1. Introduction

Collective oscillation of the surface electrons (plasmons) in metallic nanosystems that confine the electromagnetic radiation into ultra-small mode volumes have been extensively used to enhance the light-matter interaction at the nanoscale [1, 2]. Various nano-architectures and metamaterials have been used for optical sensing [3–6], spontaneous emission enhancement [7–10] and enhanced nonlinear effects [11–21]. The limiting factors in these experiments are typically associated with radiative damping and Ohmic losses which can reduce e.g. the sensitivity of the measurement or the efficiency of nonlinear effects [22]. The damping times can be estimated using either the local field enhancement factors or, more conveniently, the Q factors of the resonances: τ = Qλ/2πc, where λ and c are the pump wavelength and the speed of light, respectively [23, 24]. Scattering or absorption losses of plasmonic antennas can be effectively suppressed by coupling them to other metallic elements. For example, placing a plasmonic nanodisk on top of a thick metal ground separated by a few nanometer-thick dielectric layer ensures strong coupling between the nanodisk resonance and the metal ground. This coupling will efficiently suppress the far-field scattering enabling these structures to be used as perfect absorbers [4]. If the metal ground is much thinner than its skin depth, the absorption loss instead of the far-field scattering would then be suppressed [24]. In addition, by exciting the “dark modes” in a plasmonic structure, the resonance Q factors can also be improved due to the destructive interference in far-field radiation [25, 26]. However Q factors in these systems are not drastically improved [4, 24, 25, 27]. Recently, it has been demonstrated that strong Mie resonances can be induced in nano-structured high-permittivity dielectric materials [23]. Strong enhancement of nonlinear processes, including second harmonic generation (SHG) and third harmonic generation (THG), have also been observed in well-designed high-permittivity dielectric nano-resonators [28–32]. Waveguides utilizing hybrid metal/high-permittivity dielectrics have been shown to possess an extraordinary ability for simultaneously reducing mode volume and maintaining high propagation lengths [33–35]. In these hybrid structures, near infrared (NIR) low-absorption high-permittivity dielectrics and metals are usually separated by a low-index medium. If this medium is thin enough, mode coupling between the metals and the high-permittivity dielectrics could happen, typically inducing a greatly improved Q factor at resonant wavelengths and longer propagation lengths. Although higher Q factor always indicates a minimized radiation leakage and absorption loss in the region of light circulation, we will show that it does not necessarily imply stronger concentrations of electromagnetic (EM) energy and stronger local field enhancement in a complex hybrid cavity.

In this paper, we propose and experimentally demonstrate a hybrid plasmonic/dielectric metasurface working in the NIR with tunable quality factors and mode overlap based on a standard nanophotonic platform. In our approach, periodic array of gold dimer nanorod antennas are fabricated on top of a silicon-on-insulator (SOI) wafer separated by a thin SiO₂ cladding layer. Plasmonic near fields induced in the dimer gap and in the ultrathin cladding layer couple to the waveguide mode of the device layer inducing strongly enhanced fields in Si. By controlling this coupling we are able to tune the Q factors of the metasurface. Furthermore, we demonstrate that in order to achieve a much higher field enhancement in the coupled plasmonic/dielectric structures, an optimized modal overlap between the plasmonic modes and the dielectric’s resonant modes should also be ensured together with the requirement of the high Q factor. For some wavelengths, while a high Q factor can be achieved easily, it is impossible to simultaneously satisfy an ideal mode field overlap. In particular, we demonstrate that there exists an optimal wavelength, where the requirement of high Q factor and mode overlap could be balanced for obtaining a maximized local field enhancement. We perform nonlinear optical measurements as a sensitive tool for probing the local fields in the metasurface and observe many orders of magnitude enhancement of the THG for the optimized hybrid cavity geometry compared to thin gold film deposited on a Si wafer.

2. Results and discussion

The unit cell of the proposed hybrid plasmonic/dielectric nano-resonators is shown in Fig. 1(a). A cleaned SOI wafer with 250 nm Si device layer and 3000 nm buried oxide layer (BOX) was selected as a sample substrate. On top of the substrate, a layer of 10 nm SiO₂ cladding layer was deposited. An array of Au dimer nanoantennas was then defined on top of the SiO₂ film using electron beam lithography and subsequent deposition of 30 nm thick metal layer (thermal evaporation) and lift-off process. The period P_y along y-axis was set to 500 nm and the period P_x along x-axis varied between 500 nm and 560 nm. Dimer antennas with varying gap size g were fabricated, however the total size of two Au patches was set at P_x/2 × 300 nm. A representative SEM image of the fabricated sample is shown in Fig. 1(b).

 

Fig. 1 a) Schematic of one unit of the hybrid plasmonic/dielectric nanoantenna array; b) A representative SEM picture of the developed nanoantennas sample; c) Local E-field distribution at the resonant wavelength (1390 nm) of the antenna (P_x = 540 nm, g = 60 nm); d) Local H-field at the resonant wavelength (1390 nm) of the antenna (P_x = 540 nm, g = 60 nm); e) and f) are local electric field enhancement profiles along z-direction at the outer edge of the Au antenna for dimers on SOI wafer and Si wafer respectively. The inset in f) shows the wavelength-dependent local field enhancement for antennas on SOI and Si wafer respectively.

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To study the optical properties of our hybrid nanoantennas, first we calculate the near field distribution at the resonant wavelength. When the sample is excited by normally incident x-polarized light, a hybridized mode with strong local E-field and H-field distribution can be excited as shown in Figs. 1(c) and 1(d), respectively. The resonant wavelength primarily depends on P_x and g. Figures 1(c) and 1(d) show the field distribution at 1390 nm resonance wavelength for P_x = 540 nm and g = 60 nm. E-field distribution at the edge of the Au antennas along z direction is shown in Fig. 1(e). As it can be seen from these simulations, strongly localized E-fields with small mode volumes can be excited not only inside the dimer gap but also inside the SiO₂ cladding layer. These cladding layer nanocavity modes are the coupled dipolar modes of the dimer elements, as regularly observed for patch antennas [36, 37]. In the Si device layer, a resonant vortex electric field is excited through the near field coupling from the Au antennas. In fact, this vortex E-field corresponds to a TM₀ waveguide mode (H-field along y axis) as shown in Fig. 1(d). Given the geometric parameters of our system the cutoff wavelength of TM mode in this planar waveguide can be calculated to be 3.75 µm and thus the excitation of modes below this wavelength can be realized in our experiment. The Si device layer plays a key role in improving the Q factor. First, most of the electromagnetic energy scattered by the plasmonic dimer can be trapped in the Si waveguide so that the leakage or the radiation loss can be effectively reduced. Second, because of the negligible absorption of Si in the infrared, the Ohmic loss of the trapped electromagnetic energy can be minimized. The Si waveguide mode is coupled to the near fields of the plasmonic antennas through the cladding layer and the varying gap sizes sustaining different range of wavevectors. Thus the gap size controls the coupling efficiency of the modes and the Q factor of the hybridized mode.

Next, we have performed linear optical measurements to characterize the metasurface. The NIR reflection spectra of the samples were measured using a NIR InGaAs linear array detector coupled with a spectrometer [Fig. 2(a)]. A 10 × objective lens with 0.25 NA and 10 mm back aperture diameter was used for the sample illumination and detection of the reflected light. The samples were illuminated at normal incidence using light polarized along the x-axis. To ensure the normal excitation condition, 1 mm diameter pinhole was placed on the optical axis of the illumination path. The spectra were normalized by the reflection measured from a 150 nm thick Au film. As shown in Fig. 2(a), the measured reflection spectra of different x-periodicities but fixed dimer gap (g≈60 nm) exhibit a broad dip around 1410 nm wavelength caused by the Fabry–Pérot resonance of the SOI wafer layers. Superimposed on this broad reflection dip, we observe a much narrower Fano type dip-peak pair. As we will discuss below, this Fano-type resonance feature is a result of the mutual coupling between plasmonic nanoantenna resonance and a propagating waveguide mode inside the Si device layer. The Q factor of the Fano feature is periodicity-dependent and is much lower when it is superimposed with the center of the broad dip. To obtain the experimental Q factors of our antenna array resonance we performed a fitting by using a combination of Fano and Lorentzian resonances. The equation used for fitting is:

 

Fig. 2 a) and b) show the measured and simulated reflection spectrum for hybrid antennas with fixed ~60 nm gap width but varying x-periodicity; c) The simulated local H field enhancement spectra for hybrid antennas with fixed ~60 nm gap width but varying x-periodicity; d) and e) are the measured and simulated reflection spectrum for hybrid antennas with fixed x-period of 520 nm but varying gap width g; f) The simulated local H-field enhancement spectra for hybrid antennas with fixed x-period 520 nm but varying gap width g. The reflection spectra are offset for clarity.

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Table 1. Fitted Q factors for the experimentally measured and numerically simulated reflection spectra in Figs. 2(a) and 2(b) (samples with fixed dimer gap g = 60 nm but varying x-periodicities). Q stands for Q factor and E stands for the local field enhancement inside the SiO₂ cladding layer.

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To verify these resonance characteristics, we performed numerical simulations of the reflection and local field enhancement spectra. All the geometric parameters in the simulations were taken from the SEM images of the fabricated samples. The wavelength-dependent complex permittivity of Au and Si were obtained from Ref [38]. and Ref [39], whereas the refractive index of SiO₂ was fixed at 1.45 for the studied wavelengths. Poynting vectors through the field-monitor-plane placed 700 nm above the Au antennas were integrated to calculate the reflection spectra. The agreement between simulated and experimental reflection spectra is excellent [Fig. 2(b)]; both the broad dip and the narrow Fano resonance are reproduced at nearly the same wavelengths. The shallower reflectivity features in experimental curves are due to the finite NA of the measuring objective. Most importantly, the simulated near field spectra [Fig. 2(c)] show that the full width at half maximum (FWHM) also reaches the largest value when the coupled resonances are shifted to the broad dip wavelength, which means a much lower quality factor. By performing the fitting procedure, we observe that the theoretically calculated Fano-type reflection of these systems [40], feature quality factors tunable between ~155 and ~314 as summarized in Table 1. As noted above, strongly localized electric fields with small mode volumes are excited inside the dimer gap and the SiO₂ cladding layer as shown in Figs. 1(c) and 1(d), and these E-field enhancement values are also listed in Table 1. The obtained strongest local E-field (Table 1) and H-field [Fig. 2(c)] all appear for 540 nm period, which do not correspond to the highest Q factor.

Remarkably, the position and quality of the resonance is also sensitive to the geometric parameters of the nano-dimers. Both in the measured and simulated reflection spectra [Figs. 2(d) and 2(e)], with fixed period of 520 nm, the spectra experience a red shift and a quick deterioration of Q factors with reducing the gap widths [Fig. 2(f)]. Thus, the gap size is an efficient knob for controlling the coupling of plasmonic and photonic modes and tailoring the optical properties of the metasurface. As mentioned above, the modes shown in Fig. 1(c) and 1(d) represent the resonant mode distributions of the sample with P_x = 540 nm and g = 60 nm [green curve in Figs. 2(a) and 2(b)]. All the other narrow Fano resonances in Fig. 2 have very similar field distribution patterns.

Based on the experimental and simulation data shown in Fig. 2, the sample with 540 nm period and 60 nm dimer gap provides the strongest local field enhancement and a Q factor of ~86. While this Q value is not as high as in certain pure dielectric waveguides and nano-resonators previously reported [41–43], our structures exhibit strongly enhanced, exposed fields near the plasmonic parts of the resonators. The field enhancement observed in the SiO₂ cladding layer between the plasmonic particles and Si is remarkably large and comparable to the enhancement factors observed between two plasmonic elements [41]. Thus, our metasurface can simultaneously support strong field confinement and high quality factors of resonances. For a comparison, we have calculated near field enhancement in the gap of a similar dimer antenna fabricated on top of a regular Si wafer with a 10 nm SiO₂ cladding layer [as shown in Fig. 1(f)]. Without the BOX layer and Si device layer waveguide, the pure plasmonic mode shows a characteristic broad spectrum with a strongly deteriorated field enhancement. The strong near fields of the hybridized mode in our metasurface can be used for the enhancement of Purcell factor or for linear/nonlinear sensing [4, 9, 44].

Having experimentally characterized the far field properties of the metasurface, next we probe its near field characteristics by performing nonlinear optical measurements. The nonlinear signal generation at the nanoscale is proportional to the integral of induced local dipoles at the nonlinear frequency and thus can probe the near field enhancement of our hybrid plasmonic/dielectric cavity [12]. The wavelength-dependent THG measurements were performed by sweeping the output wavelengths of an optical parametric oscillator (OPO) pumped with a Ti:Sapph laser pulses (150 fs pulse width, 80 MHz repetition rate). The x-polarized laser beam with ~1 mm diameter was focused on the sample through a 10 × objective lens. The large back aperture (~10 mm) and the low NA (0.25) of the objective lens ensure that the laser pulses are normally incident onto the sample. The focused laser spot size on the sample plane is approximately 11 µm with calculated peak pump intensity of ~7.5 GW/cm². The THG spectra were measured for pump wavelengths 1300-1460 nm using a spectrometer coupled to a Si CCD camera.

First, we measured THG from a 30 nm Au film deposited on top of 10 nm SiO₂ layer on a Si wafer that will act as a reference sample for the metasurface measurements. As expected, the smooth gold film exhibits only modest THG conversion efficiency, Fig. 3(a). For the fabricated sample with 60 nm gap width and varying x-periodicities, we observed the strongest THG enhancement at the wavelength of 1393 nm corresponding to the 540 nm period [Fig. 3(b)]. The nonlinear signal for this sample is enhanced by ~10⁵ compared to the reference thin film. This observation perfectly matches the linear experimental and simulation results proving that 540 nm period sample provides the strongest local field enhancement. In fact, the selection of different x-periodicity and dimer gap width could lead to a very different THG intensity even if two samples have the same resonant wavelength. For example, the P_x = 540 nm / g = 60 nm sample and the P_x = 520 nm / g = 22 nm sample have similar resonant wavelengths around 1390 nm. However, because of the smaller dimer gap width of the second sample, its Q factor is not as high as the P_x = 540 nm sample [Fig. 3(c) inset]. Consequently, the wavelength-dependent THG signals from the P_x = 520 nm sample [Fig. 3(d)] are only one fifth of those from P_x = 540 nm sample.

 

Fig. 3 a) reference THG spectrum obtained by pumping 30 nm Au film on top of 10 nm SiO₂ film on Si wafer; b) The largest measured THG signals for different periods but fixed dimer gap width 60 nm. Each THG spectrum represents the strongest observed signal for the given periodicity sample. c) Measured THG at different excitation wavelengths for the hybrid plasmonic/dielectric nano-resonator (60 nm gap, 540 nm period) around its resonant wavelength; inset the reflection spectra for the sample of P_x = 540 nm /g = 60 nm (blue curve) and the sample of P_x = 520 nm /g = 22 nm (red curve); d) Measured THG of the hybrid plasmonic/dielectric nano-resonator for P_x = 520 nm /g = 22 nm around its resonant wavelength.

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In order to understand why the P_x = 540nm, g = 60 nm sample exhibits the strongest local field enhancement and THG, we study the reflection spectrum and the local field distribution of a bare SOI wafer. Figure 4(a) shows the reflection spectrum of normally incident light from a bare SOI wafer featuring a broad dip. We analyze the electric field amplitude distribution [Fig. 4(b)] for two representative wavelengths: 1315 nm (wavelength A, the highest reflection) and 1410 nm (wavelength B, the lowest reflection). From these field distributions it is evident that the 3000 nm thick SiO₂ and the 250 nm thick Si device layer together form Fabry–Pérot resonators and the quasi-standing waves exist at both 1310 nm and 1410 nm. Inside the Fabry–Pérot cavity, the field amplitude at 1310 nm wavelength is weaker than that at 1410 nm wavelength since most of the incident energy at the former wavelength is reflected instead of being trapped in the Fabry–Pérot mode. Another important difference of the field distribution between the two wavelengths originates from the electric field amplitude at the top and bottom surface of the Si device layer. At wavelength B, the field at the top and the bottom surfaces of the Si layer has the largest amplitude thus facilitating the coupling of the Fabry–Pérot mode with the plasmonic dimer antenna. This field distribution is conducive to the excitation of the TM waveguide mode since the plasmonic-TM hybridized mode also has the strongest local field amplitude at the top and bottom of Si surface [Fig. 4(c)]. At 1310 nm (wavelength A) on the other hand, the top Si surface has the lowest E-field amplitude, thereby suppressing the coupling of the incident light to the resonant hybrid mode. Thus, naively, one would expect to observe the strongest local field enhancement and THG at wavelength B (1410 nm), which however is not the case in our experimental and numerical data, and the strongest effects are observed at 1393 nm. The reason lies in the reduced Q factor at 1410 nm wavelength. At wavelength B, the incident field can be easily pumped into the Si device layer and by reciprocity, the optical energy can easily leak out to the far field, thus increasing the radiation loss and reducing the Q factor of the hybridized mode. To visualize this, we calculated the radiation power directivity for the P_x = 560 nm and g = 60 nm sample with 3000 nm BOX layer [Fig. 4(d)]. At 1410 nm wavelength, the main radiation directivity is along x-axis, i.e. most of the power is confined inside the Si waveguide, however, there is also a considerable directivity and radiated power along z-axis. For a comparison, in Fig. 4(e) we plot the directivity of the same sample with the BOX layer being substituted with infinitely thick SiO₂ substrate. For this system the original Fabry–Pérot condition is destroyed and consequently the Q factor at 1410 nm is improved, resulting in much smaller radiation directivity along the z-axis.

 

Fig. 4 a) The measured (dotted curve) and simulated (solid curve) reflection spectrum for bare SOI wafer; b) Electric field distribution inside the Si device layer and the SiO₂ BOX layer of the bare SOI wafer; c) E_x field distribution of the coupled plasmonic-TM₀ waveguide mode; Calculated power radiation directivity for the sample of P_x = 560 nm period and g = 60 nm dimer gap with d) 3000 nm SiO₂ BOX layer and e) total glass substrate substituting for 3000 nm SiO₂ BOX layer.

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Based on the above discussion, the dependence of the Q factor on the gap width g can also be understood. With decreasing the gap width, the area of the metal patches would increase, which leads to a decrease of the in-coupling efficiency, due to the larger reflection by the metal patches and the decreased mode overlap. If the in-coupling efficiency cannot make up for the leakage loss, then the quality factor would become even lower.

The above analysis indicates that the modal field overlap and the Q factor are two key factors contributing to the field enhancement in complex hybrid plasmonic/dielectric nanoresonators. However, in situations when they cannot be simultaneously satisfied, a compromise can be found that balances the two factors. In our case this leads to the observation of the strongest field enhancement and THG at 1393 nm. Furthermore, when used for nonlinear signal generation the wider bandwidth of the relatively lower Q resonators can be utilized since the ultrafast pulsed lasers used in these experiments only exhibit a Q of 70-100 in the infrared range.

3. Conclusions

In conclusion, we have developed a hybrid plasmonic/dielectric cavity that can sustain strong field confinement with electromagnetic field enhancement of >30, and a high Q factor of ~100. In comparison to common plasmonic dimer nanoantennas [45], it achieves several times stronger local field enhancement and more than 10 times improvement of the experimental Q factors. In comparison to plasmonic patch nanoantennas (or metal-dielectric-metal nanoresonators), whereas the achieved E-field enhancement values are very similar, the experimentally achieved Q factors of our hybrid sample are 5 to 10 times higher [46]. While these achieved quality factors are lower than some pure dielectric waveguides or nano-resonator arrays with experimental Q values of several hundreds and theoretical Q values of more than 1000 [23, 35], our metasurface exhibits stronger nanometer-scale field confinement and exposed near fields in the plasmonic dimer gap. Furthermore, our linear and nonlinear experiments and simulations demonstrate that high Q factors alone cannot ensure the strongest local field enhancement at the resonant wavelengths. A good mode field overlap between the plasmonic antennas and the dielectric resonators is needed for achieving the strongest electric fields. The advantage of the proposed design also lies in its relatively simple fabrication. The SOI wafers are commercially available and have been widely used for integrated Si photonics. An alternative solution employing a micro-resonator to support photonic modes can be used, however this would have numerous disadvantages including only discrete eigenmodes, very limited tunability and significantly more complex fabrication process [47–53]. These properties make our platform promising for applications including nonlinear optics, Purcell factor enhancement, optical sensing and quantum optics.