Huygens' dipole for polarization-controlled nanoscale light routing

Structured illumination allows for satisfying the first Kerker condition of in-phase perpendicular electric and magnetic dipole moments in any isotropic scatterer that supports electric and magnetic dipole resonances. The induced Huygens' dipole may be utilized for unidirectional coupling to waveguide modes that propagate transverse to the excitation beam. We study two configurations of a Huygens' dipole, longitudinal electric and transverse magnetic dipole moments or vice versa. We experimentally show that only the radially polarized emission of the first and azimuthally polarized emission of the second configuration are directional in the far field. This polarization selectivity implies that directional excitation of either transverse magnetic (TM) or transverse electric (TE) waveguide modes is possible. Applying this concept to a single dielectric nanoantenna excited with structured light, we are able to experimentally achieve scattering directivities of around 23 and 18 dB in TM and TE modes, respectively. This strong directivity paves the way for tunable polarization-controlled nanoscale light routing and applications in optical metrology, localization microscopy, and on-chip optical devices.

Figure 1

Radiation patterns of Huygens' dipoles. (a) An $x$-polarized plane wave propagating along the $z$ axis excites a Huygens' dipole in a dipolar scatterer that has equal Mie coefficients $a_1=b_1$, resulting in a directivity along the $z$ axis. (b) Structured illumination provides a complex three-dimensional (3D) field distribution, allowing for an (position-dependent) excitation of a rotated Huygens' dipole also for case of $a_1\ne b_1$. The plotted Huygens' dipole shows directivity along the $x$ axis.

Figure 2

(a) Absolute values of the first- and second-order Mie coefficients of a core-shell nanoparticle with Si core of radius $r_{\text{Si}}=78$ nm and a ${\mathrm{SiO}}_2$ shell of thickness 6 nm in free space. (b) The corresponding phase difference between the first-order Mie coefficients. The dotted vertical black lines show the wavelengths ${\lambda }_i=620\mathrm{nm}$ and ${\lambda }_{ii}=520\mathrm{nm}$ where the phase difference is approximately $\pi /2$. The solid vertical black lines show the experimentally found wavelengths ${\lambda }_i^{\text{expt}}=620\mathrm{nm}$ and ${\lambda }_{ii}^{\text{expt}}=550\mathrm{nm}$ that give maximum transverse scattering asymmetry into TM- and TE-polarized modes, respectively. (c) Experimental setup. An incident radially or azimuthally polarized beam is focused by a high numerical aperture (NA) objective onto the nanoparticle, positioned on a glass substrate, which is actuated by a 3D piezostage. An immersion-type objective collects the transmitted and scattered light. The back focal plane of the collecting objective is imaged onto the polarization conversion-projection unit and imaged again onto a camera. (d) Schematic presentation of the polarization conversion-projection unit. The $\mathrm{\Theta }$ cell converts the impinging TM (radial) and TE (azimuthal) polarizations into linearly polarized Cartesian components ($x$ and $y$), respectively, introducing a $\pi$-phase singularity along $x=0$. The intensity distribution in the TM and TE modes can be measured by setting the transmission axis of the subsequent linear polarizer (LP) to $x$ and $y$, respectively, as shown for $x$.

Figure 3

(a) and (c) Polarization-resolved measurements of the far-field scattered light. The dielectric nanoantenna is positioned in the focal plane of focused radially and azimuthally polarized beams at $\mathbf{r}=(-150\mathrm{nm},0,0)$ and $\mathbf{r}=(75\mathrm{nm},0,0)$, respectively. The plots show the intensity distribution in TM- (radial) and TE- (azimuthal) polarized modes in the back focal plane (BFP) of the collecting objective. (b) and (d) Corresponding theoretical (fitted) BFP distributions calculated with Eqs. (5) and (6). The dipole moments used to plot (b) and (d) were obtained by a nonlinear least-squares fitting of (a) and (c) with Eqs. (5) and (6). The right column shows the corresponding radiation diagrams—the intensity distribution in the BFP as a function of the polar angle $\phi ={tan}^{-1}(k_y/k_x)$.