  In this work the behavior of optical micro-ring resonators, especially when
functioning as refractive index sensors, is studied in detail. Two
configurations are considered, namely a linear waveguide coupled to a circular
one and two linear waveguides coupled to each other through a circular one. The
optimum coupling conditions are derived and it is shown that in both cases the
condition for the resonant wavelength, i.e. the wavelength at which the
transmission spectrum exhibits a dip (peak), is the same and depends only on
the geometrical characteristics of the circular waveguide and the effective
refractive index of the propagating mode. The latter, as well as the
corresponding mode profile, can be easily calculated through numerical
analysis. The sensitivity of the sensor is defined based on the dependence of
the effective refractive index on the refractive index of the environment.
Using a result of waveguide perturbation theory, the geometrical
characteristics of the core of the circular waveguide that maximize the
sensitivity of the system are determined. Both single and dual core
configurations are considered. It is found that, when optimally designed, the
sensor can detect relative refractive index changes of the order of 10^-4,
assuming that the experimental setup can detect relative wavelength shifts of
the order of 3x10^-5. Finally, the behavior of the system as bio-sensor is
examined by considering that a thin layer of bio-material is attached on the
surface of the waveguide core. It is found that, when optimally designed, the
system can detect refractive index changes of the order of 10^-3 for a layer
thickness of 10 nm, and changes in the layer thickness of the order of 0.24 nm,
for a refractive index change of 0.05.
