Effect of surface-plasmon polaritons on spontaneous emission and intermolecular energy-transfer rates in multilayered geometries

We use a Green's tensor method to investigate the spontaneous emission rate of a molecule and the energy-transfer rate between molecules placed in two types of layered geometries: a slab geometry and a planar waveguide. We focus especially on the role played by surface-plasmon polaritons in modifying the spontaneous emission and energy-transfer rates as compared to free space. In the presence of more than one interface, the surface-plasmon polariton modes split into several branches, and each branch can contribute significantly to modifying the electromagnetic properties of atoms and molecules. Enhancements of several orders of magnitude both in the spontaneous emission rate of a molecule and the energy-transfer rate between molecules are obtained and, by tuning the parameters of the geometry, one has the ability to control the range and magnitude of these enhancements. For the energy-transfer rate interference effects between contributions of different plasmon-polariton branches are observed as oscillations in the distance dependence of this rate.

Figure 1

Dispersion relation of SPPs at the interface between a dielectric with ${\epsilon }_d=4$ and a lossless Drude metal. $k_P$ is the wave number corresponding to the plasma frequency.

Figure 2

Geometry of a Drude metal slab of thickness $d$ embedded in a dielectric material.

Figure 3

Dispersion relations for SPPs in a slab geometry.

Figure 4

Relative decay rates of a molecule above a Drude slab with $\gamma =2.288\times {10}^{-3}{\omega }_P$. The thickness of the slab is $d=0.01{\lambda }_P$ for the three panels on the top row and $d=0.20{\lambda }_P$ for the three panels on the bottom row. This corresponds, in a Ag/SiO${}_2$ environment, to $d=1.36$ nm and $d=27.02$ nm, respectively. (a) and (d) The decay rates as a function of both frequency and distance to the upper surface of the slab; (b) and (e) the different contributions to the relative decay rate as a function of distance to the slab at a frequency $\omega =0.40{\omega }_P$; (c) and (f) the frequency dependence of the relative decay rate for several molecule-slab separations.

Figure 5

Two configurations of molecules used in calculating the ET rate in the presence of the Drude metallic slab.

Figure 6

(a) Relative ET rate between two molecules in the configuration from Fig. 5a, with the ET rate plotted as a function of the distance $z$ between a molecule and its corresponding surface of the slab; (b) relative ET rate for the configuration from Fig. 5b, with the ET rate plotted as a function of the distance $x$ between the molecules, when the molecules are at a distance $z=0.01{\lambda }_P$ from the upper surface of the slab; (c) $\tilde{\eta }$ ratio for the configuration from Fig. 5a; (d) $\tilde{\eta }$ ratio for the configuration from Fig. 5b. The frequency is $\omega =0.40{\omega }_P$, the linewidth is $\gamma =2.288\times {10}^{-3}{\omega }_P$.

Figure 7

Geometry of the waveguide.

Figure 8

Dispersion relations for SPPs in a waveguide geometry with $\gamma =0$.

Figure 9

Relative decay rates of molecules above a planar waveguide, as a function of the distance to the surface of the waveguide, for $\gamma =0$. The frequency is $\omega =0.40{\omega }_P$, where no IASPP can be excited (see Fig. 8).

Figure 10

Relative ET rates between molecules in a planar waveguide geometry, as a function of their mutual separation along the $x$ axis, for $\gamma =2.288\times {10}^{-3}$. In the inset, which is the same for all four subfigures, the black arrow represents the donor molecule, fixed at $z_s$ and $x_s=0$, the gray arrow represents the acceptor molecule, fixed at $z$ and with varying $x$ position: (a) $d_1=0.01{\lambda }_P$, $d_2=0.01{\lambda }_P$; (b) $d_1=0.01{\lambda }_P$, $d_2=0.20{\lambda }_P$; (c) $d_1=0.20{\lambda }_P$, $d_2=0.01{\lambda }_P$; (d) $d_1=0.20{\lambda }_P$, $d_2=0.20{\lambda }_P$.