Transverse Kerker Effect for Dipole Sources

Transverse Kerker effect is known by the directional scattering of an electromagnetic plane wave perpendicular to the propagation direction with nearly suppression of both forward and backward scattering. Compared with plane waves, localized electromagnetic emitters are more general sources in modern nanophotonics. As a typical example, manipulating the emission direction of a quantum dot is of vital importance for the investigation of on-chip quantum optics and quantum information processing. Herein, we introduce the concept of transverse Kerker effect for dipole sources utilizing a subwavelength dielectric antenna, where the radiative power of magnetic, electric, and more general chiral dipole emitters can be dominantly redirected along their dipole moments with nearly suppression of radiation perpendicular to the dipole moments. This type of transverse Kerker effect is also associated with Purcell enhancement mediated by electromagnetic multipolar resonances induced in the dielectric antenna. Analytical conditions of transverse Kerker effect are derived for the magnetic, electric, and chiral dipole emitters. We further provide microwave experiment validation for the magnetic dipole emitter. Our results provide new physical mechanisms to manipulate the emission properties of localized electromagnetic source which might facilitate the on-chip quantum optics and beyond.

Figure 1

(a) Schematic of the far-field radiation power for a magnetic dipole emitter (red arrow) in a homogeneous medium. (b) By placing the dipole emitter close to a subwavelength dielectric antenna shown in (c), the far-field radiation power can be redirected along the direction of dipole moment while the radiation along the direction perpendicular to the dipole moment is substantially suppressed. The diameter $D$ and height $h$ of the cylinder are outlined in (c) and the relative permittivity of the cylinder is ${ϵ}_r$. The dipole emitter can be magnetic, electric, or chiral dipole.

Figure 2

(a) Normalized time-averaged radiated power as functions of the size parameter $kD/2$ along four specified directions ($\theta =0°$, 180° and $\theta =90°$, $\varphi =0°$, 90°) when a MD emitter (along $x$ axis) is placed above the surface of the cylinder. (b) Two-dimensional far-field scattering patterns at the size parameter of $kD/2=1.49$. Analytical results and numerical results are outlined by solid lines and symbol lines, respectively (w/o means without). Three-dimensional far-field radiation patterns without and with the resonator are presented in (c) and (d), respectively.

Figure 3

(a) Normalized time-averaged radiated power as functions of the size parameter $k{D}_x/2$ along four specified directions ($\theta =0°$, 180° and $\theta =90°$, $\varphi =0°$, 90°) when an ED emitter is placed close to a dielectric elliptical cylinder. The major axis, minor axis, height, and relative permittivity of the elliptical cylinder are $D_x=1.04{\lambda }_0$, $D_y={\lambda }_0/5.3$, $h={\lambda }_0/3.95$, and ${ϵ}_r=9.6$, respectively, as shown in the inset. The ED emitter (${\overrightarrow{p}}_x$) locates above the surface of the elliptical cylinder ($L={\lambda }_0/107$). (b) Two-dimensional far-field scattering patterns at the size parameter of $k{D}_x/2=3.25$. Analytical results and numerical results are outlined by solid lines and symbols, respectively (w/o means without). Three-dimensional far-field radiation pattern without and with the resonator are presented in (c) and (d), respectively.

Figure 4

(a) Experimental setup to measure the far-field radiative patterns. (b) Radiative patterns at the size parameter of $kD/2=1.51$, where the black solid line corresponds to the numerical result considering the material loss (loss tangent is $4\times {10}^{-4}$) on $xz$ plane and red stars indicate the experimental results.

Figure 5

(a) Normalized time-averaged radiated power as functions of the size parameter $k{D}_x/2$ along four specified directions ($\theta =0°$, 180° and $\theta =90°$, $\varphi =0°$, 90°) when a chiral dipole emitter [$\overrightarrow{m}=(ic,0,0)$, $\overrightarrow{p}=(1,0,0)$] is placed above the surface of the elliptical cylinder ($L={\lambda }_0/107$). (b) Two-dimensional far-field scattering patterns at the size parameter of $k{D}_x/2=2.95$. Analytical and numerical results are outlined by solid lines and symbols, respectively (w/o means without). Three-dimensional far-field radiation patterns without and with the resonator are presented in (c) and (d), respectively. The dielectric elliptic cylinder with a height $h={\lambda }_0/3.95$, major axis $D_x={\lambda }_0/1.07$, minor axis $D_y={\lambda }_0/4.57$, and relative permittivity ${ϵ}_r=9.6$ is used.