Design and Polarization Control of the Modal Splitting in Hybrid Anisotropic Nanocavities

The strong coupling of optical resonators results in a mode splitting proportional to the coupling strength, which can be achieved with metal‐dielectric‐metal (MDM) cavities that have similar thickness and refractive index. However, an active control of the mode coupling is challenging. Here, an alternative configuration of an MDM cavity coupled with a Guided‐Mode‐Resonator (GMR) is explored. The GMR grating is fabricated on top of the MDM cavity, such that the coupling can be tuned by the thickness of the central metal. The typical modal anti‐crossing (with a splitting of ≈50–65 meV) detected in the angular dispersion of the GMR‐MDM is observed. Excellent agreement of the experimental reflectance with simulations allows to report the angular dispersion from −50° to 50°. The anisotropy of the GMR modes enables to switch in and out of the strong coupling by changing the polarization of the incident light. Moreover, the asymmetry of the GMR‐MDM architecture induces a side‐dependent response. The MDM cavity is only transparent at its resonances, which leads to a suppression of all modes outside the resonance bands when impinging from the MDM side. These features are highly interesting for optoelectronic applications such as optical switches and multi‐level optical multiplexing.


Introduction
Optical resonators are one of the fundamental tools in optics, photonics, and optoelectronics. One of the most basic, but yet broadly used, architectures of an optical cavity is the metal-dielectric-metal (MDM) resonator, whose response can be intuitively explained by recalling the concept of a Fabry-Perot cavity.
The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adom.202202876. strong coupling dynamics in sophisticated systems involving many oscillators. [11] From a more applied point of view, the mode splitting occurring in multi-cavity resonators has been used to finely tune their resonant response to the optical transitions of perovskites. [7] Fabry-Perot cavities have also been employed for strong coupling with plasmonic nanoparticles, for example, for the purpose of water splitting. [12,13] Strong coupling of plasmonic elements can be explored to obtain highly transmissive windows in reflectance via the Plasmon Induced Transparency effect. [14] Strongly coupled resonators have also been used as optical feedback elements for frequency stabilization of semiconductor laser, [15] and even found applications as physically unclonable functions. [16] Towards external control of the mode coupling that would enable switching and multiplexing, the polarization of the incident light is an appealing parameter since it can be easily controlled by external optical elements. A promising approach could be the introduction of a highly anisotropic resonant element on top of an MDM cavity, such as Guided Mode Resonators (GMRs). GMRs are used in many applications such as high-Q filters, [17] ultra-broadband reflectors, [18] wavelength selective polarizers, [19] and phase detectors. [20] Their architecture mainly consists of a waveguide that is capped with a diffraction grating that couples the light into the waveguide, producing a leaky guided mode. This leaky mode interferes with the electromagnetic wave propagating in free space to give rise to the guided mode resonance. GMRs provide a wide range of tun-ability in the spectral response by varying the grating geometry, materials, and angle of incidence. [21] In this work, we exploit the highly anisotropic resonant response of GMRs to gain control over the strong coupling regime occurring in a GMR-MDM architecture. This allows tuning in and out of strong coupling by simply changing the polarization of the incident light. We fabricated a nanopatterned dielectric film that sustained GMR modes directly on top of the MDM cavity (see Figure 1). The two structures were designed to resonate at the same wavelength if the incident radiation is S-polarized, while they were detuned for the P-polarization. We investigated the dispersion of the individual MDM and GMR cavities, and their mode splitting in the combined GMR-MDM system by angle-and polarization-dependent reflection spectroscopy. The experimental results are supported by Rigorous Coupled Wave Analysis (RCWA) simulations. We observe the characteristic anti-crossing behavior in the angular dispersion map of the GMR-MDM system for the case of S-polarized incident light. The mode splitting strongly depends on the thickness of the top metal layer of the MDM that is in contact with the GMR cavity. We experimentally and numerically demonstrate that the mode splitting is highly polarization sensitive, in the sense that for the polarization for which the resonances are matched, the splitting occurs, while for the other polarization only the mode of the MDM cavity is observed. The large polarization sensitivity of the coupling between the GMR and the MDM leads to a remarkable change of reflection intensity at the Adv. Optical Mater. 2023, 11, 2202876 Figure 1. Schematic of an a) MDM cavity, b) TiO 2 slot grating on a thin Ag film for GMR response, c) hybrid GMR-MDM structure with TiO 2 slot waveguide on top of the MDM. (d) Top view SEM image of the hybrid GMR-MDM structure depicting the grating pitch. t tm , t bm and t d are the thicknesses of the top metal layer, bottom metal layer, and dielectric layer in the MDM structure, respectively, while t g , t wg, and t tm are the grating, waveguide, and metal layer thicknesses in the GMR, respectively. In the combined GMR-MDM device, the metal layer of the GMR (t tm ) coincides with the top metal layer of the MDM.
anti-crossing wavelength. Towards exploiting this effect for light modulation, the switching speed would depend solely on the mechanism for polarization modulation of the incident beam. Therefore, this system is highly appealing for optical and optoelectronics devices, like optical modulators and multiplexers, [6] light valves, [22] or photonic transistors. [23] As an additional feature, the asymmetric nature of the GMR-MDM system makes the optical response incidence side-dependent: the MDM functions as a color filter, thus if light impinges from the MDM side, the modes of the GMR that are not in this transparency window are filtered. This allows us to select only the hybridized modes in the GMR-MDM system and to exclude those that do not participate to the strong coupling. These properties of the GMR-MDM devices are highly appealing for new-generation light sources, modulators, and sensors in future optoelectronics applications.

Results and Discussion
For a better understanding of the observed properties, we analyze the resonant behavior of the GMR and the MDM cavities separately, and in the hybrid GMR-MDM device. The MDM nanocavity consists in a Ag/Al 2 O 3 /Ag (40/150/40 nm) multilayer, fabricated using an e-beam evaporator, as illustrated in Figure 1a. The GMR (Figure 1b) consists of a TiO 2 slot grating on a thin Ag film whose thickness t tm is 40 nm. The GMR was fabricated by e-beam lithography and evaporation processes, as described in the Experimental Section. The GMR structure can be seen as the combination of a grating and a waveguide. The grating of the GMR is characterized by period Λ = 310 nm, height t g = 60 nm, and fill factor ff = 0.6. The waveguide thickness t wg is 120 nm. These geometrical parameters were selected to obtain resonant GMR modes in the red spectral region. The hybrid GMR-MDM structure was obtained by fabricating the GMR on top of an MDM nanocavity, as illustrated in Figure 1c. Figure 1d shows a top-view scanning electron microscopy (SEM) image of the GMR-MDM structure. The cross-section of the GMR-MDM structure is presented in the supporting information Figure S1.
The number of modes that can be excited in the GMR and MDM structures depends on the thicknesses of the waveguide (t wg ) and dielectric (t d ) layers, respectively. We selected the layer thicknesses such that only the fundamental (zero-order) modes are excited with resonant frequencies in the red spectral range.

Angular Dispersion of MDM, GMR, and GMR-MDM Structures
The optical properties of the MDM, GMR, and GMR-MDM structures have been studied theoretically through RCWA simulations and experimentally by polarized reflectance measurements. Figure 2a reports the angle-dependent S-polarization reflectance map of the MDM structure. Here, the agreement between the theoretical (left red-colored side) and experimental (right blue-colored side) results allows joining them in the same panel to reconstruct the full angular dispersion from −50° to 50° with respect to the incidence angle. The modes of the MDM cavities coincide with the minima in the reflec-tance. [1] We observe a typical cavity dispersion, where the resonance is blueshifted with an increasing angle of incidence. [24] The angular dispersion of the fundamental mode of the MDM cavity with dielectric thickness t d = 150 nm falls in the wavelength range from 570 nm to 650 nm.
The S-polarization reflectance map of the unperturbed GMR structure is reported in Figure 2b. Here the fundamental mode of the GMR falls in the same spectral range as the one of the unperturbed MDM. The GMR mode redshifts with increasing angle of incidence, which is characteristic for GMR waveguides. [25] At resonance, the electric field in the MDM structure is confined in the dielectric layer, while for the GMR structure the electric field is confined in the waveguide underneath the grating structure. The electric field profiles are shown in Section 3 (see inset of Figure S3b, Supporting Information).
We now consider the GMR-MDM system, for which the coupling can be modeled by two coupled harmonic resonators. [26] When the GMR and the MDM modes are tuned to the same wavelength (or even slightly detuned), the two resonators can exchange energy through the central connecting metal layer, which results in a mode splitting. The angular dispersion of the GMR-MDM structure is reported in Figure 2c, showing an anti-crossing behavior in the S-polarization reflectance map, when the MDM mode overlaps with the GMR mode. The anticrossing of the modes in the GMR-MDM system is centered at an angle of incidence θ in = 27 o , with two hybridized modes that have bonding and antibonding characteristics. [10] The optical response of the GMR-MDM system manifests a strong dependence on the side from which it is probed. If the reflectance is measured from the GMR side (see Figure 2c), both the GMR and the MDM modes are present in the spectra. On the contrary, when impinging from the MDM side, the filtering effect of the MDM attenuates the GMR modes lying far from the MDM resonance, and only those tuned to the MDM resonances are visible (see Figure 2d). [1,27] Therefore only the modes that hybridize with the MDM resonances appear in the reflectance spectra when the system is probed from the MDM side.
The S-polarization reflectance spectra for all three structures, at the angle θ in = 27° where the strong coupling occurs, have been extrapolated from the maps of Figure 2 and are shown in  Table 1.
The S-polarization reflectance spectrum of the GMR-MDM system at θ in = 27° has two minima at 623 nm (High-Energy mode -HE, Figure 3c) and 640 nm (low-energy mode -LE, Figure 3c). The two modes present in the reflectance curve of the GMR-MDM structure are obtained by Gaussian fits and shown in Figure 3c with dashed lines (dark red for the LE and blue for the HE). To gain deeper insight into the spatial characteristics of hybridized modes, we calculated the electric field (E Z ) at the resonance frequencies via finite element method (COMSOL) simulations. The field profiles of the HE and LE are shown in the inset of Figure 3c, respectively. From the electric field profile (E Z ), we can see that the optical modes are confined in the dielectric layer of MDM and around the grating waveguide of the GMR structure. Interestingly, we observe different symmetries of the electric field polarity in the grating waveguide for LE and HE modes that resemble bonding and antibonding modes. Plotting the electric field amplitude at the bottom the GMR grating (white dashed line shown in electric field color map), we find also an E z field distribution in the x-y plane that resembles bonding (LE) and antibonding (HE) character. [28]

Strong Coupling Between MDM and GMR Modes
The coupling between MDM and GMR modes can be modeled in the framework of the classic two-oscillators [26] interaction Hamiltonian that, for our case, can be expressed as reported in Equation 1.
Here E MDM and E GMR represent the energy of the first and second oscillator, associated to the MDM and GMR modes, respectively. γ MDM and γ GMR are the linewidths of the resonant modes. The parameter ћΩ is the energy gap between MDM and GMR mode at θ in = 27°, thus at the angle at which the unperturbed MDM and GMR modes coincide in energy.
Adv. Optical Mater. 2023, 11, 2202876 The occurrence of the strong coupling between MDM and GMR modes in the GMR-MDM structure is analyzed in Figure 4. In particular, we provide a comparison between i) the theoretically calculated angular dispersion of both the unperturbed GMR (dashed orange line) and ii) the MDM structure (dashed green line), iii) the experimentally measured modes of the coupled GMR-MDM structure (red diamonds), and iv) the eigenvalues of the Hamiltonian expressed in Equation 1 (blue lines) (See Figure 4a).
As shown in Figure 4a, the angular dispersion of the unperturbed GMR would cross that of the unperturbed MDM at θ in = 27°. This mode crossing is clearly avoided by the experimentally measured modes of the GMR-MDM structure. The energy splitting calculated at the anti-crossing point (θ in = 27°) is ћΩ = 50 meV. The very good agreement between the experimentally measured modes of the GMR-MDM structure and the eigenvalues of the Hamiltonian of Equation 1 confirms the strong coupling. Another quantitative way to confirm the occurrence of strong coupling is to verify that ћΩ > (γ MDM + γ GMR )/2. [29] In our case, we have ћΩ = 50 meV, is satisfied. The mixing of the GMR and MDM modes in the coupling regime can be quantified by the Hopfield coefficients, which can be calcu-lated by solving the eigenvector of Equation 1 as detailed in the ref. [30,31] Figure 4b,c display the Hopfield coefficients related to the HE and LE branches that confirm the strong hybridization at the anticrossing point.

Coupling Strength Control
As in the case of two coupled MDM cavities, [10] also in the GMR-MDM system the coupling strength can be controlled by tuning the thickness of the central metal layer connecting the GMR and the MDM. Figure 5 shows the reflectance for GMR-MDM systems with three different metal layer thicknesses: t tm = 40 nm (Figure 5a), 30 nm (Figure 5b), and 20 nm (Figure 5c). Two effects can be appreciated: the increase of the energy splitting with decreasing t tm , which stems from more efficient energy exchange through thinner metal layers.
The second effect is a gradual red shift of the central wavelength of the anticrossing with decreasing thickness of the central metal layer, which leads to an increase in anticrossing angle from 27 o to 33 o . This behavior can be understood by the redshift of the cavity mode in the MDM structure, when the thickness of the top Ag layer is reduced with respect to the bottom one (see supporting information section S4). The resulting lower energy of the unperturbed MDM mode results in a redshifted anticrossing point, and since the energy dispersion of the GMR mode is not changed significantly by the change in metal layer thickness, the anticrossing occurs at larger angles. The angle-dependent reflection maps in Figure 5d-f for t tm = 40 nm, 30 nm, and 20 nm, respectively, confirm this behavior, which allows to finely engineer the coupling strength between the GMR and the MDM, and to tune the spectral position of the two hybridized modes.
Another way to gain control of the hybridization is by keeping the thickness of the metal layer fixed and changing the   Table 1. The insets of (c) report the electric field profiles of both hybridized resonant modes of the GMR-MDM structure at 623 nm and 640 nm calculated by COMSOL simulations. The bonding (LE) and antibonding (HE) field profile is shown along the white dashed line, thus at the bottom of the GMR grating. thickness of the dielectric spacer of the MDM cavity. By reducing the thickness of the Al 2 O 3 layer of the MDM cavity, the MDM resonance blueshifts, and therefore interaction with GMR is moved to smaller angles of incidence. One interesting case is when the MDM resonance is tuned close to the frequency of the crossing of the two GMR branches at zero angles of incidence. The GMR is highly reflective at this crossing point, and therefore the MDM mode cannot be excited with light at normal incidence from the GMR side. However, with under excitation from the MDM side, the mode is present at zero angle, even with reduced line width compared to larger angles. The related simulations of the angular dispersion of the reflectance are reported in Section S5 in the Supporting Information.

Polarization-Dependent Hybridization of the GMR-MDM Modes
The GMR-MDM structure manifests the capability to switch in and out of the strong coupling by simply changing the polarization of the incident light. This results from the strong dependence of the GMR modes on the incident polarization. We note that coupling of the same kind of oscillators typically does not lead to polarization dependence of the hybridization (Section S6 in the Supporting Information). To showcase the switching effect, we also investigated the P-polarization behavior of both the unperturbed GMR and the composite GMR-MDM system. The S-polarization angular dispersion of the unperturbed GMR system has been already reported in Figure 2b. The P-polarization response is shown in the reflectance maps of Figure 6a (RCWA simulations are displayed in the red panels while experiments are in the blue panels). The angular dispersion of the reflectance of the GMR-MDM structure is depicted in Figure 6b, where no mode hybridization is observed in the P-polarization. This happens, because for P-polarization the GMR resonator manifests no resonance in the spectral range where the MDM mode occurs (600 nm to 650 nm). Only weak-intensity higher-order harmonics are present in Figure 6a, whose contribution to mode coupling is negligible.
The P-polarization reflectance at θ in = 27° is reported in Figure 6c for the unperturbed MDM cavity (dashed red line), the GMR (dashed blue line), and for the GMR-MDM system (solid black line). A monotonically increasing reflectance is detected for the unperturbed GMR, confirming the absence of resonances in this spectral range for P-polarization. On the contrary, a single dip in reflectance is found at ≈633 nm for both the unperturbed MDM and the GMR-MDM system. This indicates that the GMR-MDM structure exhibits only the mode of the MDM, and no strong coupling is present at this angle and in this spectral range for P-polarization. This is in stark contrast to the S-polarization discussed in Figure 2 to Figure 4, where a clear mode splitting occurs, as highlighted in Figure 6d. Here, a single minimum in reflectance is visible for both the unperturbed GMR and MDM cavity, while splitting into two minima is observed for the coupled GMR-MDM architecture. Therefore, the anisotropy induced by the linear grating of GMR-MDM structure can be used as a polarization-dependent switch, for example by operating at the HE resonance at 623 nm, where a change in reflectance from 0.2 to 0.8 can be obtained by rotating the linear polarization by 90° (see supporting information section S7 for details).

Conclusions
We fabricated coupled GMR-MDM devices and demonstrated that their mode splitting follows the physics of two coupled oscillators. The different geometries and properties of the two coupled cavities bring additional parameters into play that can be used to control the response of such a photonic device: the color filter functionality of the MDM cavity leads to marked dependence on from which side (top or bottom) the GMR-MDM resonator is excited, and the uniaxial in-plane anisotropy of the GMR structure enables polarization control of the mode splitting. Therefore, GMR-MDM optical cavities provide a highly appealing platform for photonic devices and circuits  that enables optical switching and multiplexing between different resonant modes by readily accessible external parameters like the linear polarization of the incident light. Such external control of spectral reflectance is a key property for light modulation in photonic transistors, light valves, and optical switches. Furthermore, these devices can be fabricated as thin films with less than a micrometer thickness that can be integrated into a large range of current optoelectronic technologies.

Experimental Section
Fabrication of MDM and GMR Structures: The Metal-Dielectric-Metal nanocavities were fabricated, using an electron-beam evaporator (Kurt J.Lesker PVD 75), onto glass substrates with thickness of 500 µm that were previously thoroughly cleaned by Acetone, IPA, and oxygen plasma. First, a silver layer of 40 nm was deposited at a rate of 0.3 A° s −1 , followed by 150 nm of Al 2 O 3 at a rate of 1 A° s −1 . Then, a second layer of Ag of 40 nm was deposited at a rate of 0.3 A° s −1 .
For fabricating the GMR, a Ag layer of 40 nm at a rate of 0.3A° s −1 was deposited on a glass substrate, followed by 120 nm of TiO 2 at a rate of 1 A° s −1 , using an electron-beam evaporator. The sample is then removed from the evaporator, and PMMA (polymethyl methacrylate) was spin-coated at 1800 rpm to obtain a film of 150 nm thickness. Electron-beam lithography was performed using a RAITH 150-2 machine. A grating pattern with periodicity of 310 nm and fill factor of 0.6 was defined on the PMMA with an e-beam of dosage 300 µC cm −2 . The pattern is then developed in a solution of 1:3 of Methyl Isobutyl Ketone (MIBK) /Isopropanol (IPA) for 20 s. A layer of TiO 2 with thickness of 60 nm was deposited on the patterned substrate using the electron-beam evaporator. Finally, lift-off of the PMMA was done in Acetone at 50 °C for 10 min, followed by 5 min of ultrasonication.
For GMR-MDM structure, the two fabrication processes were combined by first fabricating the MDM on the glass substrate, followed by the fabrication of the patterned TiO 2 layer as described above.
Spectroscopic Ellipsometry: A Vertical Vase ellipsometer by Woollam was used to measure the dispersion of the samples. S-and P-polarized reflectance in the wavelength range of 300-900 nm with a step of 3 nm were measured at different angles. A step of 2° in angle was used to get a smooth plot, and all the spectra were normalized to the intensity of the Xe lamp.
Simulations: All the numerical computations were performed by RCWA method, using commercially available software, RSoft Diffract MOD module from Synopsys Inc.. N = 10 harmonics have been taken in a transverse direction, and an index resolution of 2.38 nm was chosen for all cases. The dielectric constants of the materials used in these computations are provided in the supporting information Section S2. The dielectric constants were extracted from the ellipsometry Here, A i corresponds to the amplitude, µ i to the central wavelength, and σ i to the linewidth of the i th oscillator. After fitting the experimental data, the optical constants n, k were extracted from the model.
The electric field profile for the coupled GMR-MDM structure and for different polarization were calculated by a finite element method with COMSOL Multiphysics. The refractive index of the materials used in the simulation were retrieved from the measured ellipsometry data. Perfectly matched layers were used as boundary conditions for top and bottom, and continuity periodic conditions were fixed at the lateral sides of the simulation region. A free triangular geometry mesh was used to model whole structure with a maximum element size of 2 nm.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.