Theory of lasing action in plasmonic crystals

We theoretically investigate lasing action in plasmonic crystals incorporating optically pumped four-level gain media. By using detailed simulations based on a time-domain generalization of the finite-element method, we show that the excitation of dark plasmonic resonances (via the gain medium) enables accessing the optimal lasing characteristics of the considered class of systems. Moreover, our study reveals that, in general, arrays of nanowires feature lower lasing thresholds and larger slope efficiencies than those corresponding to periodic arrays of subwavelength apertures. These findings are of relevance for further engineering of active devices based on plasmonic crystals.

Figure 1

Passive spectral response of the studied array of nanowires (a) and slits (b). Solid blue, red, and green lines in both panels render, respectively, the computed absorption, transmission, and reflection obtained for normal incidence. The dashed vertical lines in each panel mark the location of the bright $\left({\lambda }_B\right)$ and dark (${\lambda }_D$ and ${\lambda }_D^{\prime }$) plasmonic modes supported by each structure. Dashed green lines in both panels display the reflection spectra for an incident angle of $1^{\circ }$. The insets show schematic views of the considered systems, including the definition of the reference system and the geometrical parameters.

Figure 2

(a) Time evolution of the ${\omega }_e$ component of the calculated $E$-field (spatially averaged over the computational domain), $\langle \left|{\mathbf{E}}_e(\mathbf{r},t)\right|\rangle$, for three different values of the emission wavelength: ${\lambda }_e=710$ nm (green line), ${\lambda }_e=725$ nm (red line), ${\lambda }_e=744$ nm (blue line). The wavelength and amplitude of the pump field are, respectively, ${\lambda }_p=680$ nm and $|{\mathbf{E}}_{\mathrm{pump}}|=0.75E_0$ ($E_0$ is the saturation electric field of the gain medium). The displayed results correspond to the nanowire array considered in Fig. 1. (b) Computed steady-state values for $\langle \left|{\mathbf{E}}_e(\mathbf{r},t)\right|\rangle$ (green triangles, left $y$ axis) and lasing onset times (blue squares, right $y$ axis) as a function of the emission wavelength ${\lambda }_e$, as obtained for the same system as in (a).

Figure 3

Computed steady-state values for $\langle |{\mathbf{E}}_e(\mathbf{r},t){|}^2\rangle$ as a function of $|{\mathbf{E}}_{\mathrm{pump}}{|}^2$, as obtained for the nanowire array (blue circles) and the slit array (red squares). The geometrical parameters of both structures are optimized so that the corresponding dark plasmonic resonances are tuned to the emission wavelength ${\lambda }_e=710$ nm of the gain medium. The inset shows the time evolution of the lasing field calculated with $|{\mathbf{E}}_{\mathrm{pump}}{|}^2=0.5E_0^2$.