Spectral singularities of a complex spherical barrier potential and their optical realization

The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral singularities of a complex spherical barrier potential and study their realization as transverse spherical electromagnetic waves emitted by a gain medium with a spherical geometry. In particular, for a typical dye laser material, we obtain a lower bound on the size of the gain medium for the occurrence of this kind of spectral singularities.

► This Letter studies the spectral singularities of a spherical complex barrier potential. ► These are shown to admit a realization as a special type of spherical laser. ► A reliable perturbative analysis is performed to obtain analytical results that elucidate physical aspects of the problem. ► Numerical values of the physical parameters of the system have been obtained for a concrete spherical dye laser.