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We developed a broadband two-layer anti-reflection (AR) coating for use on a sapphire half-wave plate (HWP) and an alumina infrared (IR) filter for the cosmic microwave background (CMB) polarimetry. Measuring the faint CMB B-mode signals requires maximizing the number of photons reaching the detectors and minimizing spurious polarization due to reflection with an off-axis incident angle. Sapphire and alumina have high refractive indices of 3.1 and are highly reflective without an AR coating. This paper presents the design, fabrication, quality control, and measured performance of an AR coating using thermally sprayed mullite and Duroid 5880LZ. This technology enables large optical elements with diameters of 600 mm. We also present a thermography-based nondestructive quality control technique, which is key to assuring good adhesion and preventing delamination when thermal cycling. We demonstrate the average reflectance of about 2.6% (0.9%) for two observing bands centered at 90/150 (220/280) GHz. At room temperature, the average transmittance of a 105 mm square test sample at 220/280 GHz is 83%, and it will increase to 90% at 100 K, attributed to reduced absorption losses. Therefore, our developed layering technique has proved effective for 220/280 GHz applications, particularly in addressing dielectric loss concerns. This AR coating technology has been deployed in the cryogenic HWP and IR filters of the Simons Array and the Simons observatory experiments and applies to future experiments such as CMB-S4. more...

Telescopes measuring cosmic microwave background (CMB) polarization on large angular scales require exquisite control of systematic errors to ensure the fidelity of the cosmological results. In particular, far-sidelobe contamination from wide angle scattering is a potentially prominent source of systematic error for large aperture microwave telescopes. Here we describe and demonstrate a ray-tracing-based modeling technique to predict far sidelobes for a three mirror anastigmat telescope designed to observe the CMB from the South Pole. Those sidelobes are produced by light scattered in the receiver optics subsequently interacting with the walls of the surrounding telescope enclosure. After comparing simulated sidelobe maps and angular power spectra for different enclosure wall treatments, we propose a highly scattering surface that would provide more than an order of magnitude reduction in the degree-scale far-sidelobe contrast compared to a typical reflective surface. We conclude by discussing the fabrication of a prototype scattering wall panel and presenting measurements of its angular scattering profile. more...

We present near-field radio holography measurements of the Simons Observatory Large Aperture Telescope Receiver optics. These measurements demonstrate that radio holography of complex millimeter-wave optical systems comprising cryogenic lenses, filters, and feed horns can provide detailed characterization of wave propagation before deployment. We used the measured amplitude and phase, at 4 K, of the receiver near-field beam pattern to predict two key performance parameters: 1) the amount of scattered light that will spill past the telescope to 300 K and 2) the beam pattern expected from the receiver when fielded on the telescope. These cryogenic measurements informed the removal of a filter, which led to improved optical efficiency and reduced sidelobes at the exit of the receiver. Holography measurements of this system suggest that the spilled power past the telescope mirrors will be less than 1%, and the main beam with its near sidelobes are consistent with the nominal telescope design. This is the first time such parameters have been confirmed in the lab prior to deployment of a new receiver. This approach is broadly applicable to millimeter and submillimeter instruments. more...

We present the design, fabrication, and measured performance of metamaterial antireflection cuttings (ARCs) for large-format alumina filters operating over more than an octave of bandwidth to be deployed at the Simons Observatory (SO). The ARC consists of subwavelength features diced into the optic's surface using a custom dicing saw with near-micrometer accuracy. The designs achieve percent-level control over reflections at angles of incidence up to 20 ∘ . The ARCs were demonstrated on four 42 cm diameter filters covering the 75 to 170 GHz band and a 50 mm diameter prototype covering the 200 to 300 GHz band. The reflection and transmission of these samples were measured using a broadband coherent source that covers frequencies from 20 GHz to 1.2 THz. These measurements demonstrate percent-level control over reflectance across the targeted pass-bands and a rapid reduction in transmission as the wavelength approaches the length scale of the metamaterial structure where scattering dominates the optical response. The latter behavior enables use of the metamaterial ARC as a scattering filter in this limit. more...

Near-field radio holography is a common method for measuring and aligning mirror surfaces for millimeter and sub-millimeter telescopes. In instruments with more than a single mirror, degeneracies arise in the holography measurement, requiring multiple measurements and new fitting methods. We present HoloSim-ML, a Python code for beam simulation and analysis of radio holography data from complex optical systems. This code uses machine learning to efficiently determine the position of hundreds of mirror adjusters on multiple mirrors with few micrometer accuracy. We apply this approach to the example of the Simons Observatory 6 m telescope. more...

Controlling stray light at millimeter wavelengths requires special optical design and selection of absorptive materials that should be compatible with cryogenic operating environments. While a wide selection of absorptive materials exists, these typically exhibit high indices of refraction and reflect/scatter a significant fraction of light before absorption. For many lower index materials such as commercial microwave absorbers, their applications in cryogenic environments are challenging. In this paper, we present a new tool to control stray light: metamaterial microwave absorber tiles. These tiles comprise an outer metamaterial layer that approximates a lossy gradient index anti-reflection coating. They are fabricated via injection molding commercially available carbon-loaded polyurethane (25% by mass). The injection molding technology enables mass production at low cost. The design of these tiles is presented, along with thermal tests to 1 K. Room temperature optical measurements verify their control of reflectance to less than 1% up to 65 ∘ angles of incidence, and control of wide angle scattering below 0.01%. The dielectric properties of the bulk carbon-loaded material used in the tiles is also measured at different temperatures, confirming that the material maintains similar dielectric properties down to 3 K. more...

We present geometrical and physical optics simulation results for the Simons Observatory Large Aperture Telescope. This work was developed as part of the general design process for the telescope, allowing us to evaluate the impact of various design choices on performance metrics and potential systematic effects. The primary goal of the simulations was to evaluate the final design of the reflectors and the cold optics that are now being built. We describe nonsequential ray tracing used to inform the design of the cold optics, including absorbers internal to each optics tube. We discuss ray tracing simulations of the telescope structure that allow us to determine geometries that minimize detector loading and mitigate spurious near-field effects that have not been resolved by the internal baffling. We also describe physical optics simulations, performed over a range of frequencies and field locations, that produce estimates of monochromatic far-field beam patterns, which in turn are used to gauge general optical performance. Finally, we describe simulations that shed light on beam sidelobes from panel gap diffraction. more...

High-purity silicon is a readily available material of utility in realizing a variety of long-wavelength optical and guided wave components. The transmittance of uncompensated for silicon is measured in the far- and mid-infrared regimes at room and cryogenic temperatures. The experimental and analysis techniques used to extract the refractive index from 100-1000 c m -1 (100-10 µm) are presented, and the results are compared to the literature. An average refractive index below 300 c m -1 , n ^(300 K )=3.417+ i 8.9×10 -5 , which transitions in cooling to n ^(10 K )=3.389+ i 4.9×10 -6 , is observed. more...

Cyclic olefin copolymer (COC) is an amorphous thermoplastic with desirable dielectric and mechanical characteristics for optical applications. In particular, its low refractive index, overall mechanical strength, and absence of strong absorption features make it a promising substrate material for far-infrared applications, which include frequency-selective surfaces, scattering filters, and windows. The dielectric properties of selected COC formulations are surveyed from $ \approx 10 - 700\,\, {{\rm cm}^{ - 1}} $≈10-700cm -1 ($ 1000 - 14\,\, \unicode{x00B5} {\rm m} $1000-14µm), and representative usage as a thin film membrane structure in optical filters is presented. more...

The dielectric properties of selected conductively-loaded polyimide samples are characterized in the microwave through far-infrared wavebands. These materials, belonging to the Vespel family, are more readily formed by direct machining than their ceramic-loaded epoxy counterparts and present an interesting solution for realizing absorptive optical control structures. Measurements spanning a spectral range from 1 to 600  cm -1 (0.03-18 THz) were performed and used in parametrization of the media's dielectric function at frequencies below ≈3  THz. more...

Infrared (IR)-blocking filters are crucial for controlling the radiative loading on cryogenic systems and for optimizing the sensitivity of bolometric detectors in the far-IR. We present a new IR filter approach based on a combination of patterned frequency-selective structures on silicon and a thin (25-75 μm thick) absorptive composite based on powdered reststrahlen absorbing materials. For a 300 K blackbody, this combination reflects ∼50% of the incoming light and blocks >99.8% of the total power with negligible thermal gradients and excellent low-frequency transmission. This allows a reduction in the IR thermal loading to negligible levels in a single cold filter. These composite filters are fabricated on silicon substrates, which provide excellent thermal transport laterally through the filter and ensure that the entire area of the absorptive filter stays near the bath temperature. A metamaterial antireflection coating cut into these substrates reduces in-band reflections to below 1%, and the in-band absorption of the powder mix is below 1% for signal bands below 750 GHz. This type of filter can be directly incorporated into silicon refractive optical elements. more...

Refractive optical elements are widely used in millimeter and sub-millimeter (sub-mm) astronomical telescopes. High-resistivity silicon is an excellent material for dielectric lenses given its low loss tangent, high thermal conductivity, and high index of refraction. The high index of refraction of silicon causes a large Fresnel reflectance at the vacuum-silicon interface (up to 30%), which can be reduced with an anti-reflection (AR) coating. In this work, we report techniques for efficiently AR coating silicon at sub-mm wavelengths using deep reactive ion etching (DRIE) and bonding the coated silicon to another silicon optic. Silicon wafers of 100 mm diameter (1 mm thick) were coated and bonded using the silicon direct bonding technique at high temperature (1100°C). No glue is used in this process. Optical tests using a Fourier transform spectrometer show sub-percent reflections for a single-layer DRIE AR coating designed for use at 320 μm on a single wafer. Cryogenic (10 K) measurements of a bonded pair of AR-coated wafers also reached sub-percent reflections. A prototype two-layer DRIE AR coating to reduce reflections and increase bandwidth is presented, and plans for extending this approach are discussed. more...

An absorptive half-moon aperture mask is experimentally explored as a broad-bandwidth means of eliminating spurious spectral features arising from reprocessed radiation in an infrared Fourier transform spectrometer. In the presence of the spatial filter, an order of magnitude improvement in the fidelity of the spectrometer baseline is observed. The method is readily accommodated within the context of commonly employed instrument configurations and leads to a factor of two reduction in optical throughput. A detailed discussion of the underlying mechanism and limitations of the method are provided. more...

Silicon oxide thin films play an important role in the realization of optical coatings and high-performance electrical circuits. Estimates of the dielectric function in the far- and mid-infrared regime are derived from the observed transmittance spectrum for a commonly employed low-stress silicon oxide formulation. The experimental, modeling, and numerical methods used to extract the dielectric function are presented. more...

High-sensitivity receiver systems with near-ideal polarization sensitivity are highly desirable for development of millimeter and submillimeter radio astronomy. Multimoded bolometers provide a unique solution to achieve such sensitivity, for which hundreds of single-mode sensors would otherwise be required. The primary concern in employing such multimoded sensors for polarimetery is the control of the polarization systematics. In this work, we examine the angular- and polarization-dependent absorption pattern of a thin resistive grid or membrane, which models an absorber used for a multimoded bolometer. The result shows that a freestanding thin resistive absorber with a surface resistivity of η/2, where η is the impedance of free space, attains a beam pattern with equal E- and H-plane responses, leading to zero cross-polarization. For a resistive-grid absorber, the condition is met when a pair of grids is positioned orthogonal to each other and both have a resistivity of η/2. When a reflective backshort termination is employed to improve absorption efficiency, the cross-polar level can be suppressed below -30 dB if acceptance angle of the sensor is limited to ≲60°. The small cross-polar systematics have even-parity patterns and do not contaminate the measurements of odd-parity polarization patterns, for which many of the recent instruments for cosmic microwave background are designed. Underlying symmetry that suppresses these cross-polar systematics is discussed in detail. The estimates and formalism provided in this work offer key tools in the design consideration of the instruments using the multimoded polarimeters. more...

High-performance, integrated spectrometers operating in the far-infrared and submillimeter ranges promise to be powerful tools for the exploration of the epochs of reionization and initial galaxy formation. These devices, using high-efficiency superconducting transmission lines, can achieve the performance of a meter-scale grating spectrometer in an instrument implemented on a 4 inch silicon wafer. Such a device, when combined with a cryogenic telescope in space, provides an enabling capability for studies of the early universe. Here, the optical design process for Micro-Spec (μ-Spec) is presented, with particular attention given to its two-dimensional diffractive region, where the light of different wavelengths is focused on the different detectors. The method is based on the stigmatization and minimization of the light path function in this bounded region, which results in an optimized geometrical configuration. A point design with an efficiency of ~90% has been developed for initial demonstration and can serve as the basis for future instruments. Design variations on this implementation are also discussed, which can lead to lower efficiencies due to diffractive losses in the multimode region. more...

The increasing scale of cryogenic detector arrays for submillimeter and millimeter wavelength astrophysics has led to the need for large aperture, high index of refraction, low loss, cryogenic refracting optics. Silicon with n=3.4, low loss, and high thermal conductivity is a nearly optimal material for these purposes but requires an antireflection (AR) coating with broad bandwidth, low loss, low reflectance, and a matched coefficient of thermal expansion. We present an AR coating for curved silicon optics comprised of subwavelength features cut into the lens surface with a custom three-axis silicon dicing saw. These features constitute a metamaterial that behaves as a simple dielectric coating. We have fabricated silicon lenses as large as 33.4 cm in diameter with micromachined layers optimized for use between 125 and 165 GHz. Our design reduces average reflections to a few tenths of a percent for angles of incidence up to 30° with low cross polarization. We describe the design, tolerance, manufacture, and measurements of these coatings and present measurements of the optical properties of silicon at millimeter wavelengths at cryogenic and room temperatures. This coating and lens fabrication approach is applicable from centimeter to submillimeter wavelengths and can be used to fabricate coatings with greater than octave bandwidth. more...

Silicon nitride thin films play an important role in the realization of sensors, filters, and high-performance circuits. Estimates of the dielectric function in the far- and mid-IR regime are derived from the observed transmittance spectra for a commonly employed low-stress silicon nitride formulation. The experimental, modeling, and numerical methods used to extract the dielectric parameters with an accuracy of approximately 4% are presented. more...

We explore a free-space polarization modulator in which a variable phase is introduced between the right- and left-handed circular polarization components and used to rotate the linear polarization of the outgoing beam relative to that of the incoming beam. In this device, the polarization states are separated by a circular polarizer that consists of a quarter-wave plate in combination with a wire grid. A movable mirror is positioned behind and parallel to the circular polarizer. As the polarizer-mirror distance is changed, an incident linear polarization will be rotated through an angle that is proportional to the introduced phase delay. We demonstrate a prototype device that modulates Stokes Q and U over a 20% bandwidth, from 77 to 94 GHz. more...

The future needs of space-based, observational planetary and astronomy missions include low mass and small volume radiometric instruments that can operate in high-radiation and low-temperature environments. Here, we focus on a central spectroscopic component, the bandpass filter. We model the bandpass response of the filters to target the wavelength of the resonance peaks at 20, 40, and 60 µm and report good agreement between the modeled and measured response. We present a technique of using standard micromachining processes for semiconductor fabrication to make compact, free-standing, resonant, metal mesh filter arrays with silicon support frames. The process can be customized to include multiple detector array architectures, and the silicon frame provides lightweight mechanical support with low form factor. more...

We investigate the polarization modulation properties of a variable-delay polarization modulator (VPM). The VPM modulates polarization via a variable separation between a polarizing grid and a parallel mirror. We find that in the limit where the wavelength is much larger than the diameter of the metal wires that comprise the grid, the phase delay derived from the geometric separation between the mirror and the grid is sufficient to characterize the device. However, outside of this range, additional parameters describing the polarizing grid geometry must be included to fully characterize the modulator response. In this paper, we report test results of a VPM at wavelengths of 350 μm and 3 mm. Electromagnetic simulations of wire grid polarizers were performed and are summarized using a simple circuit model that incorporates the loss and polarization properties of the device., (© 2012 Optical Society of America) more...

Far-infrared bolometric detectors are used extensively in ground-based and space-borne astronomy, and thus it is important to understand their optical behavior precisely. We have studied the intensity and polarization response of free-space bolometers and shown that when the size of the absorber is reduced below a wavelength, the response changes from being that of a classical optical detector to that of a few-mode antenna. We have calculated the modal content of the reception patterns and found that for any volumetric detector having a side length of less than a wavelength, three magnetic and three electric dipoles characterize the behavior. The size of the absorber merely determines the relative strengths of the contributions. The same formalism can be applied to thin-film absorbers, where the induced current is forced to flow in a plane. In this case, one magnetic and two electric dipoles characterize the behavior. The ability to model easily the intensity, polarization, and straylight characteristics of electrically small detectors will be of great value when designing high-performance polarimetric imaging arrays. more...

We develop the Jones and Mueller matrices for structures that allow control of the path length difference between two linear orthogonal polarizations and consider the effect of placing multiple devices in series. Specifically, we find that full polarization modulation (measurement of Stokes Q, U, and V) can be achieved by placing two such modulators in series if the relative angles of the beam-splitting grids with respect to the analyzer orientation are appropriately chosen. Such a device has several potential advantages over a spinning wave plate modulator for measuring astronomical polarization in the far infrared through millimeter: (i) The use of small, linear motions eliminates the need for cryogenic rotational bearings; (ii) the phase flexibility allows measurement of circular as well as linear polarization; and (iii) this architecture allows for both multiwavelength and broadband modulation. We also present initial laboratory results. more...