Control and dynamic competition of bright and dark lasing states in active nanoplasmonic metamaterials

Active nanoplasmonic metamaterials support bright and dark modes that compete for gain. Using a Maxwell-Bloch approach incorporating Langevin noise we study the lasing dynamics in an active nanofishnet structure. We report that lasing of the bright negative-index mode is possible if the higher-$Q$ dark mode is discriminated by gain, spatially or spectrally. The nonlinear competition during the transient phase is followed by steady-state emission where bright and dark modes can coexist. We analyze the influence of pump intensity and polarization and explore methods for mode control.

Figure 1

Electric field enhancements and charge distributions on the metal films inside the double fishnet unit cell for the bright negative-index mode (left) and the dark quadrupole mode (right). The direction of the electric field in the $x$-$z$ plane is indicated by the white arrows.

Figure 2

(a) Far-field intensity in transmission and (b) energy and average inversion (red solid line, right axis) inside the nanofishnet metamaterial over time. The signals, time averaged over $0.4\text{ps}$ (black), are decomposed into the pump mode at $680\text{nm}$ (green dashed line), the bright mode at $717.25\text{nm}$ (white solid line), and the dark mode at $731.8\text{nm}$ (yellow dashed-dotted line). (c) Inversion profiles in the $x$-$y$ plane centered between the metal films at the times indicated in (b).

Figure 3

(a) Dependence of the average energy densities of the bright (red dots) and dark mode (black squares) on the pump mode average energy density. The inset illustrates how the energy densities follow the rampdown of the pump starting at the pump intensity marked by the arrow. (b) Mode intensity (left), inversion (middle), and local gain [right, see Eq. (1) in the $x$-$y$ plane centered between the metal films.

Figure 4

Dependence of steady-state emission into dark and bright modes on emission wavelength and polarization. (a) The emission line (here displayed for ${\lambda }_e=718\text{nm}$) and dark and bright mode lines are shown schematically indicating the maximum emission at ${\lambda }_e$ and how it is shifted for control. (b) Average mode energy densities during steady state in dependence of the emission wavelength of the dye for $E_x$ (I) and $E_y$ polarization (II) of the pump field with intensity $10.75\text{MW}{\text{cm}}^{-2}$. The bright mode is given by the red line and dots, the dark mode by the black line and squares. (c) Inversion profiles before the onset of relaxation oscillations for $E_x$ (I) and $E_y$ polarization (II) highlighted by the black arrows.