Design of antenna-coupled lumped-element titanium nitride KIDs for long-wavelength multi-band continuum imaging

Many applications in cosmology and astrophysics at millimeter wavelengths including CMB polarization, studies of galaxy clusters using the Sunyaev-Zeldovich effect (SZE), and studies of star formation at high redshift and in our local universe and our galaxy, require large-format arrays of millimeter-wave detectors. Feedhorn and phased-array antenna architectures for receiving mm-wave light present numerous advantages for control of systematics, for simultaneous coverage of both polarizations and/or multiple spectral bands, and for preserving the coherent nature of the incoming light. This enables the application of many traditional "RF" structures such as hybrids, switches, and lumped-element or microstrip band-defining filters.

Simultaneously, kinetic inductance detectors (KIDs) using high-resistivity materials like titanium nitride are an attractive sensor option for large-format arrays because they are highly multiplexable and because they can have sensitivities reaching the condition of background-limited detection. A KID is a LC resonator. Its inductance includes the geometric inductance and kinetic inductance of the inductor in the superconducting phase. A photon absorbed by the superconductor breaks a Cooper pair into normal-state electrons and perturbs its kinetic inductance, rendering it a detector of light. The responsivity of KID is given by the fractional frequency shift of the LC resonator per unit optical power.

However, coupling these types of optical reception elements to KIDs is a challenge because of the impedance mismatch between the microstrip transmission line exiting these architectures and the high resistivity of titanium nitride. Mitigating direct absorption of light through free space coupling to the inductor of KID is another challenge. We present a detailed titanium nitride KID design that addresses these challenges. The KID inductor is capacitively coupled to the microstrip in such a way as to form a lossy termination without creating an impedance mismatch. A parallel plate capacitor design mitigates direct absorption, uses hydrogenated amorphous silicon, and yields acceptable noise. We show that the optimized design can yield expected sensitivities very close to the fundamental limit for a long wavelength imager (LWCam) that covers six spectral bands from 90 to 400 GHz for SZE studies.

Excess phase (frequency) noise has been observed in KID and is very likely caused by two-level systems (TLS) in dielectric materials. The TLS hypothesis is supported by the measured dependence of the noise on resonator internal power and temperature. However, there is still a lack of a unified microscopic theory which can quantitatively model the properties of the TLS noise. In this thesis we derive the noise power spectral density due to the coupling of TLS with phonon bath based on an existing model and compare the theoretical predictions about power and temperature dependences with experimental data. We discuss the limitation of such a model and propose the direction for future study.

Measurements of mantle velocities of P waves with a large array

A large array has been used to investigate the P-wave velocity structure of the lower mantle. Linear array processing methods are reviewed and a method of nonlinear processing is presented. Phase velocities, travel times, and relative amplitudes of P waves have been measured with the large array at the Tonto Forest Seismological Observatory in Arizona for 125 earthquakes in the distance range of 30 to 100 degrees. Various models are assumed for the upper 771 km of the mantle and the Wiechert-Herglotz method applied to the phase velocity data to obtain a velocity depth structure for the lower mantle. The phase velocity data indicates the presence of a second-order discontinuity at a depth of 840 km, another at 1150 km, and less pronounced discontinuities at 1320, 1700 and 1950 km. Phase velocities beyond 85 degrees are interpreted in terms of a triplication of the phase velocity curve, and this results in a zone of almost constant velocity between depths of 2670 and 2800 km. Because of the uncertainty in the upper mantle assumptions, a final model cannot be proposed, but it appears that the lower mantle is more complicated than the standard models and there is good evidence for second-order discontinuities below a depth of 1000 km. A tentative lower bound of 2881 km can be placed on the depth to the core. The importance of checking the calculated velocity structure against independently measured travel times is pointed out. Comparisons are also made with observed PcP times and the agreement is good. The method of using measured values of the rate of change of amplitude with distances shows promising results.

Finite-Element Simulations of Earthquakes

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_w 7.0 to 7.1) and a thrust fault (M_w 6.6 to 7.0). The directivity of the ruptures creates large displacement and velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.