1. Introduction

High-index dielectric nanostructures are emerging as alternatives to plasmonic resonators in manipulating light at the nanoscale [1–3]. They possess unique optical properties that are difficult to realize with plasmonic structures. For example, exciting a magnetic dipole mode in a plasmonic structure requires complex geometrical designs [4,5], whereas it is possible to excite multipoles of both electric and magnetic Mie modes in a single dielectric nanodisk [6]. Unlike plasmonic structures, fields can be localized inside the dielectric nanostructures, which allows for light-matter interactions within the structure. However, in most cases, light confinement in dielectric resonators is weaker compared to plasmonic resonators. Therefore, a hybrid design consisting of metal and dielectric nanostructures benefits from the merits of the two systems. For example, by aligning the resonant modes of a dielectric resonator and a plasmonic resonator, the directionality of the scattered light can be better controlled [7–9]. Exciting a plasmon and a Mie mode in a hybrid structure also enhances the local electric field that can further boost the non-linear optical effects from the nanostructures [10].

In the context of mode interactions in photonic/plasmonic structures, there are several coupling regimes based on the coupling strength () and the damping rates (γ₁, γ₂) of the two coupled modes. Broadly, the coupling is classified as weak if $g \ll \; \mathrm{\gamma }1,\mathrm{\;\ \gamma }2$ and as strong, if $g \gg \; \mathrm{\gamma }1,\mathrm{\;\ \gamma }2$ [11]. To attain optical strong coupling, the quality factor of the modes should be large and modal volume should be small [12]. Even though the quality factors of the individual resonators (plasmonic or dielectric) may not be very large, they offer small mode volumes by confining light in the subwavelength regimes. Therefore, to reach strong coupling between two resonators it is crucial to excite tightly confined optical modes in them. When the modes interact strongly, hybrid modes are created whose optical characteristics have properties of both the individual modes [12,13]. In this context, resonant coupling of plasmonic and dielectric structures offer unique possibilities to obtain such hybrid modes. Studies of plasmonic-dielectric hybrid systems are still at an early stage [14–16]. Plasmonic nanostructures are very efficient in confining light at subwavelength scales, while the performance of dielectric nanostructures in this aspect is poor. However, in recent years, optical states such as anapole and bound states in a continuum (BIC) have been demonstrated to show strong confinement of light in dielectric nanostructures [17–19]. The anapole optical state (hereafter, simply referred to as anapole) can be excited efficiently in a high-index dielectric nanodisk of a specific aspect ratio, where the diameter of the disk is large compared to the thickness. Such a nanodisk supports Cartesian electric and toroidal dipoles moments whose far-field radiation patterns are similar. The anapole is generated when the two modes are out-of-phase and destructively interfere in the far-field [17]. This results in a scattering minimum in the far-field and a strong enhancement of light in the near-field. These distinctive optical feature of anapoles, along with low loss in dielectrics, pave way for exciting nanophotonic applications. For example, by exciting anapole modes in hollow nanocuboids and by operating the nanostructure in electromagnetically induced transparency (EIT)-like regime, ultrahigh quality factor (∼10⁶) can be achieved [20]. In another study, using a high-q anapole resonance, room-temperature lasing has been demonstrated in InGaAsP split-nanodisk arrays [21].

Near-field coupling between a plasmon mode and an anapole state is interesting to study due to the possibilities of novel light interactions. In recent studies, designs to couple anapole state and plasmonic modes have been explored in different ways. Placing a nanodisk which supports anapole on a perfect electric conductor (PEC) surface can enhance electromagnetic energy within the nanodisk by an order and such a hybrid design is useful in refractive index sensing, efficient higher harmonic generation, and other applications [22]. Recently, a metallo-dielectric hybrid nanostructure design has been proposed to enhance third harmonic generation (THG) by coupling an anapole mode to a plasmon mode. It is shown that a sub-radiant octuple plasmon mode in an Ag double rectangular nano-ring can be excited through near-field coupling of anapole state in a Si nanoplate. Strong interaction between the modes leads to splitting of modal energies. Due to the field enhancement, energy inside such a hybrid structure can be three to four times higher in comparison with isolated nanostructures and consequently, boost nonlinear optical processes [23]. In another work, it has been shown that strong coupling is possible between a dark plasmonic mode and anapole by placing double nanostrip gold dimers inside silicon nanodisk Mie resonator. Excitation of hybrid modes in the nanostructure results in anti-crossing of the modes with a Rabi splitting of ∼120 meV. However, realizing such a hybrid structure requires a multi-step nanofabrication process [15].

In this work, we present a metallo-dielectric hybrid metasurface that makes use of an anapole to tightly confine light inside a high index dielectric nanostructure and a surface plasmon polariton (SPP) mode on the metal-dielectric interface to achieve strong coupling between the anapole and the SPP. Specifically, the investigated metallo-dielectric hybrid metasurfaces consists of a high-index dielectric (silicon) nanodisk array on top of a metal layer (aluminum) separated by an oxide (silica) layer. The physical dimensions of the Si nanodisks are optimized to support the anapole state and the nanodisk array is designed to excite surface plasmon polariton (SPP) at the metal-buffer oxide interface. These parameters are tuned to excite the respective modes at normal incidence of light in the visible-NIR (400-900 nm) wavelength range. The two modes strongly couple at zero detuning of the resonances when the spacer (SiO₂) thickness layer is ∼200 nm. The avoided crossing of the modes observed in the reflectance spectra and in the spectral profile of light absorption inside the Si nanodisk are signatures of strong coupling. A vacuum Rabi splitting of up to ∼ 129 meV is achievable in the proposed metallo-dielectric hybrid metasurface. Such designs have previously been demonstrated for strong coupling between localized surface plasmons (LSPs) and SPPs, but not in analogous metallo-dielectric hybrid designs [24,25]. Recently, a similar metasurface design was used to demonstrate beam steering by coupling Mie and SPP modes [8]. However, the work addresses only electric and magnetic dipoles in the nanodisks and the coupling between Mie and SPP modes is not in the strong regime. In our work, novelty is in the simpler design of the metasurface, where nanodisk array is on top of a metal surface to realize strong-coupling between the anapole state and the SPP. Importantly, the materials chosen for nanodisk (Si), buffer oxide (SiO₂) and metal surface (aluminum) are all compatible with Si based fabrication technology. The metasurface can therefore be used as an on-chip open cavity system for the applications in active control of molecular dynamics, quantum light sources, ultrafast optical switches, and in demonstration of Bose-Einstein condensates [26–31]. Also, the coupling strength between nanoresonator modes and SPP can be modified in our metasurface by using materials whose refractive indices are tunable (ex. GST), allowing for an active control over the strong coupling in the system [8]. Furthermore, it is possible to boost non-linear effects, such as lasing action, nonlinear optical absorption and second harmonic generation, using high-index nanoarray on metal by exploiting the enhancement of fields within the nanodisks due to anapole coupling to SPP [21,32,33].

2. Metasurface design and optical simulations

For the proposed hybrid metasurface [ Fig. 1(a)], the electromagnetic design and simulations are performed using a commercial FDTD tool – Lumerical [34]. The metasurface consists of silicon (Si) nanodisk arrays in a square lattice on top of a thin (spacer) oxide (SiO₂) layer followed by an optically thick aluminum (Al) film on a substrate. The nanodisk dimensions are tuned to support anapole and the grating array, in our case a square lattice, is designed to excite SPP at the Al-SiO₂ interface. A schematic representation of the metasurface design is shown in Fig. 1(a). The refractive index values for Al, SiO₂ and Si were taken from Palik database. Total-Field Scattered-Field (TFSF) source was used to calculate the scattering cross-section of an isolated nanodisk. The induced electric fields inside the nanodisk were also collected from the same simulations to estimate multipole contributions to the total scattering cross-section. The multipole decomposition (MPD) of the induced fields was evaluated using an in-house multipole analysis code based on a method developed by Alee et al., [35]. Plane-wave source was used to simulate the total reflectance from the hybrid metasurface. The source was injected along the z-axis. Periodic boundary conditions were used in x and y-normal plane, whereas perfectly matched layer (PML) boundary conditions were used in the z-normal plane.

 

Fig. 1. (a) A schematic of metallo-dielectric hybrid metasurface. (b) A typical scattering cross-section of a Si nanodisk (height 50 nm and diameter 350 nm) supporting an anapole state. Also shown is the multipole decomposition of the total scattering cross-section. Excitation of the anapole results in a distinctive scattering dip (@ 680 nm) and a strong light confinement within the nanodisk as seen in the cross-sectional field intensity profile (inset). (c) The anapole resonance position in a Si nanodisk can be spanned across Vis-NIR (400-900 nm) wavelengths by changing the nanodisk diameter from 100 to 500 nm. (d) The graph describes the range of grating periods required to tune (1,0) SPP resonance mode in the given wavelength range (400-900 nm), for two different media (n_air= 1 and n_SiO2= 1.45) on top of Al film. Using the data from Fig. 1(c) and (d), the wavelength region for spectral overlap of the resonances can be chosen

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Figure 1(b) shows the scattering cross-section of an isolated silicon disk (diameter D = 350 nm, height H = 50 nm) supporting an anapole. The multipole decomposition of the total scattering cross-section shows that the major contribution to the overall scattering comes from the electric dipole. The influence of the magnetic dipole is minimal in these wavelength ranges due to low aspect ratios (shorter height and larger diameter). The excitation of anapole results in a characteristic dip (@680 nm) in the scattering cross-section as seen in Fig. 1(b). Strong localization of the electric fields inside Si nanodisk is evident from the field profiles shown in the inset of Fig. 1(b); the two regions of circulating electric fields that are typical in an anapole are also illustrated. However, there is a finite light scattering from the magnetic quadrupole close to the anapole resonance position due to which a complete suppression of scattering in the far-field is not possible. The dominant phenomena close 680 nm wavelength is anapole and not the magnetic quadrupole. Scattering from rest of the Mie modes are negligible. The anapole resonance wavelength is tunable [Fig. 1(c)], almost linearly, by changing the nanodisk diameter. For a disk height of 50 nm, increasing the disk diameter from 100 to 500 nm results in a shift of the anapole resonance wavelength by as much as 400 nm, between 400-900 nm. A surface plasmon polariton (SPP) mode is excited at Al-SiO₂ interface through grating coupling method. The Si nanodisk square array on top of the spacer oxide serves as a 2D grating necessary to couple incoming light to the SPP mode. For a given period of the 2D grating ($\mathrm{\Lambda }$), the SPP excitation wavelength ($\lambda $) is estimated using the SPP dispersion relation and the momentum matching conditions. At normal incidence of light,

3. Results and discussion

As mentioned previously, the SPP resonance is tuned by changing the nanodisk grating period, whereas the anapole is tuned by varying the diameter of the nanodisk. The two resonances can couple when the nanodisk is in the vicinity of the SPP near-field at the metal-dielectric interface, implying that the nanodisk grating must be placed within the penetration depth of the SPP into the dielectric region. The proximity of the Si nanodisk grating from the Al surface can be varied by changing the spacer layer thickness (and/or the refractive index). In the wavelength range of 400-900 nm, the penetration depth of SPP (at Al-SiO₂ interface) into the dielectric region is roughly 125-450 nm. Therefore, the oxide thickness was varied from 25 nm to 200 nm to examine the effect of spatial separation of the modes on their coupling. The coupling between the modes were investigated in the far and near-field regimes. In the far-field regime, reflectance from the metasurface is simulated. The anapole and the SPP mode manifest as dips in the reflectance spectra. In the near-field regime, light absorption within the Si nanodisk is calculated. Si absorbs light in the considered wavelength region (400-900 nm). By studying the frequency dependent absorption one can investigate near-field interactions of the modes [19]. The total power absorbed within a material with volume V is given by $\mathop \smallint \limits_V^{} 0.5\omega \varepsilon ^{\prime\prime}|E{|^2}dV$, where $\omega $ is the angular frequency of the incoming light, $\varepsilon ^{\prime\prime}$ is the imaginary part of the permittivity of the material and E is the induced electric field inside the material. A power absorption analysis tool available in Lumerical was used for this purpose. The grating period and the nanodisk diameter were taken as two independent parameters so that only one of the modes is spectrally tuned while the other is kept constant. Figure 2(a) describes change in the reflectance from the metasurface when the grating period is varied from 400 to 600 nm and the diameter of the nanodisk is kept constant at 350 nm. Here, the thickness of the oxide layer is 200 nm. The (1,0) SPP mode, excited at Al-SiO₂ interface, is tuned from wavelengths 600 to 850 nm. The avoided crossing of the two modes is clearly visible between the spectra corresponding to the grating periods of 480 nm to 530 nm, where a spectral overlap of their resonances is expected. The shift in SPP (1,0) wavelength position with changing period, calculated from the momentum matching condition [Eq. (1)], is also shown as black dashed line in Fig. 2(a). The dashed line overlaps the shift in the reflectance dip with changing period of the nanodisk array, except for the larger period, where it slightly deviates from the SPP (1,0) line. This shows that SPP is the dominant mode responsible for shift in the dip position with changing period. Similarly, avoided crossing between the modes is also observed [Fig. 2(b)] by tuning the diameters of the nanodisk from 180 nm to 370 nm and by keeping the grating period constant at 430 nm. Unlike in a plasmonic resonator-on-metal setup, SPP near-field can penetrate the dielectric resonators of the hybrid metasurface, thereby interact with the modes confined inside the individual nanodisk resonators. The wavelength dependent light absorption profiles are shown in Fig. 2(c) and (d) for the two parameter sweeps. The avoided crossing of the modes in the absorption profiles is clearly visible confirming the presence of a strong coupling of the anapole and the SPP mode.

 

Fig. 2. Total reflectance from the hybrid metasurface when (a) the grating period is varied from 400-600 nm to tune the (1,0) SPP mode (at Al-SiO₂ interface) and the Si nanodisk diameter is kept constant at 350 nm. Also shown (black dashed line) is the shift in SPP (1,0) wavelength position with changing period, calculated from the momentum matching condition [Eq. (1)] and (b) the diameter is varied from 180-370 nm to tune anapole and the grating period is kept constant at 430 nm. Spectral profile of the light absorption within the silicon nanodisk for the case of (c) period sweep and (d) diameter sweep.

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The anapole state for an isolated silicon nanodisk of diameter 350 nm is expected to be around 680 nm [Fig. 1(a)], but we observe that the anapole dip position in the reflectance and power absorptance spectra red shifts with the array period [Fig. 2(a), (c)]. This behavior can be attributed to the effect of the lattice on both electric and other multipoles [36,37]. Recently, lattice dependent absorption of anapole in GaP nanodisk arrays was reported, in which the shift in the extinction spectra was attributed to the interference of a periodicity dependent lattice mode with the electric and toroidal dipoles [38]. Additionally, there is a resonance shift in the SPP mode due to changing diameter of the nanodisks in the array. This can be attributed to a change in the fill factor of the 2D grating layer with increasing diameter that affects the effective refractive index of the layer. Therefore, the shift in the SPP position with the grating period [Fig. 2(a), (c)] doesn’t overlap with the shift in SPP position for the case of semi-infinite dielectric medium with refractive index of 1.45 [Fig. 1(d)] above metal layer. Another parameter that affects the coupling between the modes is the spacer layer thickness. The total reflectance simulations on the hybrid metasurface with different spacer layer (SiO₂) thickness (Supplement 1, Fig. S1, S2) shows that decreasing the SiO₂ layer thickness reduces the coupling strength between the two modes. A clear avoided crossing of the modes starts appearing only for SiO₂ layer thicknesses above 150 nm and below 300 nm. The dielectric above the metal surface cannot be treated as a continuous medium with a fixed refractive index. Rather, one must take into account an effective refractive index which is determined by the refractive index of the spacer oxide and the nanodisk array (material and spatial arrangement). For example, using zeroth order effective medium theory (EMT), a 2D silicon grating can be converted to a slab waveguide that incorporates both TE and TM effective refractive indices. Such a formulation has been used recently to elucidate the relation between Mie and leaky Bloch mode resonances in an array of scatterers [39]. The effective refractive index above the metal changes since high index (Si) grating is closer to the metal surface. This not only affects the momentum matching condition and consequently, the SPP excitation wavelength, but also changes the penetration depth of SPP into the dielectric region. With lower effective index above the metal interface, the confinement of SPP or the field enhancement near metal-dielectric interface may reduce. Furthermore, in Supplement 1, Fig. S1, it can be seen that the SPP dip moves away from (1,0) line for Al-SiO₂ interface, when the buffer thickness is reduced, indicating the changing effective refractive index [40,41].

The presence of metallic film under dielectric nanodisk modifies its Mie scattering response. Such a design (Mie resonator on metal) has been investigated in several recent works [8,42,43]. Bringing dielectric resonator close to a metallic surface boosts magnetic hotspot due to PEC surface effect. Due to the induced image dipoles, the magnetic field at the interface gets enhanced. This magnetic hotspot further boosts electric and toroidal dipole modes. It has been experimentally demonstrated that the third harmonic generation is enhanced for nanodisks placed on metal compared to nanodisk placed on an insulator substrate [42]. Therefore, it is important to show electric field intensity maps of the nanodisks close to wavelengths where modes are hybridized (or coupled) in order to verify the dominant modes (anapole and SPP). Figure 3 shows electric field profiles of a unit cell in the metasurface with Si nanodisk array on top of Aluminum with SiO₂ buffer thickness of 200 nm. The nanodisk diameter and periods are chosen such that the spectral response is close to anti-crossing region in Fig. 2(a), (b). In this wavelength region, the modes are hybridized and signatures of both the modes are seen at wavelengths where we observe anti-crossing. In the case of period sweep, the anti-crossing of the modes occurs for disk diameter of 350 nm and period 480 nm. Figure 3(a), (b) show the cross-sectional view (XZ plane) of electric field intensity in nanodisk and the metal-dielectric interface at wavelength 693 nm and 734 nm. Figure 3(c), (d) show field intensity profiles across the nanodisk (XY plane) for the same set of wavelengths. It can be seen in Fig. 3(a), (b) that SPP mode is dominant at 693 nm and anapole is dominant at 734 nm. But near-field signatures of both the modes are present at the two wavelengths. However, the field intensity of anapole mode at 693 nm is not intense enough to discern in Fig. 3(a). But the XY profile of nanodisks [Fig. 3(c), (d)] shows the presence of anapole modes at 693 nm and 734 nm. Both the profiles show typical anapole characteristics of field localization and circulating electric field at the two corners of the disk. The hybrid modes are more apparent in field profiles from the metasurface with nanodisk diameter 250 nm and array period 430 nm. In case of diameter sweep, the anti-crossing of modes occurs at the specified set of nanodisk diameter and array period of the metasurface. Figure 3(e), (f) shows the cross-sectional view (XZ plane) of electric field intensity in nanodisk and the metal-dielectric interface at wavelength 609 nm and 650 nm. Figure 3(g), (h) shows field intensity profiles across (XY plane) the nanodisk for the specified wavelengths. Here too, near-field profiles of both the hybridized modes are observable. The field intensity profiles, and the field vector lines indicate that both the anapole and the SPP features exist in the two new hybridized modes. Furthermore, we investigated the near-field profile of metasurface with diameter and array period combinations, where the two modes are completely decoupled. These results are presented in Supplement 1, Fig. S3(a-h).

 

Fig. 3. Electric field profiles of a unit cell in the metasurface with Si nanodsik array on top of Aluminum with SiO₂ buffer thickness of 200 nm. The profiles are taken at wavelengths where hybridized modes are expected in the two sweep cases – period and diameter [Fig. 2(a), (b)]. For period sweep case, the hybrid modes appear at wavelengths 693 nm and 734 nm for the metasurface with nanodisk diameter of 350 nm and array period of 480 nm. (a), (b) show XZ cross-sectional profile of the metasurface at wavelengths 693 nm and 734 nm respectively. Here, the profile plane bisects the nanodisk. (c), (d) show XY profile of nanodisk at the same wavelengths. Similarly, for the diameter sweep case, the hybrid modes appear at wavelengths 609 nm and 650 nm for nanodisk diameter of 250 nm and array period of 430 nm. (e), (f) show XZ cross-sectional profile of the metasurface at wavelengths 609 nm and 650 nm respectively. (g), (h) show XY profile of nanodisk at the same wavelengths. In both cases, at wavelengths close to anti-crossing region, near field enhancement at metal dielectric interface (SPP mode) and inside the nanodisk (anapole) is observed.

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A metasurface consisting of high-index nanodisks can efficiently scatter an incoming light especially at wavelengths near Mie resonances supported by the nanodisks. In the presented metasurface design, we specifically look at anapole state which results in near-field enhancement and low far-field scattering. This field-enhancement can lead to nonlinear effects and higher order dispersion terms that in turn influence the mode response [42,44]. Figure 3(c), (d), (g) and (h) show the field enhancement inside the nanodisk. For a given nanodisk diameter (D) and array period (P) of a metasurface, we observe from the simulations that, in Fig. 3 (d) (D = 350 nm, P = 480 nm), the maximum normalized field intensity at the center of the nanodisk is about ∼32. The electric fields within the nanodisk are normalized with respect to the incident electric field of 1V/m. Therefore, the field intensity enhancement is about an order higher than incident light intensity. Similarly, in Fig. 3(h) (D = 250 nm, P = 430 nm), the normalized field intensity at the center of the nanodisk is ∼20, an order higher than the incident field intensity. Such field enhancements can lead to nonlinear effects within the nanodisks [45]. As Si is a centrosymmetric crystal, second order nonlinear coefficients do not influence the overall dispersion. However, the third order susceptibility term χ⁽³⁾ is important in the case of Si, which can lead to both light intensity dependent dispersion and dissipation. The Kerr coefficient (${n_2}$) and intensity-dependent absorption (${\alpha _2}$) terms are related to χ⁽³⁾ of the material. But the value of these coefficients is in the order of 10⁻¹⁸ [45]. Hence, to achieve any appreciable dispersion or dissipation through third order nonlinearity requires extremely high light intensities. In a study, G. Grinblat et al., estimate the change in refractive index due to femto-second laser pulse with fluence of 28J/m, to be about $\mathrm{\Delta }n$∼0.005. This amount of dispersion introduces a red shift of only about 1.2 nm in the scattering cross-section of a silicon nanodisk supporting first order anapole [46]. Therefore, higher order non-linearity induced dispersion and dissipation is negligible in our metasurface, where the field intensity enhancement is about an order higher.

There are several methodologies to establish coupling between two optical modes. The coupling between an optical mode in dielectric and surface plasmon mode on the metal surface can be analyzed using the method called coupled mode theory. Using this method, R.F. Oulton et al., have shown that a cylinder waveguide mode in a nanowire can be coupled to an SPP mode excited on a metal layer beneath the nanowire [47]. Furthermore, with this method, the hybridization of the two modes has been formulated using effective index of the fundamental cylindrical mode and effective index of the SPP, including the measure of hybridization between the two modes. However, based on the results from such previous studies, we assume that coupling exists between an SPP mode and the anapole state inside the nanodisk structure, to simplify the analysis [15, 19, 47,48]. With this assumption we have used coupled mode theory, to directly calculate the strength of coupling between the modes and establish the strong coupling nature of the metasurface. In this model, the energies (${E_ + }\; $ upper branch, ${E_ - }$ lower branch) of the hybrid modes for a lossless coupled resonator system is given by [15,49]

Figure 4(a) and (b) describe the extinction spectra (1-Reflectance) for the period sweep (400–600 nm @ nanodisk diameter of 350 nm) and the diameter sweep (180-360 nm @ grating period of 430 nm), respectively. In the figures, the wavelength ranges (400-900 nm) are expressed in corresponding energy scales (2.25-1.65 eV). The variation of the anapole and the SPP resonance positions with array period is shown on Fig. 4(a), dashed lines. The lattice parameters affect the absorption of anapole in the nanodisk [38], due to which the anapole dip position shows a small red shift (∼ 45 nm) with increasing grating period. Therefore, the fitting parameters to the anapole are extracted from the extinction spectrum of the lattice rather than from the scattering spectrum of an isolated individual nanodisk. The SPP resonance position shows the expected shift with the array period. For the case of period sweep [Fig. 4(a)], in the range 400–600 nm), the detuned resonance positions of the anapole and the SPP mode are considered at the grating period of 600 nm with the nanodisk diameter of 350 nm. Whereas, in the case of diameter sweep [Fig. 4(b)], the detuned resonance positions of the anapole and the SPP mode are considered at disk diameter of 360 nm with the grating period of 430 nm. For the above two cases, the Fano and Lorentzian fits for the decoupled anapole and the SPP modes are shown in the Fig. 4(c) and (d), respectively. For the case of period sweep [Fig. 4(c)], the anapole linewidth is ${\gamma _A}$= 21.4 meV and the SPP linewidth is ${\gamma _{SPP}}$= 65.9 meV and for the case of diameter sweep (Fig. 4(d)), the anapole linewidth is ${\gamma _A}$ = 9.8 meV and the SPP linewidth is ${\gamma _{SPP}}$=59.0 meV. Equation (2) was fit to the normal modes in the extinction spectra with g (coupling strength) as a single fitting parameter. The fit results in a coupling strength of ∼49 meV and ∼64.5 meV for the cases of period and diameter sweep respectively. With the calculated damping factors and coupling strengths, Eq. (3) is satisfied in both the cases and demonstrates that the system is in the strong coupling regime. The corresponding vacuum Rabi splitting energies are ∼98 meV and ∼129 meV. These values are comparable with the recent results of vacuum Rabi splitting from strong coupling in Mie resonator based open cavities [1,4,8].

 

Fig. 4. Coupled oscillator model (COM) fit for the normal modes in the extinction spectra (1-Reflectance). (a) The extinction spectra obtained from the grating period sweep (400–600 nm) with fixed nanodisk diameter (350 nm). E₊ upper branch and E_- lower branch fits are indicated with solid white lines. The green dashed line and the yellow dashed lines show the decoupled SPP and the anapole modes respectively. (b) A similar fit procedure conducted for the case of diameter sweep (180 nm to 360 nm) and a fixed grating period of 430 nm. (c) Fano and Lorentzian fits on the decoupled modes (@ grating period of 600 nm and nanodisk diameter of 350 nm) in period sweep [Fig. 4(a)] and (d) Fano and Lorentzian fits on the decoupled modes (@ nanodisk diameter of 360 nm and grating period of 430 nm) in diameter sweep [Fig. 4(b)]. The fit parameters are used in estimating the line width and resonance energy values of the modes.

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4. Conclusion

In summary, we have proposed a metallo-dielectric hybrid metasurface design consisting of high index (Si) nanodisks square array grating on top of a metal film (Al). The 2D grating is separated from the metal surface by a spacer oxide (SiO₂) layer. Nanodisks with specific geometries – larger diameter compared (∼200 - 350 nm) to the thickness (∼50 nm) - support a tightly confined anapole state in visible wavelength ranges. The grating array (period∼400 -600 nm) of the nanodisks can excite SPP modes at Al-SiO₂ interface through grating coupling in the wavelength range of 400- 900 nm. The anapole resonance position can be tuned in a simple way by changing the diameter of the nanodisk and the SPP resonance can be tuned by changing the period of the 2D grating. FDTD simulations show that a strong coupling of the anapole and the SPP mode is possible at normal incidence of light, when the spatial location of the grating is in the vicinity of the near-field of the excited SPP and at zero detuning of the two modes. The total reflectance from the hybrid metasurface shows avoided crossing of the modes hinting at a strongly coupled system. The avoided crossing is also observed in the near field absorption of the modes inside the Si nanodisk. The variation in the coupling strength could be due to changing effective refractive index above the metal-dielectric interface that influences SPP dispersion and field confinement. Coupled oscillator model was implemented to estimate the vacuum Rabi splitting. For an optimized hybrid metasurface design, splitting of up to ∼129 meV is possible. The advantages of the investigated hybrid metasurface are that it enables a room temperature open cavity system supporting strongly coupled modes, the design is simple, and fabrication is relatively straightforward using materials that are compatible with Si technologies. Although the investigation focuses on normal incidence of light, interesting possibilities to tune the mode-coupling can be anticipated at off-normal incidence of light, since the anapole states are relatively insensitive to the angle of incidence. Such hybrid metasurfaces with strong mode-coupling could be of high relevance in the fast developing on-chip photonic quantum device technologies.