Linear absorption and dispersion properties, as well as Kerr nonlinear index, of three-level
atomic systems can be greatly modified under the condition of electromagnetically induced
transparency (EIT). By placing such EIT atoms in a vapor cell inside an optical ring cavity, the cavity
transmission spectrum can be altered and controlled. We show that the cavity transmission linewidth
can be narrowed substantially comparing to the empty cavity linewidth due to the sharp normal (linear)
dispersion associated with the EIT resonance (which can be considered as photons traveling with a
slower speed inside the optical cavity). On the other hand, the Kerr nonlinear dispersion has the
opposite slope comparing to the linear dispersion near the EIT resonance, which can be used to balance
the linear dispersion and lead to total anomalous dispersion for the intracavity atomic medium (with
``superluminal photon speed'' inside the optical cavity). Such anomalous dispersion in the intracavity
medium makes the cavity transmission linewidth broader than the empty cavity linewidth. Under
certain parameters, the so called ``white-light cavity'' condition can be satisfied, which makes the
cavity transmission linewidth very broad and, at the same time, have high cavity transmission. Such
modified and controlled cavity transmission linewidths can have many interesting applications in
frequency locking, cavity ring-down spectroscopy, nonlinear optical spectroscopy, cavity-QED, and
even recycling cavity of the gravitational-wave detector.
