  In this article, we investigate the spontaneous emission properties of
radiating molecules embedded in a chiral nematic liquid crystal, under the
assumption that the electronic transition frequency is close to the photonic
edge mode of the structure, i.e. at resonance. We take into account the
transition broadening and the decay of electromagnetic field modes supported by
the so-called `mirror-less' cavity. We employ the Jaynes-Cummings Hamiltonian
to describe the electron interaction with the electromagnetic field, focusing
on the mode with the diffracting polarization in the chiral nematic layer. As
known in these structures, the density of photon states, calculated via the
Wigner method, has distinct peaks on either side of the photonic band gap,
which manifests itself as a considerable modification of the emission spectrum.
We demonstrate that, near resonance, there are notable differences between the
behavior of the density of states and the spontaneous emission profile of these
structures. In addition, we examine in some detail the case of the logarithmic
peak exhibited in the density of states in 2D photonic structures and obtain
analytic relations for the Lamb shift and the broadening of the atomic
transition in the emission spectrum. The dynamical behavior of the atom-field
system is described by a system of two first order differential equations,
solved using the Green's function method and the Fourier transform. The
emission spectra are then calculated and compared with experimental data.
