  The analogy between mechanical and electromagnetic resonators has been a
celebrated paradigm of science and engineering. Exploration of this analogy in
recent years has resulted in several exciting research directions, including
cavity optomechanics[1], phononic bandgap materials[2] and phononic
metamaterials[3-5]. In these examples, progress in electromagnetic research has
usually led the way for their mechanical counterparts. Here, we contribute to
this analogy from a different perspective by adapting a sensing technique
originally developed for mechanical devices to increase the capabilities of
sensors based on electromagnetic fields. More specifically, multimode resonance
techniques, which enable spatial resolution in inertial mass sensing
experiments with nanoelectromechanical systems (NEMS), are tailored for use in
microwave resonant sensing, which is commonly employed in microfluidics. We
show that the use of higher-order modes of such sensors can provide electrical
volume, position and geometric size data. The combination of such spatial
features implies the potential for image reconstruction when a large number of
modes are used. With the analytical and experimental framework presented here,
we can move beyond simple counting and achieve the sizing and imaging of
analytes with impedance spectroscopy.
