Ultracompact and unidirectional metallic antennas

We investigate the angular redistribution of light radiated by a single emitter located in the vicinity of dipolar silver nanoparticles. We point out the fundamental role of the phase differences introduced by the optical path difference between the emitter and the particle and demonstrate that the polarizability of the metallic nanoparticle alone cannot predict the emission directionality. In particular, we show that collective or reflective properties of single nanoparticles can be controlled by tuning the distance of a single emitter at a $\lambda /30$ scale. These results enable us to design unidirectional and ultracompact nanoantennas composed of just two coupled nanoparticles separated by a distance achievable with biological linkers.

Figure 1

(a) Sketch of a dipolar emitter oriented along the $z$ axis and located at a distance $d$ from the surface of a silver nanosphere. The refractive index of silver is taken from Ref. 37. Silver nanospheres are embedded in a polymer of refractive index 1.5. (b) The spherical coordinates used in the analytical expressions.

Figure 2

(Color online) (a) A dipolar emitter oriented along the $z$ axis is located at a distance $d=30\text{nm}$ from a silver sphere of diameter 90 nm. The phase difference between the emitting and induced dipoles (circles, left scale) and reflection efficiency (right scale: full line: complete calculation, triangles: dipolar approximation) as a function of the emission wavelength. Emission patterns of the oscillating dipole at (b) $\lambda =510\text{nm}$ and (c) $\lambda =600\text{nm}$ in the $x\text{O}z$ plane, $\left(d=30\text{nm}\right)$ calculated by plotting the radial component of the Poynting vector normalized by the forward emitted value as a function of the polar angle.

Figure 3

(a) Phase differences normalized by $\pi$ between the dipolar emitter and the induced dipolar moment of the nanoparticle and (b) reflection ratio defined as the ratio of the power emitted toward the right and left half spaces respectively as a function of the wavelength of emission and the distance $d$ between the emitter and the metallic surface of a 90 nm silver sphere. (c) and (d) show similar results as (a) and (b), respectively, but for a 60 nm sphere.

Figure 4

(Color online) (a) The nanoantenna is composed of two identical silver nanoparticles of diameter 60 nm. The emitter is located at 10 nm from the left particle, and at 40 nm from the right particle. (b) Full line, right scale: reflection efficiency as a function of the emitted wavelength; circles and squares, left scale: dephasing of the emitting and induced dipoles supported by the 60nm sphere for 40nm (circles) and 10nm (squares) spacings. (c) Emission pattern of the oscillating dipole at $\lambda =550\text{nm}$ in the $x\text{O}z$ plane.

Figure 5

(Color online) (a) The nanoantenna is composed of silver particles of diameter 60 and 90 nm. The emitter is located at 30 nm from both particles. (b) Full line, right scale: reflection efficiency as a function of the emitted wavelength; circles and squares left scale: dephasing of the emitting and induced dipoles supported by spheres of diameter 90 nm (circles) and 60 nm (squares). (c) Emission pattern of the oscillating dipole at $\lambda =550\text{nm}$ in the $x\text{O}z$ plane. (d) Full and circles, left scale: radiative (dashed lines) and total (full line) decay rates enhancements as a function of the wavelength emission. Full $\text{line}+\text{squares}$, right scale: quantum efficiency (the intrinsic quantum efficiency is equal to 1).

Figure 6

(Color online) (a) Sketch of the ultracompact $\text{nanoantenna}+\text{super}$ emitter: the dipolar source is longitudinally coupled with two 60 nm silver particles on the $z$ axis, with an emitter-particle distance of 8 nm. The emitter-particle distances on the $x$ axis are equal to Fig. 5a at 30 nm. (b) Radiative and total decay rate enhancements as a function of the emission wavelength. (c) Quantum efficiency as a function of the emission wavelength. (d) Emission pattern of the oscillating dipole at $\lambda =610\text{nm}$ in the $x\text{O}z$ plane.