Spatial distribution of lasing at the edge of a photonic stop band in dye-doped cholesteric liquid crystals

We find a ring structure in the far field of laser radiation emitted from a dye-doped cholesteric liquid crystal (CLC) film. This is a consequence of angular confinement of radiation at the frequency of the mode propagating normal to the molecular layers, which lies closest to the reflection band edge. This is a result of the increase in frequency of the band edge with increasing angle from the normal, which places oblique radiation at the frequency of the band edge for normally propagating radiation inside the photonic gap. As a result, the intensity along the output surface of the film decays exponentially on a length scale that can be much larger than the film thickness. This in turn give rise to a ring structure in the far field that is similar to Fraunhofer diffraction of a plane wave by an aperture. These results apply not only to CLC films but also to binary layered media.