Optical detection of target molecule induced aggregation of nanoparticles by means of high-Q resonators

We theoretically investigate a novel scheme to detect target molecule induced, or suppressed, aggregation of nanoparticles. High-Q optical resonators are used to both optically trap gold nanoparticle clusters and to detect their presence via a shift in the resonance wavelength. The well depth of the optical trap is chosen to be relatively low compared to the thermal energy of the nanoparticles, so that trapping of single nanoparticles is marginal and results in a comparatively small wavelength shift. Aggregation of functionalized gold nanoparticles is mediated or suppressed via binding to a target molecule. The well depth for the resulting nanoparticle clusters scales much more favorably relative to Brownian motion, resulting in large nanoparticle concentration enhancements in the evanescent field region of the resonator. We predict a target molecule sensitivity in the tens of fM range. In order to predict the resonator response, a complete theory of time resolved nanoparticle cluster trapping dynamics is derived. In particular, the formalism of Kramers' escape time is adapted to 2D (silicon wire) and 3D (ring resonator) optical traps.