Investigation of dipole emission near a dielectric metasurface using a dual-tip scanning near-field optical microscope

1 Introduction

Designing photonic nanostructures to manipulate electromagnetic field distribution allows more precise control of the light–matter interaction on a fundamental level. As one of the most promising examples, the emission and absorption of light by quantum emitters depends sensitively on the nano-environment into which the quantum emitters are integrated. Consequently, integrating quantum emitters into photonic systems enables novel single-photon technologies for quantum information processing [1, 2] and quantum sensing [3–5]. Different designs for suitably nanostructured environments, either made from plasmonic [6, 7] or dielectric [8, 9] photonic materials, were considered to control the emission of the quantum emitters. The quantity describing the quantum emitter’s interaction with photonic systems is the local density of optical states (LDOS). It quantifies the number of modes the emitter couples into at a particular spatial position and emission frequency. According to its definition, the LDOS is related to the imaginary part of the dyadic Green’s function [10]. Here, the Green’s function expresses the field in a given system in response to an electric or magnetic dipolar point source. Thus, the Green’s function can be the basis to explain a wide range of optical phenomena. We stress that the Green’s function can also be defined for higher-order multipolar emitters. Nevertheless, the electric and magnetic dipoles remain most central thanks to the correspondence to suitable emitters. Scanning near-field optical microscopy was one of the first techniques proposed to measure the LDOS of nanostructured optical systems using the dipole emission of the SNOM’s probe. When operated in the illumination mode, the light emanating from the SNOM’s probe mimics the dipole radiation. It was shown theoretically and experimentally that the detected signal in the far-field using the illumination SNOM is related to the partial LDOS [11, 12]. The excitation and detection through one probe in the illumination/collection SNOM configuration with just a single tip were also used to measure the near-field spectra of quantum emitters embedded in photonic crystal cavities [13, 14]. Recently, illumination/collection SNOM measured the imaginary and real part of the electric and magnetic mode volume from selected photonic crystal nanocavities [15, 16]. Likewise, SNOM has mapped Anderson localization, and the speckle pattern in the near-field of disordered photonic crystals where light interference leads to random mode confinement with a small spatial extent [17–20]. However, the single-tip illumination/collection SNOM cannot map the near-field pattern around the excitation point and the extent of the near-field distribution. In complex structured media, the complicated spatial near-field distribution is described by the spatial correlation function [21]. The imaginary part of the dyadic Green’s function is also responsible for the spatial correlation function in the near-field region of a random medium [22]. Moreover, the cross density of states (CDOS) that accounts for the spatial coherence between the point source dipole and the point of interest in a disordered photonic system is related to the imaginary part of the Green’s function [23–25]. All the quantities mentioned above are associated with the dyadic Green’s function of a photonic system [26]. Hence, measuring the dyadic Green’s function as the system response function provides deeper insights into the underlying physics of optical phenomena in complex photonic systems. These measurements require a technique with a simultaneous dipole excitation and detecting the amplitude and phase of the electromagnetic near-field components with a high spatial resolution. While microwave measurements of the Green’s function have been recently reported [27], the measurement for a visible and near-infrared spectrum has not been addressed yet due to experimental challenges. Regardless of the experimental challenges, the automated dual-tip SNOM is potentially the only instrument that opens avenues toward measuring the near-field dyadic Green’s function for the visible and near-infrared spectra [28]. The dual-tip SNOM is composed of two aperture tips, which simultaneously excite and detect electromagnetic fields within the near-field region. In perspective, the integration of phase-sensitive measurement into the dual-tip SNOM would even enable the full vectorial measurement of all electromagnetic field components [29, 30].

Thus far, the dual-tip SNOM was merely used to map the near-field distribution of the plasmonic modes on flat and unstructured metallic surfaces [31–34]. Attempts toward bringing two tips as close as possible to each other led to the realization of a fully automated dual-tip SNOM, capable of collecting optical signals even closer to the excitation point [28]. Nevertheless, the capability of the automated dual-tip SNOM to map out near-fields of structured materials has remained elusive until now.

In this work, the automated dual-tip SNOM has been used to investigate, as a proof of principle, the position-dependent near-field intensity distribution and directional mode propagation upon dipole emission near a nanostructured sample. For this purpose, we used a silicon all-dielectric metasurface since it is a promising platform to realize complex photonic systems [35, 36]. The coupling strength of the illumination into the metasurface varies with the position of the point source excitation relative to the metasurface [37]. Despite the weak light scattering caused by silicon nanodisks at the resonance wavelength, dual-tip SNOM allowed mapping the distinct near-field intensity patterns. Finally, we have verified that the integrated mapped near-field using the dual-tip SNOM can be related to the partial LDOS. This work is also one step further toward mapping the dyadic Green’s function and the CDOS for the complex nanophotonic systems.

2 Experimental setup

Our experimental setup consists of two SNOM scanning heads (MV-4000, Nanonics Imaging Ltd) with two aperture tips for excitation and detection below the diffraction limit. In the experiment, the excitation tip illuminated a dielectric metasurface with the dipole-like emission, and the detection tip simultaneously scanned the near-field of the metasurface, mapping optical near-field information around the excitation tip (Figure 1A). The aperture tips in the dual-tip SNOM setup are tapered optical fibers with 200–300 nm Cr–Au coating. The fiber tips make an angle of 30° with the surface normal. The excitation tip, a single-mode fiber, is connected to a tunable laser source (Tunics Reference, Anritsu), whereas a multi-mode fiber tip as a detection tip is connected to a single-photon detector (id220, ID Quantique). The aperture diameters of the excitation and detection tips are about 350 nm (Figure 1C and D). In the dual-tip SNOM configuration used for near-field measurements, the excitation tip is stationary and placed at the position of interest on the top of the metasurface inside a scan window, e.g., a square area where the detection tip performs scanning around the excitation tip. A fully digital scanning probe microscope controller (R9, RHK Technology) governs the tip-sample distance during the scan and enables an automated collision prevention scheme to prevent the collision between the two tips when they are laterally close.

Figure 1:

(A) Dual-tip SNOM configuration on top of a silicon nanodisk metasurface. (B) Two aperture tips when they are positioned at the minimum distance from each other. The red dashed arrows show the direction of the scan. The length of the double-sided blue arrow indicates the minimum distance between the apertures. The parabolic white area is the avoidance area (the red dashed curve corresponds to its boundary). The red cross denotes the vertex of the avoidance area. Scanning electron micrograph of the aperture of the (C) excitation tip and (D) detection tip. Scale bars are 0.5 μm.

In the measurements by dual-tip SNOM setup, the detection tip starts scanning toward the excitation tip (Figure 1B) along the negative x-direction from the corner of the scan window. Optical and topography data are mapped simultaneously (Figure S1, Supplementary Information). The detection tip is controlled in such a way that it does not collide with the excitation tip [28]. Since the geometry of the tips’ apex is almost conical, a parabolic-like region called the avoidance area is created during the scan. The parabolic red dashed curve in Figure 1B indicates the boundary of the avoidance area. The geometries of the excitation and detection tips define the boundary of the avoidance area, where the detection tip cannot scan further and sweeps back to the beginning of the next scan line.

A minimum distance between the excitation and detection tip can only be determined when the detection tip scans along the line, which crosses the vertex of the avoidance area (red cross in Figure 1B). The minimum distance corresponds to the distance from the center of the detection tip to the center of the excitation tip. Therefore, the scanning electron microscope (SEM) images of the excitation and detection tips are required before the experiment in order to calculate the minimum distance. The SEM images of the excitation and detection tips are shown in Figure 1C and D, respectively. In these measurements, the minimum distance (Figure 1B, double-sided blue arrow) is about 650 nm between the excitation and detection tip (center to center).

One additional parameter that should be known prior to performing the dual-tip SNOM measurements is the polarization characteristic of the excitation aperture tip. Mode losses due to the fiber bend along the tapered region lead to polarization filtering of the modes propagating inside the fiber. Likewise, a bend in the detection tip results in a polarization-sensitive detection. However, the polarization filtering effect is less pronounced for the multi-mode fiber used for a near-field detection. Since the bend of the fiber determines the polarization of the mode that reaches the exit of the aperture [38], the emission pattern of the excitation tip should be characterized before performing the dual-tip SNOM measurements on the metasurface. We used the dual-tip SNOM setup to characterize the polarization of the emission from the excitation tip aperture. In this regard, we have analyzed the propagation direction of the SPPs excited on a gold film by the excitation tip. The propagation direction of the excited SPPs corresponds to the polarization of the electric field at the exit of the aperture tip [39, 40]. In the corresponding simulation to reproduce the emission pattern of the aperture tip at air-gold interface, an in-plane magnetic dipole perpendicular to the direction of the electric field polarization was used to model the emission pattern [28, 40]. The same magnetic dipole was used to numerically simulate the emission of the excitation tip on the metasurface.

3 Near-field excitation and detection of the metasurface by the dual-tip SNOM

Before performing the dual-tip SNOM measurements, we used a far-field spectroscopy setup to determine the spectral characteristics of the metasurface. The metasurface consists of silicon nanodisks with a radius of r = 317 nm and a height of h = 237 nm arranged in square lattice with a lattice constant of L = 915 nm on a glass substrate. Figure 2A shows the measured transmittance of the metasurface. The inset of the figure shows the SEM image of the silicon metasurface. For comparison, a simulated spectrum is also included. The numerical simulations were carried out with a commercial FDTD solver, Lumerical.

Figure 2:

(A) Measured and simulated transmittance for the nanodisk silicon metasurface depicted in the inset with the 1 µm scale bar. Two minima correspond to the wavelengths of the magnetic dipole (MD) and electric dipole (ED) modes of the metasurface. In-plane (B) electric and (C) magnetic field intensity for the ED mode in one unit cell of the metasurface. The white arrows illustrate the polarization vectors of the fields.

Although the measurements show a slightly higher transmittance than the simulations, which is due to fabrication imperfections, the metasurface shows very strong dipole resonances. The two minima in Figure 2A correspond to the magnetic dipole (MD) and electric dipole (ED) modes of the metasurface. Figure 2B and C shows the simulated electric and magnetic intensity patterns for one unit cell at the wavelength of the ED mode (λ = 1624 nm), in the plane z = 20 nm above the nanodisk. The excitation source was a plane wave with a y-polarized electric field, which illuminated the metasurface from the far-field. White arrows denote the in-plane polarization vectors of the electric and magnetic fields. We performed the position-dependent near-field measurements of the dielectric metasurface using the dual-tip SNOM. The excitation tip illuminates the metasurface at the ED mode wavelength λ = 1624 nm. The excitation tip is stationary throughout all measurements. A nanopositioning piezoelectric stage displaced the metasurface relative to the excitation tip. Figures 3A–D and 4A–E are the near-field intensity distributions mapped by the detection tip for the successive displacements of the metasurface along the x- and y-axis, respectively. The initial position of the excitation tip with respect to the metasurface in Figure 3A, Δx = 0 and Figure 4A, Δy = 0 was selected arbitrarily. The metasurface displacements Δx and Δy from the initial position are shown on top of each column. The total displacement of the metasurface was about one lattice constant. Due to mechanical and thermal drifts of the excitation tip, we observed an error of ±0.05 µm for the excitation tip position in each displacement. While it is possible to use smaller displacement steps to cover the displacement of about one lattice constant, we avoided using more steps to prevent the drift of the excitation tip caused by a longer measurement time. For the data normalization in Figures 3A–D and 4A–E each panel was divided by the same value. Once the value was the maximum measured intensities of all panels 3A–D for the metasurface displacements along the x-axis and then for all panels 4A–E for the metasurface displacements along the y-axis. In the numerical simulations, the emission from the excitation aperture tip is represented by the in-plane magnetic dipole [41–43]. The white dots with the purple arrows in the middle denote the excitation aperture tip position and the orientation of the magnetic dipole used in the numerical simulations. The magnetic dipole orientation in the simulations was along the x-axis. There is an error of ±0.1 µm to determine the absolute initial position of the excitation aperture with respect to the metasurface. The gray parabolic-like region is the avoidance area, where no optical signal can be detected in the near-field measurement. White circles mark the edges of the nanodisks. The aperture tip mostly mapped in-plane components of the electromagnetic fields. However, the tilt of the detection tip in the dual-tip SNOM setup, leads to the collection of the electromagnetic components normal to the metasurface plane. These contributions to the collected signal can be considered as negligible due to its smaller magnitude in comparison with the in-plane electromagnetic components near the metasurface. Due to the sensitivity of the detection tip to magnetic fields, only in-plane magnetic field components were considered in the numerical simulations [40, 42, 44]. Figures 3I–L and 4K–O show the simulation results of the magnetic field intensity distributions monitored in a plane 20 nm above the metasurface when it is excited by a magnetic dipole in the same plane. The metasurface was displaced in each simulation with the corresponding retrieved displacements from the experiment. In Figures 3I–L and 4K–O the simulated results are plotted for the same scale to increase the visibility of the details in the near-field intensity distributions. However, the comparison between the measured near-field intensities and the simulation results in Figures 3I–L and 4K–O is not straightforward due to the avoidance area in the measurements where the detection tip cannot map any optical signal. For the sake of comparing the simulations and measurements, in Figures 3I–L and 4K–O, the calculated intensities corresponding to the avoidance area were set to zero. Figures 3E–H and 4F–J show the simulation results, with the intensities being zero in the avoidance area. For the data normalization after setting the data of the avoidance area to zero in Figures 3E–H and 4F–J, each panel was divided by the same calculated value. Once the value was the maximum calculated intensities of all panels 3E–H for the metasurface displacement along the x-axis, and then the maximum calculated intensity of all panels 4F–J for the metasurface displacement along the y-axis. The measurements and the calculated intensities with the avoidance area share the same color scale. The numbers on the right bottom corners of each panel denote the maximum intensity in the respective panel.

Figure 3:

(A)–(D) Measured near-field intensity distributions by the dual-tip SNOM when the metasurface is moved by a displacement of Δx along the x-axis. Δx = 0 is the initial position. ±0.05 µm is the respective error due to uncertainty to find the drifts of the excitation tip during the measurements in (B)–(D). White dots indicate the aperture position of the excitation tip in the measurements. For normalizing the data, the measured near-field intensities in (A)–(D) were divided by the maximum measured value of all panels. (E)–(H) Numerical simulations for the in-plane components of the magnetic field intensity for the metasurface displacements in (A)–(D). The gray parabolic-like regions represent the avoidance area. Purple arrows show the position and direction of the magnetic dipole used in the simulations. The simulated intensities with the avoidance area are also normalized, after setting the intensities inside the avoidance area to zero, to the maximum value of the calculated near-field intensity in (E)–(H). Panels (A)–(D) and (E)–(H) share the common color scale while the numbers on the right bottom corners are the maximum normalized intensities in each panel. (I)–(L) Simulation results for the in-plane magnetic field intensities. All the simulation results are shown for the same intensity value to increase the visibility of the near-field intensity patterns. The black scale bar is 1 µm.

Figure 4:

(A)–(E) Measured near-field intensity distributions for the metasurface displacements Δy along y-axis. The initial position is Δy = 0. White dots indicate the position of the excitation aperture in the measurements. ±0.05 µm is the error in the displacements (B)–(E) due to the drifts of the excitation tip during the measurements. The measured near-field intensities were divided by the maximum measured value for the normalization. (F)–(J) Numerical simulations of the in-plane magnetic field intensity components for the metasurface displacements in (A)–(E). The gray parabolic-like region is the avoidance area. The purple arrow denotes the magnetic dipole direction and position in the simulations. The simulated intensities, after setting the intensities inside the avoidance areas to zero, were normalized to the maximum calculated near-field intensity. Panels (A)–(E) and (F)–(J) share the common color scale while the numbers on the right bottom corners are the maximum normalized intensities in each panel. (K)–(O) Simulation results (F)–(J) without covering the avoidance area. The simulation results are shown for the same intensity value to increase the visibility of the near-field patterns. The black scale bar is 1 µm.

4 Mapped near-field intensity and partial LDOS

In earlier studies using the single-tip SNOM, the capability of the SNOM to map the partial LDOS was demonstrated theoretically and experimentally [11, 12, 45]. The partial LDOS was mapped using the particular configuration of the illumination SNOM (forbidden light SNOM) [46]. In the forbidden light SNOM, propagating components of the electromagnetic fields were filtered, and the evanescent waves were converted into traveling waves and detected in the far-field below the sample, similar to the leakage radiation microscopy [47]. Thus, the details of the mapped partial LDOS were determined by the amount of evanescent waves that reached the far-field. In contrast to the forbidden light SNOM, the detection tip of the dual-tip SNOM can directly map the evanescent waves above the metasurface. The integrated mapped near-field intensity in the plane of detection using the dual-tip SNOM is also expected to be proportional to the partial LDOS at the location of the excitation tip’s aperture, similar to the intensity measured using the forbidden light SNOM [12]. Therefore, mapped near-field intensities by the dual-tip SNOM at different excitation points could always be used to compare the partial LDOS at corresponding positions on the nanostructures. More importantly, the mapped near-field intensity provides valuable information concerning the correlation between the excitation and detection points (CDOS). Hence, verifying the relationship between the integrated near-field intensity and the partial LDOS would also allow the measurement of the CDOS in disordered and complex photonic systems by the dual-tip SNOM [21, 48].

In the dual-tip SNOM measurements, the dipole-like emission from the excitation aperture tip corresponds to the emission of a magnetic dipole oriented along the x-direction. Therefore, the magnetic partial LDOS is the relevant quantity in our measurement. The magnetic partial LDOS quantifies the number and strength of the excited modes at a certain position based on the strength and polarization vectors of the magnetic field projected along the magnetic dipole direction [10]. According to Figure 2C, visualizing the magnetic field intensity of the ED mode and the in-plane polarization vectors, the maximum contribution to the partial LDOS from the ED mode is obtained for a magnetic dipole polarized along the x-axis and placed at the position where the magnetic field has maximum intensity. Although the partial LDOS takes into account the contribution of all available modes, and not only a single mode, at the ED resonance wavelength of (λ = 1624 nm), modes are dominated by the ED contribution as it can be observed from the multipolar decomposition of the scattering cross-section for a single nanodisk of the metasurface (see Figure S3 in the Supplementary Information). The behavior of the mapped near-field intensity distributions by the dual-tip SNOM can be explained with the same argument. Since the polarization of the dipole-like emission from the excitation tip is fixed during the measurement, the partial LDOS is different for various positions of the excitation tip relative to the metasurface. The change of the partial LDOS is reflected in the distinct near-field intensity patterns around the excitation tip. However, from different near-field patterns, it cannot be concluded that the LDOS is modified. The modification of the partial LDOS would result from the change of the integrated near-field intensities (powers) over the scan window.

The partial LDOS is indeed related to the power radiated by a dipole [26]. In other words, the power radiated by the dipole emitter is proportional to the partial LDOS. In this regard, we have calculated the normalized power and compare it with the integrated measured near-field intensities. Since both normalized radiated power and integrated near-field intensity should be proportional to the partial LDOS, we expect that they follow the same behavior.

Figure 5A shows the normalized integrated intensity calculated from the mapped intensity patterns in Figure 3A–D (measurement) and Figure 3E–H (simulation) for the metasurface displacements along the x-axis. The intensity values are integrated over the scan window, excluding the avoidance area. Likewise, Figure 5C exhibits the normalized integrated mapped near-field intensities in Figure 4A–E (measurement) and Figure 4F–J (simulation) for the metasurface displacements along the y-axis. In Figure 5A and C, raw data of the measured integrated near-field intensities, after subtracting the constant value due to the measurement noise, were scaled to the maximum value of the integrated intensities in the simulations. In Figure 5A and C, the horizontal error bars for the measured data indicate the error in determining the displacement of the metasurface along the x- and y-axis due to the excitation tip’s drift during the measurements. This error could be one reason for the observed difference between the integrated near-field intensities of the measured and calculated data. Moreover, the influence of the two tips when they are laterally close within the region of shear forces could be another reason for the observed discrepancy in the measured near-field intensity comparing with simulation. It is important to note that the integrated near-field intensity can only determine the partial LDOS qualitatively. In other words, when the near-field intensity is mapped for different positions of the excitation tip relative to the nanostructures using the dual-tip SNOM, the partial LDOS at the respective position is one of the quantities that can be calculated.

Figure 5:

(A) Normalized integrated intensities for the measurements in Figure 3A–D and simulations in Figure 3D–H for Δx displacements. The error bar only shows the error in finding displacements due to the drift of the excitation tip during the measurements. (B) Corresponding normalized radiative power and the power loss of the magnetic dipole. (C) Normalized integrated intensities for the measurements in Figure 4A–E and simulations in Figure 4H–J for Δy displacements. (D) Corresponding normalized radiative power and the power loss of the magnetic dipole for the same Δy displacements. The integrated intensities were calculated for the raw data of simulations and measurements. To normalize the integrated intensity of the measurements, they were scaled to the maximum value of the integrated intensity in the simulations.

Figure 5B and D shows the normalized radiated power P _rad/P ₀ and power loss P _loss/P ₀ for the metasurface displacements Δx and Δy where P ₀ is the power radiation of a dipole on a glass substrate without silicon nanodisks. We simulated the radiative and non-radiative power emitted from a magnetic dipole, located at z = 20 nm above the metasurface, for the displacement values in the measurements. In general, the dipole emission is coupled to radiative and non-radiative modes. However, the losses are negligible in the analyzed spectral range of the silicon metasurface; thus, all the emission corresponds to the radiative power.

Changes in the integrated mapped near-field intensity in Figure 5A and C follow the same trend as changes of the normalized power in Figure 5B and D, respectively. We can conclude that the integrated near-field intensity, even excluding the avoidance area, still indicates how the normalized power and, consequently, the partial LDOS changes. In addition, we calculated the integrated near-field intensity and the power radiation for smaller increments of the metasurface displacements than those performed in the experiment (see Figure S3 Supplementary Information). These simulations were performed to obtain more points in Figure 5 and corroborated that the integrated near-field intensity, excluding the avoidance area, follows the same behavior as the normalized radiation power. As a result, the dual-tip SNOM would indeed predict the behavior of partial LDOS at a certain position of the quantum emitter relative to the photonic nanostructures.

5 Conclusions

Using a dual-tip SNOM, we have shown the measurement of the near-field intensity distribution due to the dipole emission at different positions on a silicon metasurface. The mapped near-field intensities demonstrated that the direction and extent of the excited modes highly depend on the position and the orientation of the dipole emission relative to the nanostructures. More strikingly, we could show that the integrated mapped near-field intensity is proportional to the partial local density of states (LDOS) at the excitation position. Hence, the automated dual-tip SNOM can be a promising technique to measure the cross-density of states (CDOS). Moreover, the aperture tip could be replaced with the quantum emitter on the uncoated tip apex to investigate the near-field interaction of the quantum emitter with the photonic system. Although all principles that work for a single SNOM operating in illumination or detection mode are also applicable for the dual-tip SNOM [26, 30], extra challenges particular to the automated dual-tip SNOM should be addressed to enable the dyadic Green’s function measurement. In this regard, the perturbation of the near-field distribution due to the presence of two aperture tips and their influence on the image formation when two tips are laterally close should be investigated with rigorous numerical calculations. Despite all experimental challenges, the automated dual-tip SNOM technique is a step closer to mapping the dyadic near-field Green’s function and the quantities associated with it [49–51]. Thus, point source excitation and detection in the near-field, accessible by the dual-tip SNOM, can establish a novel approach to study unknown aspects of light–matter interaction in complex photonic systems.