A generalized modeling approach for the frequency shift in near-field scanning microwave microscopes

In most Near-Field Scanning Microwave Microscope (NSMM) setups, changes of the dielectric environment in the vicinity of the tip are detected by measuring the detuning of a resonator connected to the tip. In this work, we propose a novel, semi-analytic approach to model the frequency shift of this resonator. In contrast to the traditional procedures, our method allows to model arbitrary tip shapes while still offering fast computations. Specifically, we combine a static boundary element calculation with a numerical integration procedure to evaluate overlap integral occurring expressions obtained by traditional perturbation theory.