Single-Photon Excitation of Surface Plasmon Polaritons

We provide the quantum-mechanical description of the excitation of surface plasmon polaritons on metal surfaces by single photons. An attenuated-reflection setup is described for the quantum excitation process in which we find remarkably efficient photon-to-surface plasmon wave-packet transfer. Using a fully quantized treatment of the fields, we introduce the Hamiltonian for their interaction and study the quantum statistics during transfer with and without losses in the metal.

Figure 1

Single-photon excitation of SPPs using attenuated reflection. (a) A photon wave packet is injected into the system at a specific angle $\theta$, with a prism mediating an interaction between the photon and SPP modes. The minimum prism size is diffraction-limited. (b) Dispersion relations for the photon (shaded region) and SPP (curve). The prism enables mode matching. (c) Two ATR excitation geometries: (i) Otto and (ii) Kretschmann-Raether; see text for details. (d) Transfer process for the photon and SPP mode operators.

Figure 2

Photon-SPP coupling: The left (right) column corresponds to the O (KR) geometry. (a) and (b) depict the penetration factor $\mathcal{P}$. (c) and (d) show the behavior of the coupling $|\tilde{g}(\omega )|=\frac{2}{\pi }|g(\omega )|$. The optimal values of $|\tilde{g}(\omega )|$ (dashed line) are displayed in (e) and (f) along with the values of $d$ (solid line) at which they occur.

Figure 3

Damping model for propagating SPPs. (a) Bath modes interact with the SPP mode as it travels along the metal. (b) and (c) show the normalized expected mean SPP count $⟨m_e⟩/n$ at point $x$ for an $n$ photon-to-SPP wave-packet transfer via the O and KR geometries, respectively.