  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 roundtrip 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 roundtrip 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 finite-difference-time-domain solution ofMaxwell's equations in two
dimensions on a grid.
