Pathway interference in a loop array of three coupled microresonators

A system of three coupled toroidal microresonators arranged in a loop configuration is studied. This setup allows light entering the resonator setup from a tapered fiber to evolve along a variety of different pathways before leaving again through the fiber. In particular, the loop configuration of the resonators allows for an evolution which we term round-trip process, in which the light evolves from one resonator sequentially through all others back to the initial one. This process renders the optical properties of the system sensitive to the phases of all coupling and scattering constants in the system. We analyze the transmission and reflection spectra, and interpret them in terms of interference between the various possible evolution pathways through the resonator system. In particular, we focus on the phase dependence of the optical properties. Finally, we discuss possible applications for this phase sensitivity induced by the round-trip process, such as the measurement of the position of a nanoparticle close to one of the resonators and the measurement of changes in the refractive index between two resonators. Our analytical results for the applications are supported by proof-of-principle calculations based on the finite-difference time-domain solution of Maxwell's equations in two dimensions on a grid.