  We present a detailed theoretical analysis of a Fock-state filter based on
the photon-number dependent group delay in cavity induced transparency proposed
in Phys. Rev. Lett. 105, 013601 (2010). We derive a general expression for the
propagation velocity of different photon-number components of a light pulse
interacting with an optically dense ensemble of three-level atoms coupled to a
resonator mode under conditions of cavity induced transparency. These
predictions are compared to numerical simulations of the propagation of few
photon wave packets, and an estimation for experimental realization is made.
