Fig. 1. Schematic of double-concave cavity of metallic semiconductor nanolaser: (a) The structure; (b) top view of the double-concave cavity.双凹型金属半导体纳米激光器谐振腔示意图　(a)结构示意图; (b)俯视图

Fig. 2. Q values of the capsule-shaped cavities (L = 700 nm, W = 520 nm) as functions of the radius of curvature R. CSC型谐振腔(L = 700 nm, W = 520 nm) Q值与曲率半径R的关系

Fig. 3. Quality factors Q, radiation quality factors Q_rad and dissipation quality factors Q_diss of three double-concave cavities with curved sidewalls (L = 700 nm, W = 520 nm, L/R = 1.43) as functions of the W₀/W: (a) Q; (b) Q_rad; (c) Q_diss. 三种曲线侧壁的双凹型谐振腔(L = 700 nm, W = 520 nm, L/R = 1.43)的品质因子Q、辐射品质因子Q_rad和耗散品质因子Q_diss与W₀/W的关系　(a) Q; (b) Q_rad; (c) Q_diss

Fig. 4. Normalized electric field intensity distribution |E|² of the resonant mode (TE mode) in the xy-, yz- and xz-planes crossing the cavity center: (a)–(c) The capsule-shaped cavity; (d)–(f) the linear-function-shaped cavity; (g)–(i) the parabola-shaped cavity; (j)–(l) the cosine-shaped cavity. All the geometric parameters of the cavities are listed in Table 2 in detail. 不同谐振腔结构的谐振模式(TE模式)的归一化电场强度|E|²在穿过腔中心的xy、yz、xz平面的分布图　(a)— (c)为胶囊型腔; (d)— (f)为一次函数型腔; (g)— (i)为抛物线型腔; (j)—(l)为余弦函数型腔. 所有腔的几何参数详见表2

Fig. 5. The confinement factor Γ, threshold gain g_th and threshold current I_th of the metallic semiconductor nanolasers with three double-concave cavities with curved sidewalls (L = 700 nm, W = 520 nm, L/R = 1.43) as functions of the W₀/W: (a) Γ; (b) g_th; (c) I_th. 三种曲线侧壁双凹型谐振腔(L = 700 nm, W = 520 nm, L/R = 1.43)的金属半导体纳米激光器的限制因子Γ、阈值增益g_th和阈值电流I_th与W₀/W的关系　(a) Γ; (b) g_th; (c) I_th

Table 1. Curve equations of the sidewalls of the double-concave cavities

Table 2. Geometric parameters and simulation results of the metallic semiconductor nanolasers with four types of cavities.