1. Introduction

Owing to their unique ability to enhance and direct spontaneous emission from nanoscale sources, optical nanoantennas remain an important research topic in nanophotonics [1–5]. Apart from the well studied concept of plasmonic nanoantennas, dielectric nanoantennas have started to gain increasing attention during the last few years [6–9] due to their low-losses and associated high quantum yield of coupled emitter systems and multipolar Mie-resonant response. Researchers have considered primarily two alternative design concepts for directional nanoantennas. The first concept assumes engineering of a single resonant nanoparticle [10–15]. In this case, both the emission rate enhancement and the directionality rely on the excitation of resonant modes in the nanoparticle. For the specific case of low-loss dielectric nanoantennas, it was first demonstrated theoretically [10] and then experimentally [16] that a directional emission pattern can be achieved by tailoring the strengths and phases of different Mie-type modes excited in the single nanoparticle. The second common approach to design a nanoantenna is to arrange several nanoparticles in a way that the light scattered by the different nanoparticles will interfere constructively along a desired direction and destructively along all other directions. This method was employed to demonstrate directional scattering and emission in various nanoantenna architectures, ranging from rather simple systems consisting of two nanoparticles [17–20] to more complex Yagi-Uda type nanoantennas [6,21–23], periodic nanoparticle arrangements [24–28] and Bullseye antennas [29–32].

Optical metasurfaces, which are composed of planar arrangements of designed nanoresonators, allow for combining both of these nanoantenna design concepts. Indeed, plasmonic as well as dielectric metasurfaces were already demonstrated to provide many degrees of freedom for manipulating spontaneous emission from nanoscale emitters integrated in the metasurface architecture [5,33].

For example, Langguth et al. [26] reported a plasmonic metasurface imparting an asymmetric directional pattern on the spontaneous emission. While the plasmonic lattice enables directional outcoupling of light along a set of preferential directions, the predominance along a specific predefined (non-normal) direction can be introduced by tailoring the scattering properties of the individual elements. An intuitive way to describe the behavior of such systems, in the assumption of noninteracting elements, relies on consideration of the separate contributions from the arrangement ("structure factor" or "array factor" [34]) and the "form factor" that describes the properties of each individual element [5]. This comprehensive approach of combining both contributions provides additional degrees of freedom for optimization of the nanoantenna performance.

The design of a single directional element usually requires the excitation of higher order resonances [12,13]. High-refractive-index dielectric nanoparticles, such as cubes or cylinders, are a convenient platform, since they support higher order Mie-type modes and are easy to fabricate [33]. However, most works investigating directional emission from light-emitting dielectric metasurfaces so far merely utilized the dipolar modes of their constituent resonators [27,28], thus providing only low directivity from the single nanoparticle. Another important effect achievable in lattices of resonant nanoparticles is Fano resonances originating from an interplay between high-Q lattice resonances due to nanoparticle interactions and low-Q Mie-type resonances [35,36]. This feature was used to reach high brightness enhancement [28], lasing [37] and SHG enhancement [38,39] in arrays of Mie-resonators.

Here we demonstrate that by tailoring both the form factor and the array factor of a light-emitting dielectric metasurface, we can obtain control over the emission pattern. To this end, we perform back focal plane (BFP) and momentum-resolved spectroscopy measurements of the photoluminescence (PL) emission from such metasurfaces supporting magnetic quadrupole (MQ) resonances [40]. Importantly, we demonstrate that the quadrupole resonances allow for squeezing the emission into narrower lobes, compared to the dipole resonances of previously demonstrated light-emitting metasurfaces [27,41]. These properties of the quadrupole resonances make them especially suited for light-emission applications.

2. Results and discussion

In this work, we study the modification of the PL emission from InAs QDs embedded into GaAs nanocylinders [28] that are arranged into square arrays to form a metasurface. A conceptual image of the structure geometry is shown in Fig. 1. We investigate a series of samples featuring a systematic variation of the nanocylinder diameters between $340$ nm and $440$ nm in $20$ nm steps. The variation in nanocylinder diameter is implemented in order to tune the spectral overlap of the quadrupolar Mie-type resonances of the nanocylinders over the spectral PL emission bandwidth of the InAs QDs. For each value of the nanocylinder diameter we fabricate three metasurfaces with different lattice periods allowing to study the influence of the periodicity. The duty cycle, namely the ratio between the nanocylinder diameter and the lattice period, was $0.45$, $0.5$ or $0.55$ for these arrays. For fabrication of the metasurfaces, we perform electron-beam lithography on GaAs wafers incorporating functional layers of InAs QDs and an AlGaAs sacrificial layer in combination with inductively coupled plasma etching, followed by a selective oxidation of the AlGaAs layer. More details of the fabrication process and the InAs QDs properties have been previously described in Liu et al. [28]. The inset of Fig. 1 shows schematically the overall structure of a single nanoresonator. The GaAs nanoresonators have a height of $400$ nm and incorporate five layers of InAs QDs. They are positioned on low-index oxide pedestals with a height of $500$ nm and covered by $200$ nm of silica. The entire structure is supported by a bulk GaAs substrate.

 

Fig. 1. Artist’s impression of a metasurface composed of Mie-resonant GaAs nanocylinders incorporating InAs quantum dots. The inset shows the substructure of a single GaAs resonator, which is situated on a low-index oxide pedestal on top of a bulk GaAs substrate. Each GaAs nanoresonator incorporates five layers of InAs quantum dots. The resonator is covered by a low-index cap.

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A scanning electron microscopy (SEM) image of a fabricated GaAs nanocylinder metasurface is presented in Fig. 2(a). Fig. 2(b) shows the PL spectrum of the InAs QDs measured from an unpatterned portion of the wafer. The emission bandwidth covers a wavelength range from approximately $1100$ nm to $1300$ nm. In simulations we consider the QDs as emitting dipoles randomly oriented and homogeneously distributed within the GaAs nanocylinders. As a first step, in order to characterize the modal structure of the fabricated nanocylinder metasurfaces, we measure their near-normal incidence linear-optical reflectance spectra using an experimental setup with effective NA of 0.05. The exemplary results for different nanocylinder diameters and fixed duty cycle of $0.45$ are shown in Fig. 2(c). The shaded blue area indicates the emission bandwidth of the InAs QDs. For the diameter of $D=340$ nm, we observe two pronounced peaks at a wavelength of $1123$ nm and $1294$ nm corresponding to the in-plane magnetic dipole (MD) and electric dipole (ED) Mie-type resonances [33], respectively. As the nanocylinder diameter is increased, the MD and ED resonances show a clear red-shift as expected. For nanocylinder diameters of $380$ nm, $400$ nm, $420$ nm and $440$ nm, we furthermore notice another small feature (namely, a narrow dip) in the reflectance spectra at smaller wavelengths, which corresponds to the excitation of the MQ resonance (see multipole analysis below). Furthermore, the resonant features observed in between the ED and MD resonance for some of the spectra can be assigned to out-of-plane ED and MD resonances. This type of resonances was investigated in detail in our previous work [28] and is thus not further discussed in the following. For nanocylinder diameters of $420$ nm and $440$ nm, the MQ resonant wavelength falls within the InAs QDs emission bandwidth. Since the InAs QDs are placed inside the nanocylinders, thus establishing an effective spatial overlap with the enhanced local fields due to the MQ resonance, we expect a strong influence of the resonances on the QD emission characteristics. Note that so far we selected the set of data corresponding to a duty cycle of $0.45$, as it is the most representative for the tuning of the Mie-resonances over a broad range of the nanocylinder diameters. In the following, instead we focus our study on a metasurface consisting of nanocylinders with a diameter of $440$ nm and a duty cycle of $0.5$ (period $P=880$ nm). For this metasurface sample, the different features in the emission characteristics (as discussed below) were most pronounced.

 

Fig. 2. (a) Scanning electron microscopy image of a typical fabricated GaAs nanocylinder metasurface. (b) Experimentally measured InAs QD PL spectrum from an unstructured area of the wafer. (c) Experimentally measured reflectance spectra of various GaAs metasurface samples featuring a systematic variation of the nanocylinder diameter. The shadowed blue area (wavelength range between approx. $1100$ nm and $1300$ nm) indicates the InAs QDs emission bandwidth.

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As a first step, we numerically investigate the modes excited in the GaAs nanocylinders using the commercial software package COMSOL. In the numerical calculations, design values were used for all geometrical structure parameters, merely the nanocylinder diameter was allowed to vary within the accuracy limits of the nanofabrication procedure in order to globally optimize the agreement between experimental and numerical data over all resonances and all the different measurement configurations considered in this work. The silica cap and oxide pedestal were modeled with a constant refractive index of $n=1.45$ and $n=1.6$, correspondingly. For the optical material parameters of GaAs we used data from Skauli et al. [42]. Further details on the reflection calculations can be found in the SI. The best overall agreement was reached for a nanocylinder diameter of $425$ nm, slightly smaller than the value observed in SEM images. A comparison of numerically calculated and experimentally measured near-normal incidence reflectance spectra is shown in Fig. 3(a). A good overall agreement is obtained, however, the MQ resonance appears slightly red-shifted in the calculated reflectance spectrum. Furthermore, the second small dip observed in the experimental spectra at around $1242$ nm wavelength is not reproduced in the calculated spectra, which we attribute to the deviations from normal incidence excitation in the experiment. In order to study the effect of the finite numerical aperture used in experimental reflectance spectra, we calculate the reflectance spectrum of the structure for a TE-polarized plane wave incident at $15^{\circ }$. We limit the spectral range to the wavelengths where the quadrupole resonances are expected. These results are depicted in Fig. 3 (b). For comparison, the corresponding normal-incidence spectrum is also included in the figure. Clearly, an additional narrow dip occurs at around $1250$ nm for the oblique-incidence case. Next, to analyze the multipolar order of the observed resonance features, we performed a multipole decomposition using the approach described in Grahn et al.[43]. The results are shown in Fig. 3 (c,d) for normal-incidence and $15^{\circ }$-incidence excitation, respectively . Figure 3(d) allows us to identify both resonances appearing as the narrow dips in the experimentally measured reflectance shown in Fig. 3(a) as MQ resonances. These modes correspond to associated Legendre polynomials [44] $P_l^m(x)$ of the same ($l=2$) degree, but having different order of $m=\pm 1$ at $1150$ nm and normal incidence and $m=0$ at $1260$ nm and oblique incidence. At normal incidence (see Fig. 3(c)), in contrast, we can only excite one resonance at around $1150$ nm, while the other resonance is symmetry-forbidden (see Fig. 3(d)). Figure 3(e) furthermore shows the calculated electric field distribution of the two modes excited in nanocylinders by a TE-polarized plane wave incident onto the structure at $15^{\circ }$. As expected, the modes show electric field profiles characteristic for quadrupolar Mie-type resonances [33,45].

 

Fig. 3. (a) Calculated and experimental normal-incidence reflectance spectra from a sample with measured nanodisk diameter of $440$ nm and period of $880$ nm. (b) Calculated reflectance spectra for plane wave incidence at $0^{\circ }$ or $15^{\circ }$. (c,d) Multipole decomposition of the modes excited in the GaAs nanocylinders by a TE-polarized plane wave incident (c) at $0^{\circ }$ and (d) at $15^{\circ }$. The plane of the incidence is the $y-z$-plane. (e) Calculated electric field distribution at an $z-y$-plane through the center of the GaAs nanocylinder at the wavelengths of $1160$ nm (top) and $1250$ nm (bottom) wavelength for excitation by a TE-polarized plane wave incident at $15^{\circ }$.

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Based on our understanding of the mode structure of the GaAs nanocylinder metasurfaces, in the following we investigate how the coupling to the quadrupole resonances influences the QD emission properties. In Fig. 4(a) we present the measured PL spectrum from the sample with nanocylinder diameter of $440$ nm and a period of $880$ nm (duty cycle is $0.5$). The PL spectrum from the unpatterned area of the sample is also shown for reference. Most prominently, the PL spectrum from the sample shows two pronounced peaks appearing at $1150$ nm and $1250$ nm, which coincide with the spectral positions of the magnetic quadrupole resonances of the structure. To show this correspondence directly, we have included the experimental reflectance spectrum of the sample in the figure, showing that the peaks in the PL spectrum and the minima in the reflectance spectrum occur at approximately the same spectral positions. Taking into account the reduction of the amount of active material (filling factor: $20$%) for the nanocylinder metasurface with respect to the unstructured wafer, we calculate a brightness enhancement of 19 at a wavelength of $1250$ nm. We refrain from estimating the quality factor of the quadrupolar resonances based on the PL spectrum, since the width of the emission peaks is dependent on the numerical aperture (NA) of the collection objective (see Fig. 5). Apart from changing the emission spectra, the nanocylinder arrays are also expected [24–28] to affect the directionality of the QD emission. To investigate this effect, we performed BFP imaging experiments, where we mapped the angular distribution of the emission of the sample onto the sensor of an InGaAs camera (see Methods section for details). For collection, we used an $0.6$NA objective. Furthermore, to selectively record the emission patterns at certain wavelengths, we inserted various bandpass filters with passband FWHM of $10$ nm in front of the camera. The recorded BFP images are shown in the upper part of Fig. 4(a). For each of these images, the corresponding passband center wavelengths ($1143$ nm, $1150$ nm, $1237$ nm, $1250$ nm, and $1260$ nm) of the employed bandpass filters are indicated by a vertical colored line. We can clearly observe the reshaping of the angular distribution of the QD emission as a function of wavelength. While all emission patterns roughly inherit the underlying four-fold symmetry from the square lattice arrangement of the nanocylinder arrays, clear differences occur in the predominant emission directions for coupling to the two distinct quadrupolar resonances. Most prominently, the BFP images recorded at wavelengths around the $m=\pm 1$ MQ resonance exhibit an intensity maximum at the center, corresponding to QD emission with small angular spread at normal direction out of the sample plane. Such reshaping can be useful to enhance the PL collection efficiency for optical systems with low-NA objectives. For example, for our metasurface structure $25\%$ of the photons are emitted within the solid angle of 0.1NA compared to less than $1\%$ photons, that would be collected in case of a homogeneous emission pattern. The design of an optical antenna providing such preferable emission into a very low NA and consequently an enhanced collection efficiency is crucial for single-photon sources [31]. In contrast, the BFP images recorded at wavelengths around the $m=0$ MQ resonance exhibit a minimum at the center, i.e. emission normally out of the sample plane is suppressed and the light is predominantly emitted under larger angles. By reciprocity, the suppression of emission under normal direction is consistent with the above discussed observation that the $m=0$ MQ resonance cannot be excited by a normally incident plane wave. These observations are fully consistent with the analytically calculated scattering patterns of these MQ modes in a single dielectric sphere (see SI for details). We also note that the BFP images show an obvious asymmetry, which is likely due to sample imperfections such as a slight tilt of the nanocylinders as discussed in Löchner et al. [46] for nonlinear emission from similar samples. To provide this claim with a concrete evidence, we performed simulations of slightly ($2^{\circ }$) tilted nanocylinders. We indeed observed the rise of the asymmetry in the angular response of the metasurface (see SI for more details).

 

Fig. 4. (a) Experimentally measured PL spectra of a GaAs metasurface sample with nanocylinder diameter of $D=440$ nm and period of $P=880$ nm and, for reference, of an unstructured area of the wafer. The images at the top of the figure show the experimentally measured BFP images at the wavelengths marked by the vertical colored lines (bandpass $10$ nm FWHM). (b) Calculated BFP images at $1150$ nm (top) and $1250$ nm (bottom) wavelength.

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Fig. 5. (a) Cross-sections (red) of the Brillouin zone corresponding to the momentum-resolved spectroscopy measurements. (b) Momentum-resolved emission spectra of the GaAs metasurface sample with nanocylinder diameter of $D=440$ nm. The spectrometer slit is oriented along one of the lattice vectors (horizontal) of the nanocylinder array and along the diagonal of the unit cell (diagonal), respectively. (c) Corresponding numerically calculated momentum-resolved spectra.

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To compare our experimental results with theory, we numerically calculated the angle-resolved emission using the Fourier Modal Method [47,48] in combination with the reciprocity principle [49]. The use of this method to calculate emission properties of light-emitting metasurfaces has been discussed in detail in our previous works [27,28,50]. A TE or TM plane wave was incident from the air semi-space onto the metasurface. The polar angle of incidence $\theta$ was varied from $0^{\circ }$ to $40^{\circ }$ corresponding to the NA of the collection optics and the azimuthal angle of incidence $\phi$ was varied from $0^{\circ }$ to $45^{\circ }$ due to the four-fold and mirror symmetries of the metasurfaces. We added a small imaginary part to the refractive index of the nanocylinder material (GaAs), while other materials of the metasurface were assumed to be lossless within the considered wavelength range. The real part refractive index data of materials composing the metasurface was taken from Palik [51]. This allowed us to match the calculated angle-resolved absorption (summed up for both TE and TM polarization of the excitation plane wave) with far-field emission from the QDs integrated into the nanocylinder by reciprocity. Note that rigorous simulation of 5 layers of QDs inside the nanocylinders shows almost identical results for exemplary test cases while being more computationally expensive. The calculated BFP images at $1150$ nm and $1250$ nm wavelength are shown in Fig. 4(b), showing a good overall agreement with the experimentally measured images apart from the already discussed asymmetry of the experimental images for the $m=0$ MQ resonance. In particular, the maximum/minimum of emission in (near) normal direction for the $m=\pm 1$/$m=0$ MQ modes, respectively, is well reproduced. Additionally, we present the simulation of the angle-resolved emission beyond the experimental NA in the SI.

In order to investigate how the angular emission distribution is affected by the periodic arrangement of the resonators at different wavelengths, we furthermore performed momentum-resolved spectroscopy measurements [52,53] (see Methods for details). We considered two experimental configurations. In the first case, one of the lattice vectors of the nanocylinder array is oriented parallel to the entrance slit of the imaging spectrograph, which corresponds to the $\Gamma \rightarrow X$ cross-section of the Brilloin zone. In the second case, the sample is rotated around its normal by $45^{\circ }$, which corresponds to the $\Gamma \rightarrow M$ slice of the Brilloin zone (see Fig. 5(a)). The experimental data is presented in Fig. 5(b) and yields two different cross-sections of the GaAs metasurface band structure in $(\sin (\theta ),\textrm {wavelength})$ coordinates, where $\theta$ is the polar angle at which the emission is propagating with respect to the metasurface normal. The wavevector projection on the plane of the slit is $k=k_0 sin(\theta )$, where $k_0$ is the free-space wavevector. The BFP images shown in Fig. 4, in contrast, represent isofrequency slices of the band structure. For both configurations we observe the emission signatures of the two MQ resonances of the GaAs nanocylinders at $1150$ nm and $1250$ nm wavelength. The Mie-resonances show a flat dispersion, i.e. their spectral position is only weakly dependent on the angle of emission. In addition, for the case of the $\Gamma \rightarrow X$ cross-section, we notice the highly dispersive modes shown by the dashed lines. These modes are the lattice modes, when the light scattered by the GaAs nanocylinders interferes constructively along the metasurface plane [27]. Interestingly, the MQ resonance at around $1250$ nm is strongly suppressed at angles $\theta$ beyond these lattice resonances, which can be explained by the interaction between the scatterers in the 2D periodic array [5,35].

To allow for comparison of our experimental results with theoretical predictions, we numerically calculated the momentum-resolved emission spectra of the GaAs nanocylinder arrays using the same method as for the calculation of the BFP images of Fig. 4(b). Specifically, we calculated the absorption spectra of a plane wave for a systematic variation of the angle of incidence within the angular range from $\theta =0^{\circ }$ to $\theta =40^{\circ }$, corresponding to the collection NA used in the experiment and azimuthal angle took values of $\phi =0^{\circ }$ or $\phi =45^{\circ }$ [27,28,54,55]. By reciprocity, we can directly link the calculated absorption spectra to the emission in the respective direction. The results are shown in Fig. 5(c) for corresponding to the $\Gamma \rightarrow X$ and $\Gamma \rightarrow M$ cross-sections. One can note a good overall agreement with experimental data. Indeed, we can identify all the essential features observed also in the experimental momentum-resolved emission spectra, including the MQ resonance positions at $1150$ nm and $1250$ nm wavelength, the features associated with the lattice modes, and the hybridization between the particle resonances and the lattice modes [5]. However, some deviations between the experimental and numerical results are also apparent. On the one hand, additional modes appear in the calculations between $1150$ nm and $1250$ nm, which are not observed experimentally. The fact that they are not detected in the experiment may be attributed to a high sensitivity of these modes to sample imperfections as well as to the limited dynamic range of the employed InGaAs camera. Furthermore, coupling of the QD emission to these modes may be suppressed by a preferential orientation of the QD transition dipoles, which is not accounted for in numerics, where the dipoles are assumed to emit isotropically. On the other hand, the experimental momentum-resolved emission spectra exhibit clear deviations from perfect symmetry. As already discussed in the context of the experimental BFP images, the observed asymmetries are likely due to sample imperfections such as a slight tilt of the nanocylinders [46]. These asymmetries also allow for excitation of the $m=0$ MQ mode in experiment under normal incidence, although it is strictly forbidden in theory.

Finally, to investigate the influence of the lattice period on the spatial emission characteristics for both MQ modes, we recorded the experimental BFP images of the GaAs nanocylinders metasurfaces for three different lattice periods ($P=800$ nm, $P=880$ nm and $P=980$ nm). The results are shown in Fig. 6). As mentioned above, the BFP images are determined by the respective Mie- and lattice modes as well as their interplay. While the properties of the Mie-resonances are mainly governed by the dimensions of the nanoresonators, the lattice modes can be independently tailored by the lattice period. To illustrate this effect, we plot under each BFP image we plot the corresponding isofrequency contours of the dispersion of the lattice modes in 2D array of scatterers with surrounding refractive index of 1 and observe a strong dependence on the period. Clearly, the underlying features apparent in the BFP images are well reproduced by the isofrequency contours. The details on the calculations of the isofrequency contours can be found in our previous work [27]. The manipulation of the lattice modes allows for squeezing the emission into a narrow single lobe: for example, we observe the clear reduction in the solid angle into which the PL is emitted for the case of the MQ resonance excited at the wavelength of $1250$ nm for an increase of the period from $880$ nm to $980$ nm.

 

Fig. 6. (a) Top row: BFP images of the PL emission from the GaAs metasurface samples with nanocylinder diameter of $D=440$ nm and different periods varied from $P=800$ nm to $P=980$ nm, measured through bandpass filters with FWHM of $10$ nm and center wavelengths of $1250$ nm. Bottom row: corresponding lattice mode dispersion in the reciprocal space (green). The radius of the red circle is defined by the NA of the collection objective and equals to $k_0$NA, where NA=0.6. (b) Top row: BFP images of the PL emission from the same metasurfaces measured through the bandpass filters with FWHM of $10$ nm and center wavelengths of $1150$ nm. Bottom row: corresponding lattice mode dispersion in the reciprocal space (green). The radius of the red circle is defined as in (a).

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3. Conclusions

To summarize, we experimentally demonstrated spectral and directional control of spontaneous emission from QDs integrated into metasurfaces composed of dielectric nanocylinders exhibiting MQ Mie-type resonances. In particular, we show that the type of the MQ modes excited in individual particles has a significant effect on the emission pattern. Depending on the order of the MQ mode which spectrally overlaps with the emission wavelength, we can either obtain a highly directional emission pattern that is oriented normally out of the metasurface plane with a narrow beam width. Or we can choose a pattern that shows a minimum of the emission in normal direction, where the light is instead emitted in oblique directions in the form of four side lobes, in accordance with the symmetry of the excited MQ mode. Finally, we demonstrated the possibility to further tailor the emission characteristics via the lattice periodicity of the metasurface, thereby adjusting the "structure factor" contribution. Our results provide important insights for the design of novel smart light sources and new display concepts.