Novel Lasers Based on Resonant Dark States

The route to miniaturization of laser systems has so far led to the utilization of diverse materials and techniques for reaching the desired laser oscillation at small scales. Unfortunately, at some point all approaches encounter a trade-off between the system dimensions and the $Q$ factor, especially when going subwavelength, mostly because the radiation damping is inherent to the oscillating mode and can thus not be controlled separately. Here, we propose a metamaterial laser system that overcomes this trade-off and offers radiation damping tunability, along with many other features, such as directionality, subwavelength integration, and simple layer-by-layer fabrication.

Figure 1

The dark-mode laser principle of operation. (a) Perspective view of the unit cell, illustrating the spatial distribution of the dark mode, with which we work throughout this study [its operation point is marked in (b) with a red circle]. (b) Dispersion relation of the unpumped uniform dielectric slab of thickness $d$ (red line) and quantized dispersion of the composite dielectric-metal system (blue dots). Power spectrum of the $E_z$ field for several pump rates, when measured (c) inside and (d) away from the slab, without any scatterer present.

Figure 2

Coupling of stored power to radiation. (a) Output power spectrum of the $E_z$ field with scatterer placed at $\delta x=150\mathrm{nm}$ ($\delta x/a\cong 0.16$) (b) Snapshot during lasing. The unit cell position is marked with the lines framing the dark mode and its orientation is as shown in inset of (a); notice that most of the emitted power is directed to the side opposite to which the scatterer is located (calculated to be 90% of the total emitted power).

Figure 3

Scanning the position of the scatterer (normalized with the unit cell width $a$). (a) Top view of unit cell; (b) $Q$ factor; (c) radiated and dissipated power over supplied power; and (d) lasing threshold. The marked displacement $\delta x=150\mathrm{nm}$ ($\delta x/a\cong 0.16$) corresponds to the configuration for which lasing simulations are shown in Fig. 2, striking a balance between field enhancement ($Q$ factor), outcoupling, and achievable directionality. Notice that at $\delta x/a=0.5$ the $Q$ factor is the maximum possible for this configuration ($Q$ factor of the dark mode) and is limited only by the losses due to the metal. At this position the lasing threshold is the lowest possible and all lasing power, which cannot be radiated, is channeled to the metallic scatterers.

Figure 4

Directionality explained via the equivalent current sheet model. The dark mode induces polarization currents $I_1$, $I_2$ on the two scatterers, which are effectively a weighted mixture of an electric moment and a magnetic moment that radiate individually. These moments are equivalently described by an infinite electromagnetic current sheet supporting an electric current ${\mathbf{j}}_{\mathbf{e}}$ and a magnetic current ${\mathbf{j}}_{\mathbf{m}}$.

Figure 5

Directionality vs scatterer displacement (normalized with the unit cell width $a$) in the double-scatterer configuration. (a) Directionality towards $y<0$ (0–50 in scale) and $y>0$ (50–100 in scale) as each scatterer is shifted along the unit cell. (b) Vertical cross section of Fig. 5 at $\delta x_1/a\cong 0.56$. (c) Electric (solid red line) and magnetic (dotted black line) moment (same scale) vs frequency, for three characteristic cases, also noted on panels (a) and (b) with the letters $A$, $B$, and $C$: $A$, for $\delta x_2/a\cong 0.56$, purely electric moment leading to a 50%–50% power split; $B$, for $\delta x_2/a\cong 0.44$, purely magnetic moment leading to a 50%–50% power split; $C$, for $\delta x_2/a\cong 0.16$, equal electric and magnetic moment leading to a 90%–10% power split. (d) Perspective view of the double-scatterer configuration.