Analysis and calibration techniques for superconducting resonators.

A method is proposed and experimentally explored for in-situ calibration of complex transmission data for superconducting microwave resonators. This cryogenic calibration method accounts for the instrumental transmission response between the vector network analyzer reference plane and the device calibration plane. Once calibrated, the observed resonator response is analyzed in detail by two approaches. The first, a phenomenological model based on physically realizable rational functions, enables the extraction of multiple resonance frequencies and widths for coupled resonators without explicit specification of the circuit network. In the second, an ABCD-matrix representation for the distributed transmission line circuit is used to model the observed response from the characteristic impedance and propagation constant. When used in conjunction with electromagnetic simulations, the kinetic inductance fraction can be determined with this method with an accuracy of 2%. Datasets for superconducting microstrip and coplanar-waveguide resonator devices were investigated and a recovery within 1% of the observed complex transmission amplitude was achieved with both analysis approaches. The experimental configuration used in microwave characterization of the devices and self-consistent constraints for the electromagnetic constitutive relations for parameter extraction are also presented.

Micro-Spec: an ultracompact, high-sensitivity spectrometer for far-infrared and submillimeter astronomy.

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.

Properties of a variable-delay polarization modulator.

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.

Modeling the intensity and polarization response of planar bolometric detectors.

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.

The Hertz/VPM polarimeter: design and first light observations.

We present first results of Hertz/VPM, the first submillimeter polarimeter employing the dual Variable-delay Polarization Modulator (dual-VPM). This device differs from previously used polarization modulators in that it operates in translation, rather than mechanical rotation. We discuss the basic theory behind this device and its potential advantages over the commonly used half-wave plate. The dual-VPM was tested both at the Submillimeter Telescope Observatory and in the laboratory. In each case we present a detailed description of the setup. We discovered that properties of the VPM wire grids (diameter and spacing) caused behavior that differs from theoretical predictions for ideal wire grid performance. By modifying the polarimeter settings to compensate for this behavior, we found that the dual-VPM system is robust, operating with high efficiency and low instrumental polarization. This device is well suited for air- and space-borne applications.

Interferometric polarization control.

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.