Plasmonic waveguides can compress light into regions significantly smaller than the diffraction limit and have emerged as a promising candidate for achieving nanoscale field confinement. To date, various types of plasmonic waveguides have been proposed and widely used for the development of integrated optical devices, including nanolasers, modulators, splitters, and resonators. However, the strong optical-field-confinement ability of noble metal-based plasmonic devices is typically accompanied by their inherent Ohmic loss, which severely hinders their applications at the nanoscale. Recent studies show that alkali metal sodium presents lower loss than metal silver, and that the free-electron relaxation time of sodium is approximately double that of silver. The utilization of alkali metals can potentially decrease the optical loss of plasmons significantly, thus facilitating investigations into light-matter interactions at the nanoscale. In this study, we propose a hybrid surface plasmon waveguide structure comprising triangular-shaped sodium and silicon nanowires, which effectively confines light fields in the low-refractive-index spacer and at long transmission distances (>40 μm). In particular, owing to its low modal loss and excellent optical-field confinement ability, the proposed hybrid plasmon waveguide demonstrates an extremely low gain threshold and a large Purcell factor. Additionally, the effect of lateral-position deviation on modal and lasing properties is investigated, and the results show robustness against position deviations. Hence, the proposed structure is feasible as building blocks for subwavelength photonic devices, such as nanolasers and modulators.

The proposed hybrid plasmonic waveguide structure (Fig. 1) comprises a triangular-shaped sodium nanowire separated from a triangular-shaped silicon nanowire by a gap distance (g). The waveguide and lasing performances were investigated using the finite-element method (FEM) and characterized using the effective mode index [n_eff=Re(N_eff)], propagation length (L_P), normalized mode area (A_N), figure-of-merit (F_M), confinement factor (Γ), gain threshold (G_th), and Purcell factor (F_P). The eigenvalue solver was used to obtain the complex effective mode index (N_eff) and effective mode area (A_eff). The dielectric constants of silicon and silica are 12.08 and 2.09, respectively. For the metal Na, a Drude-Lorentz model was employed to calculate the dielectric permittivity, and ε_Na=-44.8325+0.6452i when the wavelength λ is1550 nm. The calculation domain measures 6λ×6λ, with a minimum mesh size of 1 nm, and a perfectly matched layer (PML) was applied around the geometry to avoid the influence of reflection. Additionally, convergence analysis was performed to ensure that the numerical boundaries and meshes do not interfere with the solutions.

The proposed waveguide exhibits strong confined modal fields with linewidths of electric-field distributions determined primarily by g. The modal-transmission properties depend significantly on g and W. When g decreases, the modal area decreases and the F_M increases (Fig. 3). Moreover, as the width W increases, the gain threshold G_th decreases until the lowest threshold of approximately 0.141 μm^-1 (Fig. 4). The Purcell factor remains consistently above 35.9. The apex angles of the sodium (α) and silicon (θ) nanowires significantly affect the modal properties. When α=π/6, the fundamental mode exhibits the strongest field-confinement ability, thus resulting in a minimum normalized mode area A_N of 6.782×10^-5. Additionally, the F_M remains consistently above 3131. Compared with the cases for α=π/6 and π/2, the mode loss is lower when α=π/3 (L_P reaches 44 μm, Fig. 5). In general, the gain threshold is less than 0.2 μm^-1 and reaches the lowest threshold of approximately 0.118 μm^-1 (Fig. 6) when α=π/3 and θ=π/6, which is significantly lower than the gain thresholds of conventional silver-based plasmonic waveguides, as shown in Table 1. Moreover, the Purcell factor ranges from 220 to 964, which indicates significant improvement. Finally, we investigate the effects of lateral manufacturing deviation on the waveguiding and lasing performances. The result shows that L_P increases by 7% when the position deviation ranges from 0 nm to 10 nm (Fig. 7). Simultaneously, G_th increases from 0.118 μm^-1 to 0.129 μm^-1, which is an increment of 9% (Fig. 8). These results indicate that the proposed device is robust against position deviations.

We proposed and investigated a hybrid plasmonic waveguide structure comprising triangular-shaped sodium and silicon nanowires using the FEM at a wavelength of 1550 nm. The mode characteristics depend significantly on the shapes of the sodium and silicon nanowires, and the linewidths of electric-field distributions are determined primarily by g. When α=π/6 and θ=π/2, we achieved a normalized mode area of merely 6.782×10^-5 and a high F_M exceeding 3131. Further investigations show that the low loss in the Na plasmon mode is key in reducing the gain threshold. Owing to the low modal loss when α=π/3 and the excellent optical-field-confinement ability, the gain threshold can reach a minimum value of 0.118 μm^-1 when θ=π/6. Additionally, we obtained Purcell factors exceeding 220. The lasing performances are relatively robust even under lateral-position deviations. This study facilitates future applications of plasmonic waveguides in nanolasers and may promote the application of alkali metal plasmons in nanophotonics.