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In this article, we investigate the spontaneous emission properties ofradiating molecules embedded in a chiral nematic liquid crystal, under theassumption that the electronic transition frequency is close to the photonicedge mode of the structure, i.e. at resonance. We take into account thetransition broadening and the decay of electromagnetic field modes supported bythe so-called `mirror-less' cavity. We employ the Jaynes-Cummings Hamiltonianto describe the electron interaction with the electromagnetic field, focusingon the mode with the diffracting polarization in the chiral nematic layer. Asknown in these structures, the density of photon states, calculated via theWigner 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 thebehavior of the density of states and the spontaneous emission profile of thesestructures. In addition, we examine in some detail the case of the logarithmicpeak exhibited in the density of states in 2D photonic structures and obtainanalytic relations for the Lamb shift and the broadening of the atomictransition in the emission spectrum. The dynamical behavior of the atom-fieldsystem is described by a system of two first order differential equations,solved using the Green's function method and the Fourier transform. Theemission spectra are then calculated and compared with experimental data.

physical review. e, statistical, nonlinear and soft matter physics

Spontaneous emission from radiative chiral nematic liquid crystals at  the photonic band gap edge: an investigation into the role of the density of  photon states near resonance