1. Introduction

Perfect absorbers (PAs) have aroused extensive research interest due to the ability to achieve near-unity absorbance of electromagnetic waves [1–9]. As a representative type, metamaterial perfect absorber (MPA) was first demonstrated in 2008 in the microwave region [10]. High degree of tunability and flexibility in design makes MPAs attractive for engineering perfect absorbers with tailored absorption characteristics over specific frequency ranges. MPAs are typically designed by employing a metal-insulator-metal (MIM) configuration [11–14], which is composed of a top metallic subwavelength array and a bottom continuous metallic film separated by a thin dielectric spacer. In this structure, the electric resonance formed by the top subwavelength nanostructures and the magnetic resonance formed by the anti-parallel current of the upper and lower metal layers can be independently manipulated to achieve impedance matching between the device and free space, leading to suppressed reflectance up to zero. Due to the bottom metallic film prohibiting any transmission, perfect absorption can be achieved. MPAs have been demonstrated in a number of practical applications [15–17], including thermal emitters [18,19], photodetection [20–22], solar photovoltaic [23,24], refractive index sensing [25–28], and surface-enhanced spectroscopy [29–32], especially surface-enhanced infrared absorption (SEIRA) spectroscopy [31,32]. MPAs are good candidates for SEIRA applications [33,34], such as the detection of a variety of molecules, due to flexible working wavelength design and strong near-field enhancement. In mid-infrared region, the wavelength of MPA can be well designed to match molecular vibrations which are linked to crucial functional groups, chemical bonds, as well as molecular configuration [34]. Therefore, the vibration signals of molecules located in the near-field of MPA are enhanced by orders of magnitude with unprecedented sensitivity [35].

Generally, molecular fingerprints often contain multiple vibrational bands in mid-infrared range. Due to the limitation of bandwidth, single-band MPA cannot adequately detect molecular fingerprints to identify molecular species unambiguously. Therefore, MPAs with dual- or multi-band characteristics shows great potential in SEIRA applications. Several dual-band MPAs of MIM structure have been reported for SEIRA applications, such as asymmetric cross antenna arrays [36], uniform arrays of multi-resonant elements [37,38], and single-sized nanodisk arrays [39]. However, it is worth noting that the top nanostructures of these MIM structures are all planar structures, resulting in the enhanced electric field being predominantly confined within the structures. Consequently, the sensitivity of sensors based on planar MIM structures is limited due to only a small amount of exposed near-fields (hotspots) overlapping with the target analyte. In contrast, complementary plasmonic arrays are commonly employed for achieving refractive index sensing and surface-enhanced spectroscopy [40–45], as the majority of excited hotspots are exposed to the surroundings. However, achieving perfect absorption is challenging for complementary plasmonic arrays, especially in dual- or multi-band perfect absorption. If the advantages of both structures are combined to design dual-band or multi-band perfect absorbers, it would be a highly desirable approach for achieving highly sensitive refractive index sensing and SEIRA applications.

In this work, we demonstrate a quasi-three-dimensional dual-band MPA with a superior spatial overlap between the exposed hotspots and the analyte, resulting in high sensitivity for simultaneous detection of multiple molecular vibrations. The proposed dual-band MPA consists of cross-shaped coupled complementary plasmonic arrays separated from an optically thick gold film by a patterned Si spacer, which is experimentally proven to achieve near perfect absorption of dual resonances (98.1% and 98.7%). The two plasmonic resonances correspond to the electric dipole-like mode of cross antenna array and the magnetic dipole-like mode of cross hole array, respectively, and can be independently tuned by changing the length of the two cross branches of the complementary arrays. The hotspots of the two resonances are mainly distributed in the vertical gap between the elevated cross antenna and its complementary structure where is easily covered by the analyte. Combined with the unique distribution of large exposed electric field, our dual-band MPA device is highly suitable for multispectral molecular sensing. A 12 nm polymethyl methacrylate (PMMA) film is spin-coated onto the device as an analyte for sensing performance characterization. The sensitivity in refractive index sensing is quantified as an 11.8 nm resonance shift per 1 nm polymer thickness. Moreover, the C = O and C-H vibrational bands of PMMA moles are simultaneously enhanced, and the anti-crossing behavior resulting from the coupling between C = O vibration and plasmonic resonance is observed, with a theoretically calculated coupling strength of 2.7 meV.

2. Device design, fabrication, and characterization

Figure 1(a) shows the schematic illustration of the proposed dual-band MPA unit, which is composed of the top cross-shaped complementary plasmonic arrays and an optically thick continuous gold film separated by a patterned Si spacer. When the dual-band MPA is illustrated by vertically incident polarized light with the direction of the electric field parallel to one branch of the cross-shaped complementary arrays, two resonance modes can be excited simultaneously [46]. One is the electric dipole-like resonance mode of the cross antenna array. Due to the orientation of the polarized light parallel to one of the branches of the raised cross antenna, induced charges accumulate at both ends of the branch, resulting in an electric dipole. The other resonance mode is the magnetic dipole-like resonance of the cross hole array. In this case, the polarized light is perpendicular to one of the branches of the cross hole, inducing charges at the edge of the aperture branch, leading to a magnetic dipole. More importantly, due to the difference in effective refractive index, the frequency positions of the two resonances are different. In the designed MIM configuration, the ground continuous gold layer can not only prevent transmission, but also combine with the top complementary plasmonic arrays to achieve the impedance matching required for zero reflection. Therefore, it is possible to achieve dual-band perfect absorption.

 

Fig. 1. (a) Schematic illustration of the dual-band MPA. (b) Simulated spectra of the dual-band MPA with two perfect absorption resonances F1 and F2. (c) Top view SEM image of the fabricated dual-band MPA. Inset is the enlarged side view SEM image of the dual-band MPA unit cell. (d) Measured spectra of the dual-band MPA. The dashed line in (d) represents the simulated reflectance spectrum. Structural parameters: ${L_ \bot } = {L_{||}} = 800\; \textrm{nm}$, $W = 200\;\textrm{nm}$, $p = 1000\;\textrm{nm}$, ${H_\textrm{g}} = 135\;\textrm{nm}$, ${H_\textrm{t}} = 130\;\textrm{nm}$, the thickness of Au cross and its complementary structure is 35 nm, and the thickness of the bottom continuous gold film is 100 nm.

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In our device, the elevated cross antenna and its complementary structure have the same thickness of 35 nm, which is convenient for device fabrication. The ground continuous gold film has a thickness of 100 nm, preventing the penetration of infrared light. The period of the complementary plasmonic arrays is fixed at 1000 nm in both lateral directions. Here, we first consider the case ${L_ \bot } = {L_{||}}$, and the case ${L_ \bot } \ne {L_{||}}$ will be discussed later. By systematically optimizing cross length $L\; ({{L_ \bot } = {L_{||}}} )$, cross width W, the gap ${H_\textrm{g}}$ between cross antenna and its complementary structure, and the gap ${H_t}$ between cross complementary structure and continuous gold film, the two resonances can simultaneously achieve near unity absorption. The simulated reflectance, transmittance, absorbance spectra are shown in Fig. 1(b). The dual-band MPA exhibits two clear absorption peaks with perfect absorption. The corresponding structural parameters are: $L = 800\;\textrm{nm}$, $W = 200\;\textrm{nm}$, ${H_\textrm{g}} = 135\;\textrm{nm}$, ${H_\textrm{t}} = 130\;\textrm{nm}$. The reflectance, transmittance, and absorbance spectra were calculated by the finite difference time domain (FDTD) method. The excitation electromagnetic wave was vertically incident along the negative direction of the z-axis with the electric field direction along the y-axis. Periodic boundary conditions were adopted in x and y-axis direction, and perfectly matched layer was used for the boundary treatment along the propagation directions. The frequency-dependent permittivity of Au was described by the Drude model ${\varepsilon _\textrm{m}}(\omega )= {\varepsilon _\infty } - \frac{{\omega _\textrm{p}^2}}{{\omega ({\omega + i\gamma } )}}$ with ${\varepsilon _\infty } = 9$, the plasma frequency ${\omega _\textrm{p}} = 2\pi \times 2175\;\textrm{}THz$, and the collision frequency $\gamma = 2\pi \times 14.5\; THz$. The relative permittivity of the Si interlayer was chosen to be ${\varepsilon _\textrm{d}} = 11.7$, while the field monitor was set to record the distribution of electric field.

We fabricated the device with a self-aligned process. First, 100 nm Au film and 300 nm Si interlayer were deposited on Si substrate with magnetron sputtering. To improve the adhesion between Au and Si, we deposited 5 nm Ti on the upper and lower surfaces of the Au film, respectively. Next, PMMA film was prepared on Si layer by spin coating and patterned with electron beam lithography (EBL, JEOL JBX-8100FS). After development in MIBK/IPA (1:3) solution, 25 nm Cr was deposited by e-beam evaporation, followed by a lift-off process in warm acetone. Cr patterns were then used as mask in the following inductively coupled plasma (ICP) etching (Oxford PlasmaLab ICP180) to form Si pillar cross array. Cr mask was removed by immersing the sample into the mixed solution of 20% HNO₃ and 20% Ce(NH₄)₂(NO₃)₆. Finally, 3 nm Cr and 32 nm Au were prepared using e-beam evaporation with self-aligned cross-shaped complementary arrays formed automatically. Figure 1(c) shows the scanning electron microscope (SEM) image of the dual-band MPA from the top view. The inset is the enlarged side view SEM image of a unit cell, which indicates the metal cross antenna and its complementary structure are separated from each other. In addition, a few gold nanoparticles are nucleated on the sidewall of the cross silicon pillar, which is formed due to gold surface diffusion on dielectric pillars and gold film surface energy minimization [42].

Figure 1(d) presents the measured reflectance, transmittance, and absorbance spectra. Two absorption bands were observed experimentally with nearly perfect absorption (98.1% of resonance F1 and 98.7% of resonance F2). Due to dimension deviations during fabrication, the frequency positions of both resonances are slightly shifted, and the full width at half maximum (FWHM) of each resonance is slightly larger than the corresponding simulated result. The frequency shifts are primarily attributed to the reduced gap ${H_t}$ between the cross complementary structure and the bottom metal film during the sample fabrication process. The simulated results indicate that as ${H_t}$ decreases, resonance F1 experiences a slight redshift, while resonance F2 undergoes a minor blueshift. The reflectance spectra were collected by Fourier transform infrared spectrometer (Bruker Vertex 70) equipped with an infrared microscope (Bruker Hyperion 1000) with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector. A Cassegrain lens was used as the objective with collimated light beam and effective numerical aperture (NA) of 0.4. Resolution and scan parameters were set to 4 cm⁻¹ and 64 scans in measurement. The reflectance spectra were normalized to Au mirror. Transmittance was zero because no light passes through the bottom continuous metal layer. Therefore, absorbance can be calculated by 1- reflectance.

3. Optical properties of the dual-band MPA

To further confirm the origins of resonance F1 and F2, two additional comparative structures were simulated together with the dual-band MPA structure. One is a similar structure without the cross antenna array, which has a resonance F1’ (Fig. 2(a)-i) with a spectral position close to resonance F1 (Fig. 2(a)-ii). The magnetic field distributions of resonance F1 and F1’ are both antiparallel dipole fields (Fig. 2(b) and 2(d)), indicating that resonance F1, like resonance F1’, also originates from the magnetic dipole-like resonance of the cross hole array. The antiparallel dipolar magnetic field for resonance F1 is perpendicular to the perforated metal film (Fig. 2(f)) since it is generated by current flow around the ends of the cross hole arm symmetric about the y-axis (Fig. 2(j)). The current flow also induces its antiparallel image current in the cross antenna (Fig. 2(h)) due to near-field coupling. Therefore, the electric field of resonance F1 is mainly localized around the two branches of the cross hole (Fig. 2(l)) and at both ends of the branch parallel to the electric field direction of the cross antenna. In contrast, the electric field of resonance F1’ is only concentrated around the cross hole branch perpendicular to the direction of the electric field. The difference between the electric field distributions for resonance F1 and F1’ is mainly due to the near-field coupling between the cross hole and the cross antenna. As a result, a large amount of local electric field is concentrated in the vertical gap of the complementary plasmonic arrays (Fig. 2(n)). The near-unity absorption at resonance F1 is not suitable to be explained from the perspective of impedance matching, as the magnetic response between the cross hole array and the bottom metal film is nonexistent or is weak enough to be ignored. However, it can be understood from the point of multiple reflections interference [1,47]. The ground metal film blocks transmission and generates multiple reflections of electromagnetic waves in the dielectric layer. These waves interfere and cancel out the total reflection at the critical coupling condition. The other structure is a similar structure but without a perforated gold film. The structure exhibits a weaker resonance F2’ (Fig. 2(a)-iii) near the dip position of resonance F2 (Fig. 2(a)-ii), but resonance F2’ and F2 exhibit nearly identical dipolar magnetic fields formed between the top cross antenna and the bottom continuous gold film (Fig. 2(c) and 2(e)). The magnetic dipole arises from the induced antiparallel currents in the top cross antenna and the bottom gold film. The result indicates that both resonances come from the electric dipole-like resonance of the cross antenna array. Attributed to the coupling between the cross hole and the cross antenna, antiparallel image current is also generated in the cross hole (Fig. 2(i) and 2(k)). As a result, the dipolar magnetic field for resonance F2 is also parallel to the perforated metal film (Fig. 2(g)). The electric field distributions of resonance F2 and F2’ are almost identical with an electric dipole at the top surface of cross antenna (Figs. 2(m)). The simulated cross-sectional electric field distribution at resonance F2 is described in Fig. 2(o). Similar to resonance F1, there is also an electric field concentrated in the gap of the cross complementary plasmonic arrays with improved enhancement due to the coupling of cross antenna and its complementary structure. The electric dipole and magnetic dipole of resonance F2 can be enable tune the effective permittivity and permeability of the MPA. When the impedance of the MPA matches that of free space, the reflection reduces to zero. Combined with the bottom metal layer blocking transmission, perfect absorption can be achieved. It is worth pointing out that the unique near-field characteristics of the dual-band MPA can significantly increase the spatial overlap between the exposed electric field and the target analyte, potentially leading to improved sensitivity in sensing applications.

 

Fig. 2. (a) Simulated reflectance spectra of the similar structure without cross antennas (i), the dual-band MPA structure (ii), and the similar structure without the perforated gold film (iii). Insets display the schematics of the corresponding structures and electric field enhancement (|E/E0|²) distributions at the top surface of comparative structures. Resonance F1 and resonance F1’ share a similar origin, as do resonance F2 and F2’, which are indicated by the arrows in the figure. (b), (d) Magnetic field distributions for resonance (b) F1’ and (d) F1 at the cross-section across cross center along the x-axis. (c), (e) Magnetic field distributions for resonance (c) F2’ and (e) F2 at the cross-section across cross center along the x-axis. (f), (g) Magnetic field distributions for resonance (f) F1 and (g) F2 at the top surface of perforated gold film. (h), (j) Surface current distributions at the top surfaces of (h) cross antenna and (j) perforated gold film for resonance F1. (i), (k) Surface current distributions at the top surfaces of (i) cross antenna and (k) perforated gold film for resonance F2. (l), (n) Electric field enhancement (|E/E0|²) distributions at (l) the top surface of perforated gold film and (n) the cross-section across cross center along the y-axis for resonance F1. (m), (o) Electric field enhancement (|E/E0|²) distributions at (m) the top surface of perforated gold film and (o) the cross-section across cross center along the y-axis for resonance F2.

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Two resonances achieving perfect absorption simultaneously can be further analyzed theoretically with the couple mode theory (CMT) [48–51]. Due to the continuous metal layer prohibiting light transmission, our dual-band MPA is essentially a one-port resonator. In a one-port resonator with multiple modes, if the FWHM of each mode is much smaller than the frequency difference between adjacent modes, each mode can be studied using the CMT of one-port single-mode resonator model [51]. Figure 3(a) presents the simulated reflectance spectra of the dual-band MPA with the gap ${H_\textrm{g}}$ varying from 90 to 180 nm while other parameters are fixed: $L = 800\;\textrm{nm}$, $W = 200\;\textrm{nm}$, ${H_\textrm{t}} = 130\;\textrm{nm}$. These results imply that two resonances of the dual-band MPA can be analyzed with one-port single-mode resonator model. According to CMT and taking account of energy conservation and time-reversal symmetry [48–50], the reflection coefficient r around resonance frequency ${f_0}$ of such model can be derived from the dynamic equations as in the following,

 

Fig. 3. (a) Simulated reflectance spectra for the dual-band MPA with different vertical nanogap ${H_\textrm{g}}$. ${Q_\textrm{a}}$ and ${Q_\textrm{r}}$ of resonance (b) F1 and (c) F2 for the dual-band MPA with varying ${H_\textrm{g}}$ retrieved from FDTD-simulated spectra. Spectra of reflection phase of resonance (d) F1 and (e) F2 for the dual-band MPA with seven different values of ${H_\textrm{g}}$ calculated from FDTD (solid lines) and CMT (pentagram dash lines).

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Figure 3(b) shows the dependence of ${Q_\textrm{a}}$ and ${Q_\textrm{r}}$ with the gap ${H_\textrm{g}}$ for resonance F1, and Fig. 3(c) shows the result for resonance F2. With the increasing of ${H_\textrm{g}}$, ${Q_\textrm{a}}$ is no significant change for resonance F1, while it slowly increases in a linear manner for resonance F2. In contrast, ${Q_\textrm{r}}$ decreases rapidly for both resonance F1 and F2 as ${H_\textrm{g}}$ increases. The result can be understood from the material properties and electric field distribution. Si dielectric is lossless in simulated structure, and the absorption of the resonator entirely originates from the ohmic loss of the metal. By increasing the height of the silicon pillar, the gap between the cross antenna and its complementary structure can be widened, without significantly affecting the absorption loss. As the gap increases, more local electric field is exposed to the surroundings rather than bound to the structure, resulting in a significant increase in radiation loss. More importantly, resonance F1 and F2 have a common critical value (${H_\textrm{g}} \approx 135\; \textrm{nm}$), where ${Q_\textrm{a}} = {Q_\textrm{r}}$. When two Q values match, perfect absorption is achieved for a resonator, which is called the critical damping condition. Therefore, with the gap ${H_\textrm{g}}$ increasing from 90 to 180 nm, both resonance F1 and F2 transit from the overdamping behavior (${Q_\textrm{a}} < {Q_\textrm{r}}$) to the underdamping behavior (${Q_\textrm{a}} > {Q_\textrm{r}}$).

However, it is difficult to distinguish the overdamping and underdamping behaviors of resonance from the reflectance spectra. Instead, we can distinguish the two behaviors by checking the phase variation range $\Delta \emptyset $ caused by resonance in frequency domain. Figure 3(d) and Fig. 3(e) display the phase spectra of the dual-band MPA with different ${H_\textrm{g}}$. for resonance F1 and F2, respectively. When ${Q_\textrm{a}} < {Q_\textrm{r}}$, the resonance is in overdamping behavior with the phase variation range less than.180°. By contrast, when ${Q_\textrm{a}} > {Q_\textrm{r}}$, the resonance becomes the underdamping behavior, and the phase can achieve a continuous 360° variation from −180° to +180°. Due to the critical transition between overdamping and underdamping behavior, perfect absorption can definitely be realized in our dual-band MPA. The simultaneous realization of perfect absorption by both resonances demonstrates the feasibility of our dual-band MPA design. Interestily, the property of the simultaneous achieving perfect absorption keeps unchanged for different sizes of ${H_\textrm{t}}$ at the same size of ${H_\textrm{g}} = 135\;\textrm{nm}$.

Next, we demonstrate that two resonant wavelengths of the dual-band MPA structure can be independently tuned by properly designing the branch length of the cross-shaped complementary plasmonic arrays. The corresponding measured reflectance spectra are shown in Figs. 4(a)–4(c) by controlling ${\textrm{L}_ \bot }$ only, ${\textrm{L}_{||}}$ only, and ${\textrm{L}_ \bot }$ and ${\textrm{L}_{||}}$ simultaneously with ${\textrm{L}_ \bot } = {\textrm{L}_{||}}$. Resonance F1 undergoes a significant redshift as $\textrm{}{\textrm{L}_ \bot }$ increases, while resonance F2 shows negligible redshift due to the fixed dimension of ${\textrm{L}_{||}}$ at 800 nm. Similarly, resonance F2 also shifts to longer wavelength with the increase of ${\textrm{L}_{||}}$, while resonance F1 exhibits a slight redshift with ${\textrm{L}_ \bot }$ being held constant at 800 nm. Therefore, increasing ${\textrm{L}_{||}}$ and ${\textrm{L}_ \bot }$ simultaneously can cause both resonances to experience a distinct redshift together. Furthermore, color contour plot of simulated reflectance spectra are displayed in Figs. 4(d)–4(f) when changing ${\textrm{L}_ \bot }$ only, ${\textrm{L}_{||}}$ only, and ${\textrm{L}_ \bot }$ and ${\textrm{L}_{||}}$ simultaneously with ${\textrm{L}_ \bot } = {\textrm{L}_{||}}$. The resonance position and reflection intensity of the simulated spectra are almost consistent with the measured spectra. The independent adjustment of the resonant wavelength can be realized by simply changing the length of one branch. The measured and simulated results also confirm that resonance F1 is magnetic dipole-like resonance caused by cross hole array, while resonance F2 is electric dipole-like resonance caused by cross antenna array. It is worth noting that the two resonances maintain nearly perfect absorption in tuning resonant wavelength. The flexible tunability of two plasmonic resonances is highly advantageous for applications that simultaneously recognize multiple molecular fingerprints.

 

Fig. 4. Experimental reflectance spectra of the dual-band MPA when changing (a) ${L_ \bot }$ only, (b) ${L_{||}}$ only, and (c) ${L_ \bot }$ and ${L_{||}}$ simultaneously with ${L_ \bot } = {L_{||}}$. Inset located at the upper part of every figure shows the parallel or perpendicular relationship between the electric field direction and the changing cross branch. Inset in the lower right corner of (a) shows SEM image of the fabricated samples with ${L_ \bot } = 500\; \textrm{nm}$ and ${L_{||}} = 800\; \textrm{nm}$. Color contour plot of simulated reflectance spectra when changing (d) $\textrm{}{L_ \bot }$ only, (e) ${L_{||}}$ only, (f) ${L_ \bot }$ and ${L_{||}}$ simultaneously with ${L_ \bot } = {L_{||}}$.

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4. Refractive index sensing of PMMA film

We first investigated the performance of dual-band MPA as the refractive index sensor. The mechanism of refractive index sensing is that an increase in the dielectric constant (refractive index) near the exposed electric field leads to an increase in capacitance, causing a resonance redshift. This can be understood through the RLC theory [52]. A 12 nm thick PMMA film was spin coated on dual-band MPA devices with ${L_ \bot } = {L_{||}}$. The thickness of PMMA was characterized by a spectroscopic ellipsometer (Horiba, Uvisel 2). After coating the dual-band MPA with PMMA, the resonances exhibit a notable red shift. This shift can be attributed to the higher refractive index of PMMA compared to air, leading to an increase in the effective refractive index. Figure 5(a) shows the measured reflectance spectra of three representative devices with different cross lengths before and after PMMA coating. For devices with cross length of 720 nm, 800 nm, and 880 nm, the spectral shifts of resonance F1 are 25 cm⁻¹ (67.3 nm), 32 cm⁻¹ (99.9 nm), and 34 cm⁻¹ (131.1 nm), and the spectral shifts of resonance F2 are 32 cm⁻¹ (53 nm), 21 cm⁻¹ (41.1 nm), and 20 cm⁻¹ (45 nm), respectively. Additionally, a strong dip overlapping with resonance F1 is observed, which is the C = O vibration of PMMA molecule and will be discussed in the subsequent section.

 

Fig. 5. (a),(c) Experimental (a) and simulated (c) reflectance spectra of three representative devices with different cross lengths before (dashed lines) and after (solid lines) PMMA coating. (b),(d) The measured (b) and simulated (d) results on the variation of resonance shift with cross length. Inset in (d) is cross-sectional schematic diagram of the device after PMMA coating.

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To determine the sensitivity of the dual-band MPA in refractive index sensing, we measured the reflectance spectra of the PMMA-coated dual-band MPA with cross length L ranging from 680 to 920 nm. The resonance shift against cross length is shown in Fig. 5(b), which is calculated by $\Delta \lambda = {\lambda _{\textrm{PMMA}}} - {\lambda _\textrm{B}}$, where ${\lambda _\textrm{B}}$ and ${\lambda _{\textrm{PMMA}}}$ are the resonance wavelengths of the bare and coated dual-band MPA, respectively. The resonance shift of resonance F1 increases rapidly with the increase of cross length, while that of resonance F2 does not show a significant increase due to measurement deviation. This can be understood from the perspective of dipole antenna theory $\Delta \lambda = \kappa \Delta {n_{\textrm{eff}}}L$ [42]. Compared with resonance F2, resonance F1 is more likely to achieve larger resonance shift, especially for longer cross length. The maximum resonance shift of resonance F1 is 141 nm (32 cm⁻¹). Based on the resonance shift result, the sensitivity of the dual-band MPA device is obtained with a 11.8 nm shift per 1 nm PMMA thickness, which is comparable to that of single molecule layer sensors [53,54].

Then, we simulated the dual-band MPA device before and after PMMA coating. In the simulation, PMMA was set as a dielectric with a refractive index of 1.49 without vibration absorption. The corresponding results are displayed in Fig. 5(c). The simulated reflectance spectra of dual-band MPA devices shift to longer wavelength after PMMA coating, which are in good agreement with the experimental results. From the simulated reflectance spectra, we can extract the resonance shifts of resonance F1 and F2, as shown in Fig. 5(d). With the increase of cross length, the resonance shifts for both F1 and F2 increase. Moreover, the resonance F1 experiences a more significant shift in wavelength, which is approximately consistent with the experimental results. The maximum spectral shift value of F1 is very close to the experimental value, indicating that the model and material properties we set up in the simulation are reasonable.

5. Vibrational sensing of PMMA molecule

The high tunability of the dual-band MPA resonance enables the simultaneous detection of two or more molecular vibrations. PMMA has multiple absorption bands, with C = O and C-H bands separated by more than 1200 cm⁻¹. Here, a dual-band MPA is well designed to match and detect the C = O and C-H vibrational bands. Figure 6(a) shows the reflectance spectrum of the dual-band MPA coated with PMMA. The characteristic vibrations of C = O and C-H are observed on the reflectance spectrum, which are marked with vertical dashed lines. The sharp dip at 1720cm⁻¹ corresponds to the C = O stretching vibration, while two weak dips at 2954 cm⁻¹ and 2996 cm⁻¹ are the spectral positions of C-H stretching vibration. The result indicates that the two vibrational bands of PMMA are enhanced by the two plasmonic resonances of the dual-band MPA. In order to clearly show the absorption of two molecular vibrations, the reflection differential spectra are shown in Fig. 6(b) and 6(c), which are calculated from the reflectance spectra of dual-band MPA before and after PMMA coating with a frequency-shifted method [36]. For each resonance, the original resonance ${R_\textrm{B}}(f )$ of the bare dual-band MPA is transformed to $R_\textrm{B}^{\prime}(f )= {R_\textrm{B}}({f - \Delta f} )$ which fairly overlaps with the one of the dual-band MPA coated with PMMA. The differential spectra are obtained by $\Delta R = R_\textrm{B}^{\prime}(f )- {R_{\textrm{PMMA}}}(f )$, where ${R_{\textrm{PMMA}}}(f )$ is the reflectance spectrum of the dual-band MPA after PMMA coating. It can be seen that the intensity of C = O stretching is significantly greater than that of C-H due to its large intrinsic dipole moment. These results indicate that our proposed dual-band MPA is not only suitable for detecting molecular vibrations with weak dipole moment, such as C-H stretching, but also suitable for simultaneous detection multiple molecular fingerprints of target molecules.

 

Fig. 6. (a) Reflectance spectrum of a 12 nm PMMA film coated on a dual-band MPA with ${L_ \bot } = 800\; \textrm{nm}$ and ${L_{||}} = 600\; nm$. Characteristic vibrations of C = O and C-H are marked with vertical dashed lines. Inset is the magnified reflectance spectrum around C-H vibrational band. Reflectance difference spectra of C = O (b) and C-H (c) vibrations. (d) Reflectance spectra of the dual-band MPA coated with a 12 nm PMMA film when changing ${L_ \bot }$ and ${L_{||}}$ simultaneously with ${L_ \bot } = {L_{||}}$. Resonance F1 is tuned through the C = O vibration (1733cm-1) which is marked with a green vertical dashed line. (e) Hybrid modes generated by the coupling between F1 resonance of the coated dual-band MPA and C = O vibration against the coated dual-band MPA resonance. The horizontal green dashed line denotes C = O vibration and the black dashed line with slope = 1 corresponds to F1 resonance of the coated dual-band MPA. Black hollow pentagrams are the extracted F1 resonance positions of the bare dual-band MPA.

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Interestingly, we note that the signal feature of the C = O vibration exhibits an asymmetric Fano-like profile rather than a symmetric Lorentz shape. This indicates the strong interaction between the PMMA molecular vibration and the plasmonic resonance of the dual-band MPA, which is also supported by evidence of a significant shift in the spectral position of C = O relative to its original position (1733cm⁻¹). To further investigate this effect, resonance F1 is tuned through C = O vibration with a series of fabricated samples that change the cross length $L\; ({{L_ \bot } = {L_{||}}} )$. Figure 6(d) shows the reflectance spectra of the corresponding dual-band MPAs after PMMA coating. The shift of C = O vibration is a common phenomenon in the interaction between molecular vibration and plasmonic resonance. Notably, the spectral position of C = O exhibits a completely different shift as the position of the plasmonic resonance changes. For plasmonic resonance greater than 1733cm⁻¹, C = O molecular vibration has a red shift, while for plasmonic resonance less than 1733cm⁻¹, C = O molecular vibration has a blue shift. In particular, the behavior similar to Rabi splitting is observed when the plasmonic resonance matches the C = O vibration.

In order to quantitatively analyze the hybrid interaction between molecular vibration and plasmonic resonance, we plotted the resonance frequency of the hybrid state against the resonance frequency of the PMMA-coated dual-band MPA which was obtained from the resonance frequency of the bare device using the frequency-shifted method mentioned earlier. As shown in Fig. 6(e), the phenomenon of mode splitting and anti-crossing is observed, which exists in different coupling systems based on plasmonic resonance [55–58]. The blue solid circles represent a hybrid state with higher energy, while the red ones correspond to a hybrid state with lower energy. The asymptotes of the hybrid modes correspond to the C = O vibration (horizontal green dashed line) and the plasmonic resonance (black dashed line with slope = 1) of the PMMA-coated dual-band MPA, respectively. Black hollow pentagrams in the figure are the extracted F1 resonance positions of the bare dual-band MPA, and the connecting line between them is not parallel to the diagonal dashed line. The result indicate the low-frequency plasmonic resonance corresponds to a significant resonance shift of the device after PMMA coating, which is consistent with the conclusion drawn from the refractive index sensing section.

Similar to the reported coupling effect of plasmonic resonance-molecular vibration [36,38,39], the Hamiltonian of our interaction system can be expressed as:

By substituting ${E_ + }$, ${E_ - }$, $E_1^{(1 )}$, and ${E_{\textrm{C} = \textrm{O}}}$ into Eq. (6), the coupling strength was calculated as 2.7 meV (21.5 cm⁻¹). Therefore, the hybrid state energy as a function of $E_1^{(1 )}$ can be plotted from Eq. (5) with the calculated coupling strength value, as shown in Fig. 6(e). The experimental values of the hybrid state energy agree well with the calculated values (blue and red solid curves). The mode splitting and anti-crossing behavior indicate that our dual-band MPA is a great platform for enhancing light-matter interaction.

The application of dual-band MPA in multispectral molecular sensing has been reported previously [36]. However, in contrast to previous work where the electric field is mainly confined within the plasmonic structure itself (the dielectric layer), large amount of field-enhancing hotspots are exposed to the surroundings in our device. Besides, apparently smaller period in our device (by a factor of 1/2.3) and hence higher hotspot density (about 5 times) contribute to the improvement of sensing performance. As a result, our device demonstrates sensing performance in both refractive index sensing and molecular vibrational sensing with larger coupling strength (mode splitting) than previous work.

6. Conclusions

We propose a dual-band MPA utilizing coupled complementary plasmonic arrays. Compared with traditional planar MIM absorbers, our devices offer enhanced near-field exposure to the surroundings, primarily concentrated within the vertical gap between the coupled complementary plasmonic arrays. This enhancement leads to a superior spatial overlap between hotspots and the analyte, resulting in high sensitivity for SEIRA spectroscopy. Based on these unique optical properties, the device demonstrates the ability to detect a 12 nm PMMA thin film, yielding a resonance shift of 11.8 nm per 1 nm of polymer thickness. Additionally, the C = O and C-H vibrational bands of PMMA moles are simultaneously enhanced with a well-designed dual-band MPA. Furthermore, the coupling between plasmonic resonance and molecular vibration also leads to mode splitting and anti-crossing behavior. The design idea of the dual-band MPA based on coupled complementary nanostructures is applicable to various shapes of nanostructures such as nanodisk, nanobar, nanosquare, split ring, bowtie and so on. The high sensitivity of our device in refractive index sensing and molecular fingerprint recognition indicates its promising prospect in biosensing, gas sensing, and other applications of light-matter interaction.