Controlling the fluorescence lifetime of a single emitter on the nanoscale using a plasmonic superlens

Coupling a single dipole emitter to a metallic nanoparticle through the optical modes of a planar superlens made of left-handed material can lead to substantial modifications of its spontaneous decay rate. We provide a quantitative study based on exact numerical simulation and show that such a scheme could allow the detection, the localization, and the control of the emitter dynamics with nanometer-scale sensitivity, as well as the determination of its transition dipole orientation.

Figure 1

(Color online) Geometry of the system. A metallic nanoparticle couples to a single emitter through a slab, in a regime where the slab behaves as a plasmonic superlens.

Figure 2

Solid line: Square modulus of the electric field (arb. units) radiated by a single electric dipole in front of a LHM slab with relative permittivity $\epsilon =-1+0.01i$ and relative permeability $\mu =-1+0.01i$. The slab lies between $z=0$ and $z=50\text{nm}$ (indicated by the gray region). The dipole is oriented along the $z$ direction and is placed at $z_s=-50\text{nm}$ (indicated by the arrow). Dashed line: same calculation in absence of the slab.

Figure 3

(Color online) Lower panel: Normalized spontaneous decay rate of a molecule interacting with a single gold nanoparticle [radius $R=10\text{nm}$, relative permittivity ${ϵ}_p=-2.335+3.61i$ at the emission wavelength $\lambda =500\text{nm}$ (Ref. 36)] through a plasmonic superlens versus the position of the nanoparticle scanning a rectangular region in a vertical plane (see the geometry in the inset). The position of the nanoparticle is defined by the distance $z_p$ between its surface and the slab surface and the lateral displacement $\rho$ with respect to the position of the molecule. The transition dipole is along the $z$ direction. Other parameters as in Fig. 2. Upper panel: same calculation without the LHM slab (molecule and nanoparticle in vacuum).

Figure 4

(Color online) Same as Fig. 3 (lower panel) for a purely metallic slab supporting surface-plasmon polaritons, with relative permittivity $\epsilon =-1+0.01i$ and relative permeability $\mu =1$.

Figure 5

Normalized decay rate of a molecule interacting with a gold nanoparticle through a plasmonic superlens versus the distance $z_p$ between the surface of the nanoparticle and the surface of the slab. The nanoparticle scans along the $z$ axis perpendicular to the slab surface (the lateral position corresponds to $\rho =0$ in Fig. 3, i.e., just above the molecule position). Geometrical and optical parameters as in Fig. 3.

Figure 6

Normalized decay rate of a molecule interacting with a gold nanoparticle through a plasmonic superlens versus the lateral displacement $\rho$ between the center of the nanoparticle and the molecule location. The nanoparticle scans along a line parallel to the slab surface, with a surface-to-surface distance $z_p=11\text{nm}$. Geometrical and optical parameters as in Fig. 3.

Figure 7

Upper panel: Decay-rate contrast defined at the ratio between the maximum value and the minimum value of the decay rate in a scan image as that in Fig. 3 versus the distance $z_s$ of the molecule to the slab surface. Other parameters as in Fig. 3. Lower panel: Lateral resolution in a decay-rate image defined as the full width at half maximum of a horizontal scan line as that in Fig. 6 versus the distance $z_s$ of the molecule to the slab surface. Other parameters as in Fig. 6.

Figure 8

(Color online) Same as Fig. 3 (lower panel) for a molecular transition dipole oriented along the $x$ direction.

Figure 9

Same as Fig. 6 for a molecular transition dipole oriented along the $x$ direction. The nanoparticle scans along a line parallel to the slab surface, with a surface-to-surface distance $z_p=17\text{nm}$.

Figure 10

Influence of the nanoparticle material. (a) Same as Fig. 5 for a nanoparticle excited at resonance with relative permittivity $\epsilon =-2+0.3i$ at the emission wavelength $\lambda =500\text{nm}$ of the molecule (solid line), for a gold nanoparticle (dotted line) and a tungsten nanoparticle (dashed line). The radius of the nanoparticle is $10\text{nm}$ in each case. (b) Decay rate of a molecule interacting with a nanoparticle through a LHM slab versus the lateral displacement $\rho$ between the center of the nanoparticle and the molecule location taken at the surface-to-surface particle distance of maximum contrast, $z_p=16\text{nm}$ (resonant particle), $z_p=12\text{nm}$ (gold particle), and $z_p=11\text{nm}$ (tungsten particle), i.e., maxima in panel (a). The remaining parameters as in Fig. 6. The same materials as in the upper figure are considered. The three curves are normalized to their maximum value.