Emission dynamics and spectrum of a nanoshell-based plasmonic nanolaser spaser

We study theoretically the emission and lasing properties of a single nanoshell spaser nanoparticle, or plasmonic nanolaser, made of an active core (gain material) and a plasmonic metal shell. Based on an analytical framework coupling together time-dependent equations for the gain and the metal, we calculate the lasing threshold with the help of an instability analysis. We characterize the regime under the threshold, where the nanoshell behaves as an optical amplifier when excited by an incident probe field. We then investigate in depth the non-linear lasing regime above the threshold, under autonomous conditions (free lasing without external drive), by computing the system's dynamics both in the transient state and in the final steady state. We show that at threshold, the lasing starts at one frequency only, usually one of the plasmon resonances of the nanoshell; then as the gain is further raised, the emission widens to other frequencies. This differs significantly from previous findings in the literature, which found only one emission wavelength above threshold. We proceed to calculate the complete (maximal) emission spectrum of the nanolaser as well as its emission linewidth, both of which are evidenced to be affected by unusually strong frequency shifts (pull-out) effects. We find that the nanolaser emission is highly asymmetrical spectrally and only occurs on one side (high-frequency) of the plasmon resonance. Finally, we show that the spectral position of the emission line can be tuned across the whole visible range, by changing the geometrical aspect ratio of the nanoshell.