1. Introduction

There has been considerable interest in one of the artificial optical properties: perfect absorption. By using multilayered films or subwavelength-scale structures, perfectly absorbing metamaterials can produce nearly 100% absorption at pre-designed resonant wavelengths. The first perfect absorber was proposed by Landy et al. [1] and experimentally verified using wire structures in the RF range. This concept was subsequently extended to optical frequencies. Perfect absorbers are usually realized based on metal-dielectric-metal (MDM) stack [2–5]. The micro- or nanostructures of the topmost metallic layer are separated from an optically thick metallic substrate by a dielectric spacer. This stack configuration can suppress both reflected and transmitted waves. Its absorption mechanism can be described in terms of impedance matching [6,7] and destructive interference [8,9]. Specifically, due to the simultaneous existence of magnetic dipole and electric dipole resonances inside the MDM structure, backscattering and in-plane scattering can be suppressed by adjusting the material and structural parameters, thus realizing zero reflection; meanwhile, the incident field and the scattered field interfere destructively, thus achieving zero transmission. At this time, the structural impedance matches the one of free space, and the system reaches critical coupling.

Perfect absorbers constructed by subwavelength-patterned MDM structures have great potential in the mid-infrared (MIR) wavelength range (typically 2-30 µm), where all biological or mechanical substances will emit thermal radiation. At the same time, MIR resonances overlap with the characteristic vibrational fingerprint of the molecule, which can be used to enhance the interaction between the interested molecules and the resonant structures. Subwavelength-patterned MDM structures, being important geometric configurations for studying the interaction of various optical modes, can support asymmetric Fabry-Perot (FP) resonances [10,11], localized surface plasmon (LSP) resonances [12,13], gap plasmon [14,15], and other photonic modes. MDM structures with perfect absorption characteristics at a specific wavelength have applications including selective thermal emitters [16], thermal detectors [17], biosensors [18], anti-reflection coatings [19], stealth devices [20], focal plane array thermal imaging [21], and MIR on-chip spectrometers [22].

In the MIR waveband, due to the absolute real part of the dielectric constants of traditional noble metals (gold, silver, etc.) being too large, its optical properties resemble those of a perfect electric conductor (PEC) [23] and cannot constitute a composite material with the dielectric, so it is difficult to observe the unique characteristics of composite materials by using noble metals. Recently, highly doped semiconductors (HDSCs) have been widely studied in the field of plasmonics [24–27]. HDSCs, which are alternative materials to noble metals in MIR, exhibit tunable optical properties, and their plasma frequency or epsilon-near-zero (ENZ) point can be modulated by a variety of technique including doping, electrical/optical pumping, etc. Among various HDSCs, group-IV n-type antimony (Sb)-doped germanium (Ge) is chosen as our target material, since it has significant advantages compared to other ones: (1) Group-IV n-type semiconductor is a more pure plasmonic material [28,29] (than p-type semiconductor and III-V n-type semiconductor) as there is almost no inter-band transition and no dipole active optical phonon in MIR (which might complicate the MIR plasmon behavior and accelerate the process of light-exciton interactions). Accurate complex permitivities near ENZ point can be obtained by fitting the reflectivity of a single-layer film with the Drude-Lorentz model, paving a way to study the peculiar characteristics of ENZ materials; (2) Molecular-beam-epitaxy (MBE) low-temperature Sb-doping technique [30,31] can achieve simultaneously a wide tuning range of plasma frequency (as high as 2395 cm-1) and low damping loss, beneficial for the field of metamaterials, narrow-band perfect absorption, biosensing, tunable thermal radiation, etc. (3) Compatibility with silicon-complementary metal oxide semiconductor (CMOS) process is the key to achieving high-integration on-chip optoelectronic systems [32].

In this work, we have demonstrated a MIR perfect absorber composed of group-IV n-type Sb-doped Ge in an all-semiconductor composite structure. Starting from the classical multilayered thin-film reflection theory, we have explored the absorption resonances from air-dielectric-metal (ADM) stacking layers to as-grown MDM structure by means of phase accumulation and effective reflection index. The topmost metallic layer of the as-grown MDM structure is then etched into subwavelength periodic ribbons, and the plasmonic behavior of the subwavelength-patterned structure is switched by altering the polarization state. In TE polarization, the dual-band absorptions come from the first-order and third-order asymmetric FP resonances, and the thickness of the dielectric is less than 1/4 of the optical wavelength due to the existence of non-trivial reflection phase shift; in TM polarization, the strong multi-band absorptions arise from the joint action of asymmetric FP interference and plasmonic resonance. While the resonance frequency of the plasmonic mode is modulated simultaneously by the horizontal (ribbon width) and vertical (spacer layer thickness) profile; that of the asymmetric FP mode is tuned merely by the vertical geometric parameters. For a preferred ribbon width, the plasmonic mode and the asymmetric FP mode can be tuned to be strongly coupled, demonstrating the subwavelength-patterned MDM structure as an ideal platform for studying mode-coupling.

2. Experimental section

2.1 Growth and fabrication

The highly doped/undoped as-grown germanium (Ge) multilayer structure is grown on a silicon (Si) substrate via molecular beam epitaxy (MBE) system. The undoped spacer layer is sandwiched between two heavily doped layers, forming a metal-insulator-metal (MIM) structure. Antimony (Sb) is used as the n-type dopant. The thickness of the Ge:Sb bottom layer (as a mirror) is 1 µm, which is thick enough to suppress the transmission of the incident light (T = 0) at the frequency below plasma edge. By optimizing growth conditions, the carrier concentration of the Ge:Sb layers can be as high as 1.5 × 10²⁰ cm^-3, extending the plasma frequency up to ∼2587 cm^-1. Detailed growth conditions for these heavily doped layers are described in previous works [30].

A periodic set of highly doped Ge ribbons are patterned on top of the topmost doped layer by e-beam lithography and inductively coupled plasma reactive ion etching technique. Negative maN-2403 resist is used to define the structure geometry with optimized exposure doses for specific stripe widths, that is dose of 650µC/cm² for Sample A-B, and dose of 850µC/cm² for Sample C-E. The top doped layer is etched using mixtures of C₄F₈ and SF₆ plasma (ratio of 1:1), and timed to stop at an etching depth of 100 nm.

2.2 Optical measurements

The reflectance spectra of the subwavelength-patterned MDM structures are measured in a reflection mode using a Hyperion 1000 infrared microscope connected to an external port of a Fourier transform infrared spectrometer (Bruker, Vertex 70). By motorize X-Y-Z sampling stage with high accuracy (<0.1 µm), the incident infrared light is focused onto each periodic structure by a 15× Cassegrain objective. A gold mirror is used as a reference to normalize the reflection intensity.

2.3 Numerical simulations

The optical response of the subwavelength-patterned MDM structures is calculated by finite-difference time-domain (FDTD), discontinuous Galerkin time-domain (DGTD) and Rigorous Coupled-Wave Analysis (RCWA) methods. To extract the complex permittivity of the heavily doped Ge for simulations, a 1 µm thick heavily Sb-doped Ge film is additionally grown on a Si substrate, and its reflectance spectra is measured and fitted with Drude-Lorentz model (See Fig. S1 in Supplement 1 for detailed fitting methods). The real and imaginary part of permittivity is shown in Fig. S1. The subwavelength-patterned MDM structures are illuminated by plane wave with either TE or TM polarization in a spectra range of 2∼24 µm.

3. Results and discussion

As mentioned in optics textbooks [33,34], when light incidents from air (n₁= 1) onto a dielectric film with thickness h₂ and refractive index n₂, deposited on a metallic substrate with complex refractive index n₃, the reflection coefficient can be represented by equations:

According to Snell’s law, the angle ${\theta _i}$ is related to the incident angle ${\theta _1}\; $ and $\; {\theta _i} = {\sin ^{ - 1}}({\sin ({{\theta_1}} )/{n_i}} )$. The reflectivity is described by $R = {|r |^2}.$

In Fig. 1(a), one of the special cases occurs if the substrate is a perfect electric conductor (PEC), which is an ideal metal with a very large plasma frequency. Given a dielectric film, air and PEC, a lossless asymmetric Fabry-Perot (FP) cavity is formed. As there is no loss in the cavity and the substrate is opaque, so the reflectance R = 1. This configuration named Gires-Tournois etalon [35], is used as a phase-shifting element with a π phase difference at the reflection interface.

 

Fig. 1. Absorption resonances for four typical layered structures. (a) Schematic of a perfect electric conductor (PEC)/low-loss metal and a lossless dielectric. For the case of PEC, as there is no loss in the cavity and the substrate is opaque, the reflectance R = 1. It can be used as phase shifting elements, known as Gires-Tournois etalon. If the PEC is replaced by a low-loss metal, then 1/4 optical wavelength anti-reflection dips are observed (dotted line in (e)). (b) An air-dielectric-metal (ADM) structure constituted by a lossless dielectric (undoped Ge with index n₂) on a highly lossy designed metallic substrate (Sb-doped Ge with index n₃), can support resonances at dielectric thickness h₂ < λ/4n₂ (h₂= 0.6 µm) (f) due to the non-trivial phase shift at the interface between dielectric and lossy metal. (c) An as-grown metal-dielectric-metal (MDM) structure with a dielectric spacer sandwiched by two lossy metallic layers. The topmost layer thickness h₁ ∼0.1 µm. (d) A subwavelength-patterned MDM structure with the topmost layer etched into periodic set of ribbons. In (f)–(h), the wavelength position of the first reflection dip remained almost unchanged at ∼4 µm in structures (b)–(d); while the second reflection dip for the as-grown MDM and the patterned MDM structure, has a blue-shift, with respect to the ADM structure.

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If a small amount of loss (considered as perturbation) is intentionally introduced in the substrate, the reflection can be mildly suppressed via destructive interference. For example, by replacing the PEC with a low-loss metal with the imaginary part of the permittivity at least an order of magnitude smaller than the real part ($\varepsilon ^{\prime} ={-} 1000$, $\varepsilon ^{\prime\prime} \le 100$), two reflection dips appear. As indicated by dotted lines in Fig. 1(e), given undoped Ge (n₂= 4; h₂= 0.6 µm) as the dielectric, the wavelength positions of the reflection dips are 3.3 µm and 9.8 µm, respectively, corresponding to the 1/4 optical wavelength anti-reflection condition: ${h_2} \cong m\lambda /4{n_2}$, where m is an odd integer. This phenomenon can be understood by decomposing incident waves into reflective partial wave r₀, r₁, r₂, …, with certain amplitudes and phases. The phase of the initial reflective partial wave r₀ is π, and all of the other reflective partial waves has phase of 0, leading to the destructive interference due to the π phase difference.

The 1/4 optical wavelength anti-reflection can be break once substituting the PEC with the Sb-doped Ge substrate (which is a lossy designed metal with $Im|{\varepsilon^{\prime\prime}} |$ in the same order of magnitude as $Re|{\varepsilon^{\prime}} |$) (seen Fig. 1(b)). This configuration is called “lossy Gires-Tournois etalon”. The non-trivial phase shifts [10,36] at the interface between the dielectric and the substrate will no longer be 0 or π. When the total phase accumulation (interface and propagation phase shifts) is close to 0 (modulo 2π) at a certain thin film thickness (${h_2} < m\lambda /4{n_2}$), the reflection is significantly suppressed, leading to a large absorption resonance; the zero-reflection phase condition is ${\phi _{23}} + 2{\phi _{prop}} - {\phi _{21}} = 2\pi m$. Figure 1(f) shows that two reflection dips appear in the as-grown air-dielectric-metal (ADM) structure, and the wavelength positions are ∼4.2 µm and ∼12.1 µm, respectively. In this case, ${h_2} \cong m\lambda /5{n_2}$, indicating that the non-trivial phase shifts allow the thickness of the dielectric less than a-quarter wavelength. The reflection phase ${\phi _{ij}}$ at the interface is calculated through the field Fresnel coefficient (${r_{ij}} = |{{r_{ij}}} |{e^{{\phi _{ij}}}}$), and the propagation phase ${\phi _{prop}}$ is calculated via $({2\pi /\lambda } ){n_2}{h_2}\cos \theta $, resulting in ${\phi _{23}} + 2{\phi _{prop}} - {\phi _{21}} ={-} 0.72 + 6.98 - 0 \cong 2\pi $, at the wavelength of ∼4.2 µm.

By adding a topmost thin metallic layer on the ADM structure, another configuration of a metal-dielectric-metal (MDM) structure is shown in Fig. 1(c). The thickness of the superstrate (Sb-doped Ge), the dielectric spacer (undoped Ge), the substrate (Sb-doped Ge) is 0.1 µm, 0.6 µm, 1 µm, respectively. It is shown in Fig. 1(g) that the wavelength positions of the reflection dips of the as-grown MDM structure are ∼4.3 µm and ∼8.5 µm, respectively. Calculating zero-reflection phase condition for the MDM structure is more complicated than that for the ADM case since phase changes caused by the transmission/reflection coefficient of the topmost metallic layer must be taken into consideration. Compared to phase calculations, an intuitive method (effective-reflection-index method [37]) is used to explain wavelength-position shifts of resonances of the MDM structure (with respect to the ADM configuration). The effective reflection index is treated as a lumped parameter, considering the combined effects of two or more films. It is derived as follows. First, the dielectric film and the metallic substrate are regarded as a whole (we called it “DM”). Given that the effective reflection index of the DM is ${n_{r1}}$ and the index of air is 1. Then the net reflection coefficient of the ADM structure (air and DM) is derived as $r = \frac{{{n_{r1}} - 1}}{{{n_{r1}} + 1}}$ (which is the same form as the Fresnel reflection equation); As shown in Fig. 1(f), at the wavelength of 4.2 µm, zero-reflection is met ($r \cong 0$), and ${n_{r1}} \cong 1.$ Second, as an iterative approach, the MDM structure is regarded as a whole, and the effective reflection index is

Furthermore, as shown in Fig. 1(d) and Fig. 2(a), a periodic set of ribbons made of highly doped Ge are fabricated by etching stripes into the as-grown MDM epilayers with a periodicity a of 3 µm and etching depth of 100 nm. The ribbon width d ranges from 206 to 1480 nm, namely Sample A: 1480 nm; Sample B: 1146 nm; Sample C: 843 nm; Sample D: 510 nm; Sample E: 206 nm. An illustration of the fabricated subwavelength-patterned MDM structures coordinated in a X-Y-Z system is depicted. The corresponding SEM (Scanning Electron Microscope) and AFM (atomic force micrograph) images are shown in Figs. 2(b)–(e). The optical response of the resulting structures is intentionally designed to be polarization dependent, which has the advantage of allowing us to compare resonances in different polarizations, so as to find the part of the resonances caused by anti-reflection or plasmonic effects.

 

Fig. 2. (a) Illustration of the fabricated subwavelength-patterned MDM structures as metamaterial perfect absorbers. A periodic set of Sb-doped Ge ribbons are stacked above a spacer layer of undoped Ge on a Sb-doped Ge substrate, where the height h₁= 100 nm, h₂= 600 nm, h₃= 1 µm, ribbon width d ranging from 0.2 µm to 1.5 µm, and periodicity a fixed to 3 µm. (b), (c) SEM images of the Sb-doped Ge ribbons in (b) planar view and (c) tiled view, respectively. The arrows indicate the X and Y directions with respect to the ribbon directions; X direction for TM polarization (red arrow) and Y direction for TE polarization (blue arrow). (d) Atomic force microscopy (AFM) of the ribbons with a dashed line across the surface, (e) indicating AFM line scan of the etching depth (∼100 nm).

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Figure 3 shows the reflectance spectra of samples A-E for TM and TE polarizations with electric field vector perpendicular /parallel to the ribbon stripes (as indicated by red/blue arrows in Fig. 2(b), respectively). In order to fully prove the accuracy of the permitivities of the highly doped Ge retrieved by using the Drude-Lorentz model (see Fig. S1 in Supplement 1 for detailed fitting methods), we use the three numerical methods (FDTD, DGTD, and RCWA) to reproduce the experimental results. FDTD and DGTD simulations are shown in Figs. 3(c), (d) and (e), (f), respectively; and RCWA calculations are plotted in Fig. S2 in Supplement 1. A good agreement between the simulation data and the experimental data is achieved.

 

Fig. 3. Reflectance spectra of Samples A-E with ribbon width d varied ranging from 206 nm to 1480 nm. Left column: TM polarization. Right column: TE polarization. Solid lines (a), (b) correspond to experimental data measured by FTIR spectrometer, and dashed lines correspond to FDTD (c), (d) and DGTD (e), (f) simulations. Four reflection dips in left column, labeled M₁, M_*, M₂, M₃, respectively, are indicated by black arrows.

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In TE polarization (see Fig. 1(h) and Figs. 3(b), (d), (f)), similar to the as-grown ADM/MDM stack, two dips are observed in the reflectivity of the subwavelength-patterned MDM structure. The wavelength positions of the first dip (∼4.1 µm) of samples A-E are independent from the ribbon width, since those of the as-grown ADM/MDM stack are overlapped near 4 µm. In addition, when ribbon width is small (for Sample E), the spectral position of the second dip (∼11.2 µm) approaches to that of the as-grown ADM structure (∼12.1 µm); when the ribbon width is large (for Sample A), it is close to that of the as-grown MDM structure (∼9.8 µm with respect to ∼8.5 µm).

In TM polarization (shown in Figs. 3(a), (c), (e)), there exist four absorption resonances (denoted as M₁, M_*, M₂, M₃, respectively) in the patterned samples. Among them, M₁ and M₂ are caused by anti-reflections (or asymmetric FP resonances) discussed above (which can be excited in multi-layered structure in both of TE and TM polarization), and M_* and M₃ are originated from plasmonic effects (which can only be excited in patterned structure in TM polarization [38,39]).

Figure 4 shows the absorption map for various dielectric spacer thickness and ribbon width. It can be summarized that (1) Thicker spacer thickness allow stronger absorption in resonance M₁, since it resulted from higher order (m = 3) FP interference; (2) While the spectral position of the observed absorption peaks M₁, M₂, and M_* remains relatively unchanged, that of M₃ is linearly red-shifted with increasing ribbon width (see Figs. 4(b)-(e)); (3) When the ribbon width d = 1.48 µm, as the thickness of the spacer layer increases, the resonance of M₁, M₂, and M_* moves proportionally to longer wavelengths, while that of M₃ follows the trend (first decrease and then increase) indicated by white dotted line in Fig. 4(a); (4) As shown in Fig. 4(e), absorption resonances of M₂ and M₃ disappear when the ribbon width is small (e.g., d = 0.206 µm).

 

Fig. 4. Absorption map (a) as a function of wavelength and dielectric spacer thickness h₂, for a grating geometry with period a = 3 µm and ribbon width d = 1.48 µm, and for various ribbon widths d at a constant dielectric spacer thickness h₂ of (b) 0.3 µm, (c) 0.4 µm, (d) 0.5 µm, (e) 0.6 µm, respectively. The resonant wavelengths of mode M₃ versus h₂ are indicated by white dash-dotted line in (a).

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To investigate the nature of these features, the electromagnetic field corresponding to these modes are analyzed in Fig. 5. Considering that H_z is the only non-zero component of the magnetic field for the TM polarization, it becomes clear when examining the magnetic field distribution H_z calculated for each absorption line for Sample A (d = 1.48 µm, h₂= 0.6 µm; in this geometry, modes M₂ and M₃ are not coupled). It is indicated that the magnetic field of M₃ (trapped underneath the ribbon) is localized both in horizontal and vertical directions, received combined modulation of ribbon width and spacer thickness; while the other three modes (M₁, M₂, and M_*) which are not confined in horizontal direction, depend only on the spacer thickness. In addition, as the lateral confinement of the magnetic field in M₃ mode gradually weakens with decreasing ribbon width d (see Fig. S3 in Supplement 1), the M₂ and M₃ modes will cease to exist when d is small. In other words, for d = 0.206 µm, the energy of the magnetic field in M₃ mode loses its characteristic of horizontal restrictions; obviously, the MDM structure no longer supports M₃ mode at a critical width of the ribbon.

 

Fig. 5. Maps of the magnetic field modulus calculated for absorption lines of Sample A (d = 1.48 µm, h₂= 0.6 µm) labeled by white triangles in Fig. 4(a).

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Furthermore, as shown in Fig. 6, the resonant wavelengths of M₃ as a function of the ribbon width d are recorded and linearly fitted for varied spacer thickness h₂, and the simple expression is written as [40,41]

 

Fig. 6. Resonant wavelengths of mode M₃ as a function of the ribbon width d with a linear fit, for a spacer thickness h₂ ranging from 0.1 µm to 0.9 µm.

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To demonstrate the coupling regime between the FP mode (M₂) and the plasmonic mode(M₃), it is a prerequisite to prefer an appropriate ribbon width. It is seen in Figs. 3(a), (c), (e) that the absorption resonances between modes M₂ and M₃ couple to each other for a ribbon width d of 0.51 µm (Sample D). The complete picture of modes coupling is depicted in Fig. 7(a) by the calculated absorption map as a function of wavenumber (in unit of cm^-1) and spacer thickness h₂ for a preferred ribbon width (d = 0.51 µm) when the two modes strongly interact. As indicated by black and red squares in Fig. 7(b), the extracted resonant frequencies of the coupled modes (FDTD data from Fig. 7(a)) display an anti-crossing, where an energy gap is observed. When no coupling occurred (denoted by blue and green dotted lines in Fig. 7(b)), the resonant frequencies ${\omega _{{r_2}}}\; $ of mode M₂ decrease monotonously with increasing spacer thickness h₂ (described by ${\omega _{{r_2}}} = \frac{{10000}}{{{\lambda _{r2}}}}$; and ${\lambda _{r2}} = 12.96{h_2} + 3.27$); and the resonant wavenumbers of mode M₃ (first increase and then decrease) are obtained by substituting ribbon width d of 0.51 µm into Eq. (5) for spacer thickness h₂ ranging from 0.1 to 0.9 µm (see Fig. 6). Based on these data in uncoupled state as an input, the anti-crossing of the hybridized modes M₂ and M₃ is modelled by an ultra-strong coupling model given by [39,40,43]

 

Fig. 7. (a)#Absorption map as a function of frequencies in wave-number units and dielectric spacer thickness h₂, for a ribbon width d = 0.51 µm. (b) Resonant frequencies (black and red squares) versus h₂ for the coupled M₃ and M₂ modes extracted from the absorption maps in (a). The blue and green dotted lines are, respectively, for M₃ and M₂ resonances in an uncoupled state. The black and red solid lines are, respectively, the M₃ and M₂ resonances calculated with the ultra-strong coupling model.

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4. Conclusion

In summary, we have constructed a subwavelength-patterned MDM structure based on highly doped and undoped Sb-doped Ge, and experimentally verified its perfect absorption characteristics in MIR. We have analyzed the resonance shift of the subwavelength-patterned MDM structure (with respect to the as-grown ADM/MDM stack) by zero reflection phase and effective reflection index, proving that the wavelength position of the higher-order asymmetric FP resonance is maintained around 4µm in all of the three structures. The spectral characteristics of the resulting structure in different polarizations are experimentally analyzed, and verified by various numerical methods (FDTD, DGTD, RCWA). In TE polarization, the dual-band absorptions come from the first-order and third-order asymmetric FP resonances, and the thickness of the dielectric is less than 1/4 of the optical wavelength due to the existence of non-trivial reflection phase shift. In TM polarization, the resulting structure produces multi-band absorptions, and a total of 4 resonance absorption modes (M₁, M_*, M₂, M₃) exist, among which M₁, M₂ are derived from asymmetric FP resonance, and M_*, M₃ are generated by plasmonic effect. It is indicated that M₃ mode localized in the double metal region, is modulated simultaneously by horizontal (ribbon width) and vertical (spacer layer thickness) profiles, while the other three modes are modulated merely by vertical (spacer layer thickness) profile. With the increase of the spacer layer thickness, the effective refractive index of the M₃ mode decreases first and then increases, which is caused by the transition of the M₃ mode from gap plasmon to LSP. By changing the horizontal geometry, the coupling state of the M₂ and M₃ modes can be adjusted. When ribbon width is 1.48µm, M₂ and M₃ modes do not couple; when ribbon width is 0.51µm, strong coupling model analysis reviews that the confinement of the plasmonic field in the FP cavity push the system into the ultra-strong coupling regime, and the huge Rabi splitting energy reaches 46% of the average energy of M₃ mode. The subwavelength-patterned MDM absorber provides a feasible way to control the energy of FP and plasmonic resonance.