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

TL;DR

This study explores how the density of photon states near the photonic band gap edge influences spontaneous emission in chiral nematic liquid crystals, revealing significant spectral modifications at resonance.

Contribution

It provides a detailed theoretical analysis of spontaneous emission near the photonic band edge, incorporating the Jaynes-Cummings model and mode decay effects, with analytic relations for Lamb shift and broadening.

Findings

Density of photon states peaks modify emission spectra near resonance

Analytic expressions for Lamb shift and transition broadening derived

Comparison of theoretical spectra with experimental data confirms model accuracy

Abstract

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.