Figure 1

(Color online) (a) An emitter coupled to a nanowire is optically excited and decays with high probability into the plasmon modes of the nanowire. A single-photon source is created by evanescently coupling the nanowire to a nearby dielectric waveguide over a length $L_{\mathit{ex}}$. The single-photon source can potentially be unidirectional, e.g., by capping one end of the waveguide with a reflective surface. (b) An internal-level scheme that allows for shaping of the outgoing single-photon pulses. An emitter that starts in state $\mid s⟩$ is coupled to excited state $\mid e⟩$ via a time-dependent external control field $\Omega \left(t\right)$. We assume that the excited state $\mid e⟩$ is coupled to state $\mid g⟩$ via the plasmon modes, causing $\mid e⟩$ to decay into $\mid g⟩$ with high probability, while simultaneously generating a single photon in the plasmon modes. The shape of the photon wave packet is determined by $\Omega \left(t\right)$. (c) A similar scheme for single-photon generation using an emitter coupled to a nanotip instead of a nanowire. Note that this scheme is naturally unidirectional, as the generated plasmons propagate in a single direction.Reuse & Permissions

Figure 2

(Color online) Allowed plasmon modes $k_{\Vert }$ as a function of $R$ for a silver nanowire embedded in a surrounding dielectric ${ϵ}_1=2$, for frequency corresponding to a vacuum wavelength ${\lambda }_0=1\mu \mathrm{m}$ and room temperature. The fundamental $(m=0)$ mode, in black, exhibits a $k_{\Vert }\propto 1∕R$ dependence, while all other modes are effectively cut off as $R\to 0$. In order of increasing cutoff radius, the other modes displayed correspond to $\mid m\mid =1,2$, and 3, respectively. Inset: the propagative losses for the fundamental mode, characterized by the ratio $\mathrm{Re}{k}_{\Vert }∕\mathrm{Im}{k}_{\Vert }$, for the same parameters.Reuse & Permissions

Figure 3

(Color online) (a) A dipole emitter positioned a distance $d$ from the center of a nanowire. For the calculations presented, the orientation of the dipole moment is assumed to be along $\widehat{\rho }$. (b) A dipole emitter positioned near the end of a nanotip. In terms of parabolic coordinates, the physical distance $d$ between the end of the tip and the emitter is given by $d=({v^{\prime }}^2-v_0^2)∕2$, while the curvature parameter $w=2v_0^2$. For the nanotip, only a dipole oriented parallel to $\widehat{z}$ couples to the fundamental plasmon mode.Reuse & Permissions

Figure 4

(Color online) (a) Solid line: Maximum Purcell factor $P={\Gamma }_{\mathrm{pl}}∕{\Gamma }^{\prime }$ for a nanowire, plotted as a function of $R$ and optimized over the emitter position. Here, $P$ is calculated in the quasistatic approximation. Dashed line: Same quantity, obtained by exact electrodynamic calculations. Dotted line: Effective Purcell factor $\tilde{P}\left(R\right)={\tilde{\Gamma }}_{\mathrm{pl}}\left(R\right)∕\tilde{\Gamma }\left(R\right)$ for a nanotip of final radius $R$, optimized over nanotip shape and emitter position. Solid points: Same quantity, calculated using numerical simulations (boundary element method). (b) Contour plot of ${\log }_{10}P$ for a nanowire, as functions of $R$ and $d∕R$. (c) Contour plot of ${\log }_{10}P$ for a nanotip, as functions of $w$ and $d∕w$.Reuse & Permissions

Figure 5

(Color online) Numerically calculated fields due to a dipole emitter near a conducting nanotip, obtained by the boundary element method. (a) The energy flux $\mid \mathrm{Re}(\mathbf{E}\times {\mathbf{H}}^{*})\mid$, in arbitrary units. The position of the emitter is denoted by the blue circles, while the boundary of the nanotip is given by the dotted lines. The plots shown are for a final nanotip radius of $k_{0}R=0.3$, curvature parameter $k_{0}w=0.022$, and emitter positions $k_{0}d=0.002$, 0.2, and 0.7. It can be seen that both the total spontaneous emission rate ${\Gamma }_{\text{total}}$ and the emission rate into plasmons increase as the emitter is brought closer to the nanotip. (b) The quantity $\mid \mathrm{Re}(\mathbf{E}\times {\mathbf{H}}^{*})\mid ∕{\Gamma }_{\text{total}}$, for the same parameters. This quantity is proportional to the energy flux normalized by the total power output of the emitter. The $k_{0}d=0.002$ plot is mostly dark, indicating that most of the decay is into nonradiative channels. The $k_{0}d=0.2$ case is characterized by bright spots along the entire edge of the nanotip, which indicates efficient plasmon excitation. The $k_{0}d=0.7$ case exhibits the typical lobe pattern associated with radiative decay of a dipole.Reuse & Permissions

Figure 6

Wave vector $k_{\Vert }$ of the fundamental guided modes of a cylindrical dielectric waveguide with core permittivity ${ϵ}_c=13$ and surrounding permittivity ${ϵ}_1=2$, plotted as a function of core radius $R_g$.Reuse & Permissions

Figure 7

(a) Optimized efficiencies of single-photon generation vs $R$. We have assumed that coupling to waveguide modes other than the fundamental mode is negligible, i.e., the waveguide is effectively in the single-mode regime. Solid (dashed) line: theoretical efficiency using a nanowire, using spontaneous emission rates obtained by quasistatic (fully electrodynamic) calculations. Dotted line: theoretical efficiency using a nanotip. Solid points: nanotip efficiency based on boundary element method simulations, combined with coupled-mode equations. (b) Optimal coupling length $L_{\mathit{ex}}$ for a nanotip as a function of $R$. Here, $L_{\mathit{ex}}$ is given in units of the plasmon wavelength ${\lambda }_{\mathrm{pl}}$ at that particular $R$.Reuse & Permissions

Figure 8

(Color online) The plasmon dissipation rate due to radiative scattering off of surface roughness, ${\Gamma }_{\mathrm{rad},\text{rough}}∕s^2\omega$, as functions of wire radius $R$ and correlation length $a∕R$. The numbers are calculated for a silver nanowire at ${\lambda }_0=1\mu \mathrm{m}$ and ${ϵ}_1=2$.Reuse & Permissions