Intensity-dependent frequency shift in surface plasmon amplification by stimulated emission of radiation

The operation of a surface plasmon amplification by stimulated emission of radiation- (spaser)-based nanolaser is theoretically investigated. We find that the lasing frequency undergoes a shift as the lasing intensity increases, a result that agrees with recent experiments. We show that the mechanism of the intensity-dependent shift involves a spatial deformation of the lasing mode, which is induced by the spatial hole burning in the surrounding gain media. We develop a general analytical scheme to account for the mode deformation. Our numerical calculations demonstrate good correspondence of the lasing frequency shift with the experimental data for the simplest (spherical) geometry of the spaser.

Figure 1

The model under study. Straight lines denote the transition rates, and wavy lines denote the frequencies of the transitions.

Figure 2

Emission intensity. Main panel: the dependence of the dimensionless stimulated emission intensity $I$ on the dimensionless pumping intensity $I_p$. Inset: the tangent of the angle of the main graphic, depending on the inverse equilibrium inversion at threshold $N_{s,th}$.

Figure 3

The dependence of the lasing frequency on the pump intensity. Main panel: the dependence of the lasing frequency shift ${\delta }_L$ from the threshold value ${\omega }_{L,th}$ on the inverse pump intensity normalized at the threshold. Inset: the asymptotic value of the frequency shift at the limit of strong pump intensities as a function of the inverse value of the inverse population at the threshold $1/N_{s,th}$.