. Themeasured polarization performance indicates a cross-polarizationleakage less than 0.6%. We also successfully tested the polarizationmodulation system, which is provided by a rotating half waveplate. We demonstrate the full mapmaking pipeline using datafrom this measurement campaign, effectively giving an end-to-endcheckout of the entire QUBIC system, including all hardwaresubsystems, their interfaces, and the software to operate the wholesystem and run the analysis. Our results confirm the viability ofbolometric interferometry for measurements of the CMB polarization.

Polarimetry for measuring the vacuum magnetic birefringence with quasi-static fields: a systematics study for the VMB@CERN experiment

We present an experimental systematics study of a polarimetric method for measuring the vacuum magnetic birefringence based on a pair of rotating half-wave plates. The presence of a systematic effect at the same frequency as the sought for magneto-optical effect inhibits the use of strictly constant magnetic fields. We characterise this systematic, discuss its origin and propose a viable workaround.

Glucose sensing in the presence of scattering by analyzing a partial Mueller matrix

We propose a method to analyze a partial Mueller matrix to retrieve the optical rotation and depolarization properties simultaneously for measuring glucose concentration in the presence of scattering. A Mueller matrix polarimeter using dual photoelastic modulators and rotating half wave plates that can retrieve four partial Mueller matrices (nine elements each) for a particular orientation of half wave plates has been applied for this purpose. We verify the proposed technique by measuring different glucose concentrations from the normal to diabetic range in the absence and presence of scattering. A measurement precision of 0.004° in optical rotation and 0.0004 in depolarization is achieved, so that the sensitivity of detecting glucose concentration is obtained as low as 20 mg/dl for a 40 mm path length cuvette, even in the presence of scattering medium.

Implementation of a complete Mueller matrix polarimeter using dual photoelastic modulators and rotating wave plates

We propose a complete Mueller matrix polarimeter using dual photoelastic modulators and rotating half wave plates. The complete Mueller matrix of a sample is obtained by combining four partial Mueller matrices (nine elements each), by rotating the half wave plates in four different orientations. By considering the effect of retardance errors of the wave plates, a more general calibration method is developed. We demonstrate the accuracy of the system by measuring a Babinet–Soleil compensator and the scattering coefficient of an intralipid sample, whereas the depolarization characteristics is shown for different column density of intralipid. Simultaneous determination of optical rotation and depolarization is verified by conducting studies on glucose concentrations ranging from 0 to 400 mg/dl mixed with $$2\%$$ v/V intralipid.

Note: Lossless laser beam combiner employing a high-speed rotating half-wave plate.

We have developed a laser beam combiner employing a high-speed rotating half-wave plate based on the specific requirements of the Thomson scattering measurement systems in the ITER. The polarization extinction ratio of the output beam may exceed 1000 and was maintained for more than 1 h via feedback control of the half-wave plate rotation speed. The pointing fluctuations introduced by rotating the half-wave plate were in the order of microradians. The high-speed rotating half-wave plate provides a lossless means of combining laser beams together with stable beam pointing.

Single-Tone Optical Frequency Shifting and Nonmagnetic Optical Isolation by Electro-Optical Emulation of a Rotating Half-Wave Plate in a Traveling-Wave Lithium Niobate Waveguide

In this paper, we demonstrate a frequency shifter at 780 nm based on an X -cut Z -propagating lithium niobate waveguide platform with an isotropic orientation. The electro-optic effect modulates the signal with traveling-wave configuration. The frequency-shifting device emulates a rotating half-wave plate when it converts left circular polarized input light to right circular polarized output light and changes the original optical frequency by its modulation frequency. We characterize the device by conducting the polarization conversion experiment and achieve the frequency shift at up to 2 GHz and more than 20 dB extinction ratio. The device needs 30 dBm RF power to perform a frequency shift with high extinction ratio. With the same device, we also demonstrate optical isolation with 18.5 dB extinction ratio.

Optimization of the half wave plate configuration for the LSPE-SWIPE experiment

The search for the B-mode polarization of Cosmic Microwave Background (CMB) is the new frontier of observational Cosmology. A B-mode detection would give an ultimate confirmation to the existence of a primordial Gravitational Wave (GW) background as predicted in the inflationary scenario. Several experiments have been designed or planned to observe B-modes. In this work we focus on the forthcoming Large Scale Polarization Explorer (LSPE) experiment, that will be devoted to the accurate measurement of CMB polarization at large angular scales. LSPE consists of a balloon-borne bolometric instrument, the Short Wavelength Instrument for the Polarization Explorer (SWIPE), and a ground-based coherent polarimeter array, the STRatospheric Italian Polarimeter (STRIP). SWIPE will employ a rotating Half Wave Plate (HWP) polarization modulator to mitigate the systematic effects due to instrumental non-idealities. We present here preliminary forecasts aimed at optimizing the HWP configuration.

QuickPol: Fast calculation of effective beam matrices for CMB polarization

Current and planned observations of the cosmic microwave background (CMB) polarization anisotropies, with their ever increasing number of detectors, have reached a potential accuracy that requires a very demanding control of systematic effects. While some of these systematics can be reduced in the design of the instruments, others will have to be modeled and hopefully accounted for or corrected a posteriori. We propose QuickPol, a quick and accurate calculation of the full effective beam transfer function and of temperature to polarization leakage at the power spectra level, as induced by beam imperfections and mismatches between detector optical and electronic responses. All the observation details such as exact scanning strategy, imperfect polarization measurements, and flagged samples are accounted for. Our results are validated on Planck high frequency instrument (HFI) simulations. We show how the pipeline can be used to propagate instrumental uncertainties up to the final science products, and could be applied to experiments with rotating half-wave plates.

Multi-octave metamaterial reflective half-wave plate for millimeter and sub-millimeter wave applications.

The quasi-optical modulation of linear polarization at millimeter and sub-millimeter wavelengths can be achieved by using rotating half-wave plates (HWPs) in front of polarization-sensitive detectors. Large operational bandwidths are required when the same device is meant to work simultaneously across different frequency bands. Previous realizations of half-wave plates, ranging from birefringent multi-plates to mesh-based devices, have achieved bandwidths of the order of 100%. Here we present the design and experimental characterization of a reflective HWP able to work across bandwidths of the order of 150%. The working principle of the novel device is completely different from any previous realization, and it is based on the different phase-shift experienced by two orthogonal polarizations reflecting, respectively, off an electric conductor and an artificial magnetic conductor.

A cryogenic rotation stage with a large clear aperture for the half-wave plates in the Spider instrument.

We describe the cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the cosmic microwave background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015. The mechanisms operate at liquid helium temperature in flight. A three-point contact design keeps the mechanical bearings relatively small but allows for a large (305 mm) diameter clear aperture. A worm gear driven by a cryogenic stepper motor allows for precise positioning and prevents undesired rotation when the motors are depowered. A custom-built optical encoder system monitors the bearing angle to an absolute accuracy of ±0.1(∘). The system performed well in Spider during its successful 16 day flight.

Characterizing Atacama B-mode Search Detectors with a Half-Wave Plate

The Atacama B-Mode Search (ABS) instrument is a cryogenic ($\sim$10 K) crossed-Dragone telescope located at an elevation of 5190 m in the Atacama Desert in Chile that observed for three seasons between February 2012 and October 2014. ABS observed the Cosmic Microwave Background (CMB) at large angular scales ($40<\ell<500$) to limit the B-mode polarization spectrum around the primordial B-mode peak from inflationary gravity waves at $\ell \sim100$. The ABS focal plane consists of 480 transition-edge sensor (TES) bolometers. They are coupled to orthogonal polarizations from a planar ortho-mode transducer (OMT) and observe at 145 GHz. ABS employs an ambient-temperature, rapidly rotating half-wave plate (HWP) to mitigate systematic effects and move the signal band away from atmospheric $1/f$ noise, allowing for the recovery of large angular scales. We discuss how the signal at the second harmonic of the HWP rotation frequency can be used for data selection and for monitoring the detector responsivities.

Influence of ghost coupling points on distributed polarization crosstalk measurements in high birefringence fiber and its solution.

Ghost coupling points in distributed polarization crosstalk measurements adopting a white light interferometric method are analyzed under the circumstances of anisotropy perturbation induced polarization crosstalk and principal axis misalignment induced polarization crosstalk in polarization-maintaining fiber. The relationship between the intensities of the ghost coupling points and the real crosstalk points, as well as the relationship between their positions, are theoretically analyzed and proved by experiment. A simple method has been developed to identify the ghost coupling points by using a rotatable half-wave plate to adjust the angle between the principal axis of the analyzer and the exciting mode propagating in the polarization-maintaining fiber. The experimental results have a good agreement with the theoretical results.

Procedure for aligning polarization modulator link for amplitude modulation applications.

A procedure is detailed for aligning the transmitted output states of a polarization modulated signal to the analyzer states of a polarizing discriminator in an analog photonic link. The steps in the procedure insure optimal amplitude modulation in the link. Experimental results are presented for biasing in two ways: either the DC bias on the modulator or a rotatable half-wave plate can be used. The corresponding theory is included.

An Easily Designed and Constructed Optical Polarimeter for Small Telescopes

We have designed, constructed, and tested an optical polarimeter for use with the Virginia Military Institute (VMI) 0.5 m, f/13.5 Cassegrain telescope. Our instrument is based on the common dual-beam design that utilizes a rotatable half-wave plate and Wollaston prism to image starlight onto a CCD detector after it has passed through a broadband filter. The usable field of view is ≲10′′ and the operational range of the instrument is 400–700 nm. Measurements of unpolarized stars demonstrate that the instrumental polarization is ≲0.05%. Observations of seven standard stars were in agreement with their accepted values by an order of Δp(%) ≲ 0.23 for the degree of polarization and Δθ(°) ≲ 0.94 for the position angle.

Full-field optical coherence tomography by achromatic phase shifting with a rotatinghalf-wave plate

An achromatic phase shifter with a rotating half-wave plate (HWP) and a full-field opticalcoherence tomography (FF-OCT) system based on it are presented. The novelconfiguration of this phase shifter in the FF-OCT system can achromaticallyprovide a phase shift of eight times the rotation angle of the HWP. The theoreticalcalculation of the phase shift and numerical analysis of the phase shift error,as well as the amplitude ratio, are conducted by means of Jones matrices. Theactual phase shift has also been measured to confirm the validity of the ‘8θ phase shift—HWProtation angle θ’ relation. The coherent image of a mirror has been obtained by using the Hariharanalgorithm to verify the phase shifter’s feasibility. Using traditional phase shiftingalgorithms, en-face images of a coin have been measured at different depths to illustrate thetomographic capability of this FF-OCT system. In comparison with other current systems,our design has several advantages, and high-resolution high-speed FF-OCT imaging can beenvisioned. The phase shifter can be used for common path setups and is verysuitable for implementing the phase shifting of a broad-spectrum light source.