Analysis of a multi-mode plasmonic nano-laser with an inhomogeneous distribution of molecular emitters

摘要

We extend Lamb's reduced density matrix laser theory to analyze theinhomogeneous molecular couplings and the mode-correlation in a plasmonicnano-laser consisting of a gold sphere and many dye molecules interacting witha driving optical field and with the quantized plasmon modes. The molecularinhomogeneity is accounted for by simulating their random distribution aroundthe sphere. Our analysis shows that in order to obtain lasing we must employ alarge number of strongly driven molecules to compensate strong damping of theplasmon modes. The compact molecular arrangement, however, can lead tomolecular energy-shifts and thus reduce the excitation of the plasmon modes andultimately suggests a maximum limit for the plasmon excitation for any specificsystem.