Modelling the response of whispering-gallery-mode optical resonators for biosensing applications

In recent years, sharp photonic resonances of dielectric microspheres, so-called whispering gallery modes (WGMs), have emerged as powerful transducer for sensing applications. The long photon lifetime of the modes together with the small surface area of the microresonator is promising for their use as sensitive probes of changes in the surrounding medium. In this work we present a theoretical analysis of the response of WGMs for biosensing applications, studied numerically in microcylinders and semi-analytically in microspheres. In both cases, we consider a layout where WGMs are excited via frustrated total internal reflection from a planar substrate, as reported in recent experiments. The effect of single and multiple particles is calculated, simulating biological analytes of different sizes and polarizabilities attached to the microresonator surface. For microcylinders, cylinder-shaped particle are considered, to retain a 2D numerical problem. Besides WGM frequency shifts, we find that also broadenings and splittings (from lifted rotational symmetry) appear due to particles attachment and/or the vicinity to the planar substrate. In particular, for a single analyte, both particle size and refractive index can be determined from the WGM broadening and shift, opening the perspective to a new biosensing modality. In microspheres, a perturbation method is used to model shifts and splittings of WGMs in the presence of point-like particles and global shape perturbations. Due to the large azimuthal degeneracy of the modes without perturbation, the resulting mode spectrum is rich and offers a fingerprint of the perturbation