  Superconducting coplanar-waveguide (CPW) resonators are one of the key
devices in circuit quantum electrodynamics (cQED). Their performance can be
limited by dielectric losses in the substrate and in the material interfaces.
Reliable modeling is required to aid in the design of low-loss CPW structures
for cQED. We analyze the geometric dependence of the dielectric losses in CPW
structures using finite-element modeling of the participation ratios of the
lossy regions. In a practical scenario, uncertainties in the the dielectric
constants and loss tangents of these regions introduce uncertainties in the
theoretically predicted participation ratios. We present a method for combining
loss simulations with measurements of two-level-system-limited quality factors
and resonance frequencies of CPW resonators. Namely, we solve an inverse
problem to find model parameters producing the measured values. High quality
factors are obtainable by properly designing the cross-sectional geometries of
the CPW structures, but more accurate modeling and design methods for low-loss
CPW resonators are called for major future improvements. Our nonlinear
optimization methodology for solving the aforementioned inverse problem is a
step in this direction.
