Advanced Numerical and Experimental Analysis of Ultra-Miniature Surface Resonators

Many scientific and technological applications make use of strong microwave fields. These are often realized in conjunction with microwave resonators that have small geometric features in which such fields are generated. For example, in magnetic resonance, large microwave and RF magnetic fields make it possible to achieve fast control over the measured electron or nuclear spins in the sample and to detect them with high sensitivity. The numerical analysis of resonators with small geometric features can pose a significant challenge. This paper describes a general method of analysis and characterization of surface microresonators in the context of electron spin resonance (ESR) spectroscopy and spin-based quantum technology. Our analysis is based on the Electric Field Integral Equation (EFIE) and the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation. In particular, we focus on a class of resonator configurations that possesses extremely small subwavelength features, which normally would require an ultra-fine mesh. We present several efficient techniques to numerically model, solve, and analyze these types of configurations for both normal and superconducting structures. The validation of these techniques is established both numerically and experimentally by the S₁₁ parameters as well as the provision of direct mapping of the resonator's microwave magnetic field component using a unique electron spin resonance micro-imaging method.