Optical Patch Antennas for Single Photon Emission Using Surface Plasmon Resonances

Single photon sources can greatly benefit from specially designed structures that modify the properties of the photon emitter. Dielectric cavities are often discussed, but they require a compromise between the spectral width and Purcell factor. In this Letter, we introduce plasmonic cavities as promising alternatives. We first study how the emitter couples with the modes of such structures. We then show how a patch antenna configuration simultaneously presents a large Purcell factor, collection efficiency, and spectral width.

Figure 1

(a) Schematical side view and coordinate axis for the flat disk, where the angles $\theta$, $\varphi$ define the emission direction. The structure is rotationally symmetric with respect to the $z$ axis, as stressed by the three-dimensional image in (b). (c) Radiative ${\Gamma }_R/{\Gamma }_0$ and (d) nonradiative ${\Gamma }_{\mathrm{NR}}/{\Gamma }_0$ change on the emission rate for a disk with $R=600\mathrm{nm}$ radius, $t=20\mathrm{nm}$ thickness and quantum emitter oriented vertically along the $z$ axis and situated over the center of the structure, at $d=20\mathrm{nm}$ from the top surface. The dashed red lines correspond to the excitation frequency at which $R=m{\lambda }_{\mathrm{sp}}^{\mathrm{sr}}/2$; $m$ takes the integer values 1 to 5, with 1 corresponding to the longer wavelength. The solid blue vertical line at ${\lambda }_0=358.3\mathrm{nm}$ marks the frequency at which $\mathrm{Re}[{ϵ}_{\mathrm{Ag}}]=-{ϵ}_g$, the value of the resonance for a vertical quantum emitter in front of a silver half-space. (e1),(f1) show the directivity $D(\theta )$ for same conditions at the maxima labeled $e$ (${\lambda }_0=1763\mathrm{nm}$) and $f$ (${\lambda }_0=759.9\mathrm{nm}$) in (c). (e2),(f2) show the amplitude of the electric field module in the $xz$ plane, in logarithmic scale and arbitrary units, in the proximity of the disks for the same wavelengths.

Figure 2

(a) Purcell factor ${\Gamma }_T/{\Gamma }_0$ for the $R=600\mathrm{nm}$ flat disk and for an infinite film of same thickness $t=20\mathrm{nm}$ and distance $d=20\mathrm{nm}$ to the emitter. (b) ${\xi }_{zz}(K)$, function that describe the LDOS in $K$ space as ${\rho }_z^e={\rho }_z^{e0}[1+{\int }_0^{\infty }{\xi }_{zz}(K)dK]$, for a 20 nm thick infinite film, ${\lambda }_0=750\mathrm{nm}$ and $d=20\mathrm{nm}$. The narrow and broad peaks correspond to the long and short range plasmons, respectively.

Figure 3

(a),(d) Purcell factor ${\Gamma }_T/{\Gamma }_0$, (b),(e) radiative yield $\eta ={\Gamma }_R/{\Gamma }_T$ in the absence of intrinsic losses and (c),(f) directivity $D(\theta )$ for: (a)–(c) a 600 nm radius and 20 nm thick silver disk with a 20 nm high protuberance at the symmetry axis, with a vertically oriented quantum emitter at 10 nm distance over the top of the protuberance; (d)–(f) The solid black line corresponds to a vertically oriented quantum emitter at 20 nm of the surface of two rotationally symmetric silver disks, one of radius $R=600\mathrm{nm}$ and thickness $t=20\mathrm{nm}$ and the second of $R=1000\mathrm{nm}$ and $t=100\mathrm{nm}$. The center of the two disks and the dipole are aligned along $z$. The dashed blue line in (d) corresponds to a similar scenario, but with infinite films of the same thickness instead of the disks. (c) corresponds to the main peak in (a), ${\lambda }_0=603.4\mathrm{nm}$, and (f) to the second larger peak in (d), ${\lambda }_0=1381\mathrm{nm}$. All structures are included in glass ${ϵ}_g=2.25$ and the disks have rounded edges.