How latitude location on a micro-world enables real-time nanoparticle sizing

We have devised a method for using the nanoparticle induced frequency shift of whispering gallery modes (WGMs) in a microspheroid for the accurate determination of the nanoparticle size in real time. Before the introduction of this technique, size determination from the mode shift could only be obtained statistically based on the assumption that the largest perturbation occurs for binding at the equator. Determining the latitude of the binding event using two polar WGMs results in an analytic method for size determination using a single binding event. The analysis proceeds by incorporating the binding latitude into the Reactive Sensing Principle (RSP), itself containing a shape dependent form factor found using the Born approximation. By comparing this theory with experiments we find that our theoretical approach is more accurate than point dipole theory even though the optical size (circumference/wavelength) is considerably less than one.