1. Introduction

Plasmonic metamaterial absorbers (PMAs) are arrays of subwavelength-spaced metallic nano-objects (also termed as optical antennas [1]) whose primary function is to concentrate the propagating light into regions much smaller than the wavelength and efficiently dissipate the optical energy into heat via localized surface plasmon resonance (LSPR) [2–4]. Beyond the enhanced light absorption, PMAs can also resolve the fundamental properties of light such as wavelength, polarization states and incident angle by adjusting the geometrical parameters of the optical antennas, such as size, shape, and orientation across the array [5], or by leveraging the dispersion in the material optical properties [6]. Due to their wide range of possible designs leading to unprecedented functionalities, PMAs have evolved as a versatile multifunctional platform for applications that require light trapping/focusing and near-field enhancement such as optical sensing [7], advanced thermal detectors [8,9] and thermal emitters [10,11], photovoltaic [12] and medical therapy [13], to name a few.

The ease of fabricating PMAs allows for their direct integration with optoelectronic devices such as light sources, sensors, and detectors towards unprecedented or expanded functionalities. Taking infrared detectors as an example, when integrated with PMAs, the detector pixels can independently resolve the parameters of the incident electromagnetic wave such as wavelength and polarization states [8,14–20], and this opens up the way towards advanced imaging modalities such as hyperspectral imaging and polarization imaging. However, since the footprints the detector pixels keep scaling down, the available space for integrating PMAs is also shrinking. For example, the number of pixels of the state-of-the-art microbolometer based focal plane arrays (FPAs) has surpassed 10⁶ level [21], while the pixel pitch has been reduced from 50 μm to 10 μm and is now evolving toward 5 μm [22]. To this end, the size of PMAs should also be reduced to fit such small detector pixels. However, in the mid-infrared or THz frequency range, noble metals such as gold behave more like perfect conductors in which the electric field penetration and high spatial confinement vanish [23]. As a result, it becomes increasingly challenging to realize deep subwavelength detector pixels with PMAs. To accommodate the ever-shrinking size of infrared detector pixels, the antennas that constitute the PMAs need to be miniaturized without compromising the resonant wavelength and the infrared absorption.

In this letter, we demonstrate a metal-insulator-metal based PMA with deep-subwavelength optical antenna that can adapt to the pixels of infrared FPAs as small as 5 μm. We show that the strong coupling between the localized surface plasmon resonance (LSPR) in the antenna with the vibrational modes in the dielectric spacer causes high absorption in the infrared atmospheric window (8 μm - 14 μm). As shown in Fig. 1(a), the MIM absorber consists of a periodic array of meander line antenna (MLA) atop a silicon dioxide spacer and a gold backplate. The MLA is constructed by folding the four arms of a nano-cross antenna into a meandered configuration to minimize the antenna footprint without reducing the resonant wavelength [24,25]. The relevant parameters in Fig. 1(a) include the pitch size P of the unit cell of the antenna array, the side length of the antenna P·Ratio, the gap size g and the width W of the nanostrip. L and d₂ are the length and width of the elongated part, respectively. d₁ is the distance between the elongated part and the center of the unit cell. d₃ is the distance between the elongated part and the edge of the MLA. Figure 1(b) shows the SEM image of the MLAs with a pixel pitch P = 1.47 μm fabricated by standard electron-beam lithography and metal lift-off process. As illustrated in Fig. 1(c), a 2 × 2 array of such PMAs can be implemented onto infrared pixels as small as 5 μm.

 

Fig. 1. (a) Schematic illustration of the MLA based PMA and the relevant parameters. (b) The SEM image of the MLAs. Scale bar = 3 μm. (c) Conceptual drawing of microbolometer array integrated with finite-size MLAs array. (d) Optical properties of silicon dioxide in the mid-infrared range. The dielectric functions of silicon dioxide display an epsilon-near-zero point at 8 μm and two epsilon-near-pole points at 9.4 μm (ENP₁) and 12.5 μm (ENP₂), respectively. (e) Red dash-dotted line and solid black line: the simulated and measured spectral absorption of the MLA based PMA, respectively. The measured spectral absorption is obtained by Fourier transform infrared spectroscopy (FTIR). The three high absorption peaks of the absorber are labeled as M₁, M₂, and M₃, respectively.

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2. Results and discussion

Note that using the meander line configuration to reduce the antenna footprints is a well-developed technique in the radio-frequency regime. However, the refractive indices of the substrates for radio-wave frequency antennas are usually non-dispersive. In contrast, common dielectric materials such as silicon dioxide [26,27] and silicon nitride [28,29] can be highly dispersive in the optical regime due to the intrinsic vibration modes (optical phonons). The strong coupling between these fundamental excitations and the localized plasmonic resonances provide a new route to tailor the responses of the optical antennas atop [6,30–32]. Taking silicon dioxide as an example, the real part Re(ε) and the imaginary part Im(ε) of the dielectric function of silicon dioxide presented in Fig. 1(d) are highly dispersive from 6 μm to 15 μm, containing both positive values and negative values in Re(ε). The cross-over point between positive Re(ε) and negative Re(ε) at ∼ 8 μm resulting in the “epsilon-near-zero” (ENZ) regions related to longitudinal optical (LO) phonon; while the two peaks in Im(ε), one at ∼ 9.3 μm and the other at ∼ 12.5 μm are termed as “epsilon-near-pole” (ENP₁ and ENP_2, respectively), both related to transverse optical (TO) phonon [6]. Figure 1(e) plots the simulated and measured spectral absorption of the PMA comprising a layer of 50 nm thick MLAs atop a 600 nm thick silicon dioxide spacer and a 100 nm thick gold backplate. The parameters of the MLA are: P = 1.47 μm, Ratio = 0.9, g = 385 nm, W = 105 nm, L = 162.4 nm, d₁ = d₂ = d₃ = 98 nm, respectively. The simulations are performed using the commercial finite-different time-domain software FDTD Solutions from Lumerical Inc (See Methods chapter for more details). The spectral reflectivity of the fabricated absorbers is characterized by an infrared microscope (Hyperion 2000) with 15× Schwarzschild objective coupled to a Fourier transform infrared (FTIR) spectrometer (Bruker Vertex 70). The reflective 15×, NA 0.4 objective operates with a weighted average view angle of 16.7° incidence and has a collection cone apex angle of ±7°. A gold mirror from Thorlabs Inc. is used as reference. Since the transmission is eliminated by the gold backplate, the calculation of absorption is simplified to A = 1 – R. As the measured spectrum is obtained by an oblique excitation, a simulated absorption spectrum at an incident angle of 16.7° is presented in Fig. 1(e) for comparison purpose. It should be note that the red dash-dotted line in Fig. 1(e) is the arithmetically average value of the absorption spectra of TE and TM excitations to emulate an unpolarized excitation. The three peaks in the measured absorption spectrum are 98.2% at 7.93 μm, 93.1% at 11.88 μm and 93.2% at 13.22 μm. The broadened high absorption range is centered at λ_center = 12.6 μm with an FWHM of 3.94 μm and the corresponding compress ratio $\eta $ = 8.57, where $\eta $ is defined as λ_center / P. This clearly shows that the optical MLA can achieve a more advanced spectral line shape than radio-wave frequency MLA by leveraging on the strong coupling between the localized surface plasmon resonances and the vibration modes in silicon dioxide.

The gap plasmon-polariton (GPP) mode is a highly localized surface plasmon (LSP) mode between two metal structure separated by a thin dielectric spacer, which occurs in some MIM nano-resonators and is responsible for the absorption characteristics of many MIM absorbers [33]. When the gap size becomes large (above ∼ 200 nm), the GPP mode for wide gaps transforms into a slow surface plasmon-polariton (SPP) strip mode and becomes decoupled from the lower surface. This slow SPP mode goes back and forth between the ends of the nanostrip, resulting in a Fabry-Perot-type resonance [34]. Therefore, the proposed PMA sustain horizontal Fabry-Perot type of resonance for slow SPP mode trapped below the MLA that are bouncing back and forth inside the resonator, giving rise to strong local-field enhancement and absorption. The resonance wavelengths ${\lambda _{\textrm{res}}}$ ruled by the phase-matching condition can be obtain from [35]:

Therefore, the parameter $\eta $ quantitatively indicates the MLA’s ability to compress the footprint, considering that the period P is very close to the side length of the antenna P·Ratio (Ratio = 0.9). Table 1 compares our design with other broadband PMAs that work in the mid-infrared range [40–54], literatures are sorted in descending order of compression ratio. It clearly illustrates that the proposed design achieves a high compress ratio, while also achieving broadband high absorption. Most of the literatures that achieve high compression ratios are based on a high refractive index dielectric spacer [40,41,43–47], and the underlying mechanism can be easily understood from the Eq. (3).

 

Fig. 2. (a) The local electric field intensity |E| and the current density vector J in the x–y cut plane at half of the antenna thickness for MLA antenna at 11.88 μm. (b) Phase-matching condition ${\lambda _{\textrm{res}}} = 2{n_{\textrm{eff}}}{L_\textrm{r}}$ for the fundamental mode (FM) and effective extinction coefficient ${k_{\textrm{eff}}}$. (c) The simulated spectral absorption of the MLA based PMA as a function of the scale factor. The white square markers highlight the resonant wavelengths of upper branch (UB), lower branch (LB) and FM of LSPR. The white dash lines label the case of the scale factor = 1. The dimensions of the MLAs is varied by multiplying the antenna parameters (P, g, W, L, d₁, d₂, and d₃) by the scale factor.

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Table 1. Comparison between our work and the previous work about broadband PMAs that working in mid-infrared range (3-14 μm)

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To better understand the strong coupling between the LSPR in the optical antennas and the vibrational modes in the silicon dioxide spacer, we vary the size of the MLA by the scale factor. The thicknesses of the antenna, the spacer, and the backplate are kept unchanged. In Fig. 2(a), as the scale factor increases from 0.4 to 1.4, the resonant wavelength of the LSPR redshifts from 10 μm to 15 μm. In particular, when the scale factor approaches 1.0, the LSPR is spectrally aligned with the vibrational mode in the silicon dioxide spacer, and two spectral branches appear on the two sides of the fixed TO phonon at the ENP₂. The white markers highlight the resonant wavelengths of the upper branch (UB) and lower branch (LB), and an anti-crossing behavior is clearly observed. The obtained spectral splitting is as large as 10.45 meV. This kind of anti-crossing has been observed in various physical systems and is the signature of the strong coupling between two coupled resonant modes [55]. We can estimate the coupling strength in our hybrid plasmon/phonon structure. According to the two-coupled damped oscillator model, we obtain the following relationship between spectral splitting Ω and coupling strength V [56]:

Since an effective absorber should maintain a high absorption under a wide range of incident angle [4], we numerically simulate the spectral absorption of the MLA based PMA as a function of the incident angle. From Fig. 3(a) and 3(b), one can see that in TE polarization case, the broadened high absorption due to strong coupling in the ENP₂ region can maintain from 0° to 40°. In contrast, for TM polarization, the high absorption can maintain up to 60°. Moreover, the high absorption of the fundamental mode near the ENZ region can maintain above 90% even when the incident angle θ reaches 60° for TE polarization. To further obtain the physical explanation of various absorption peaks in the ENP₁ and ENZ regions. We illustrate in Fig. 3(c) and 3(d) the absorption spectrum of a two-layer structure with 600 nm silica above a 100 nm gold backplane under TE and TM polarization at different incident angles, respectively. In Fig. 3(d), one absorption peak is at λ ≈ 9.66 μm, which corresponds to the peak of the ${n_{\textrm{SiO}2}}$ as well as the largest difference between ${n_{\textrm{SiO}2}}$ and ${k_{\textrm{SiO}2}}\; $ [57]. The maximum of this absorption mode increases from 0.69 to 0.83 as incident angle shifts from 0° to 60°. Since this mode also appears at TE polarization incidence, it undoubtedly originates from the material loss near ENP₁. The same absorption peak also exists in Fig. 3(a) and 3(b), but the peak maximum is slightly reduced due to the high reflection of gold nanoantenna in a non-resonant state. As we know, a thin polar dielectric film supports a leaky mode in the light cone called Berreman mode and a surface mode beyond the light cone called ENZ mode at the frequency where the dielectric permittivity vanished [58]. The Berreman mode is a radiative mode that can be excited directly from free space by TM-polarized light illuminating at oblique incidence [59]. The ENZ mode is a confined mode whose dispersion lies on the right of the light line thus can not be excited from free space unless using the Kretschmann geometry or grating couplers. It should be noted that the ENZ mode can appear only for nanoscale thickness given by H < λ_P/50, where λ_P is the plasma wavelength (zero crossing of the permittivity, ∼ 8 μm for SiO₂) [60]. Therefore, ENZ mode is not supported in our structure, but the Berreman mode exists. As shown in Fig. 3(d), the Berreman absorption feature observed only for TM-polarized light illuminating at the incident angle greater than 15° close to the ENZ was attributed to the excitation of the Berreman mode. Moreover, the interaction of the electromagnetic field with the dielectric enhanced by oblique incidence, which enhanced the absorption relevant to Berreman mode. In Fig. 3(b), the resonance peak of the fundamental mode of the PMA is just near ENZ under normal incidence. In the case of TM polarization oblique incidence, the Berreman mode is excited, then the plasmon mode and the Berreman mode strongly coupled, and the coupling strengthen with the increase of the incident angle which can be derived from the broader spectral splitting in the Fig. 3(b) (See Appendix C for more details).

 

Fig. 3. (a) and (b) the simulated spectral absorption of the PMA as a function of the incident angle for TE polarization and TM polarization for the PMA. (c) and (d) the simulated spectral absorption of the PMA without MLA as a function of the incident angle for TE polarization and TM polarization, respectively.

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We now delve into the near field optical properties of MLA. Figure 4(a)–4(c) plot the local magnetic field magnitude |H| in the x-y cut plane at half of the antenna thickness for (a) M₁ at 7.93 μm, (b) M₂ at 11.88 μm, and (c) M₃ at 13.22 μm, respectively. It is well known that the two spectral peaks M₂ and M₃ cannot be viewed individually. They are a part of the coupled hybrid system when strong coupling between the electron-hole dipoles (plasmons) and the lattice vibrations (phonons) occurs at zero detunings [61]. As such, the near field distributions at M₁, M₂, and M₃ should be identical since they all correspond the fundamental optical resonance mode of the MIM structure. Indeed, this is evidenced by the simulated magnetic field magnitudes shows in Fig. 4 (b) and Fig. 4(c). Figure 4(d) plots the color map of the local magnetic field intensity |H| and the magnetic field vector in the y–z cut plane at x = 0 at 11.88 μm. The red dash lines in Fig. 4(b) label the position of the x-z cut plane. We then plot in Fig. 4(e) the local magnetic field intensity |H| and the current density vector J of the PMA in the x–z cut plane at y = 0. The white dash lines in Fig. 4(b) label the position of the x-z cut plane. The MLA resonators act as a slow SPP strip resonator, which is decoupled from the lower metal surface. Therefore, the oscillating current only exists in the antenna layer (as shown in Fig, 4(e)), and the magnetic field vector is excited by the surface current, showing a magnetic dipole—the magnetic field vector surrounds the top antenna (as shown in Fig. 4(d)). This uncoupled surface current results in the power absorption density mostly confined inside the top antennas and adjacent lossy dielectric layer, as can be seen from Fig. 4(f).

 

Fig. 4. (a) The local magnetic field magnitude |H| in the x-y cut plane at half of the antenna thickness for (a) M₁ at 7.93 μm, (b) M₂ at 11.88 μm and (c) M₃ at 13.22 μm, respectively. (d) The local magnetic field intensity |H| and the magnetic field vector in the y–z cut plane at x = 0 at 11.88 μm. (e) The local magnetic field intensity |H| and the current density vector J in the x–z cut plane at y = 0 of the PMA based on MLA antenna at 11.88 μm. (f) The distribution of the power absorption density in the x–z cut plane at y = 0. The incidence light is set to be polarized in the x-direction for all the simulations.

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We also examined the infrared absorption performances of PMAs with finite array sizes to show that the proposed design offers new possibilities for realizing miniaturized optical absorbers or thermal emitters. According to Kirchhoff's law of thermal radiation, the emissivity of a PMA in thermodynamic equilibrium is equal to its absorptivity [24]. Therefore, the thermal absorptivity of the fabricated PMAs can be characterized using a thermal imaging microscope (Optotherm Sentris). A group of PMAs based on the MLA with array sizes ranging from 5 μm × 5 μm to 150 μm × 150 μm are fabricated on the same sample. The sample is then placed on the thermal stage so that the temperature is uniform across the sample and can be precisely controlled. The thermal image of the sample heated up to 60 degrees Celsius is shown in Fig. 5(a). At thermal equilibrium, the variation in the temperature reported by the thermal imaging microscope among different PMAs is due to the differences in their emissivity. It should be noted that the temperature measured by the infrared microscopy system is not the true temperature of the sample, but the calculated temperature converted from the received thermal radiation energy. The SEM images about the details of the 5 μm × 5 μm array and 15 μm × 15 μm array are also shown in Fig. 5(b) and Fig. 5(c). It is clearly seen that due to the minimized antenna footprint, the MLA can be packed densely into a limited area. Later we will numerically show that the MLA based absorber can even adapt to infrared focal plane arrays with a pixel size smaller than 5 μm. Figure 5(d) plots the temperature of our proposed PMAs as a function of the array size, measured by the thermal imaging microscope. It is found that when the array size is above 100 μm, the measured temperature of the PMAs shows asymptotic behavior. In this case, the performance of the finite size PMA is almost equivalent to an infinite array and the temperature of this asymptote can truly reflect the emission ability of the PMAs. However, the system resolution is additionally limited by the diffraction of the optics. In practice, to achieve accurate temperature measurement, the object's size should be at least 4 times the minimum spatial resolution [62]. For our infrared microscopy system with a spatial resolution of 5 μm, this value is 20 μm. Therefore, the measured temperature of a structure less than 20 μm cannot truly reflect the corresponding emission performance. In Fig. 5(d), the measured temperature of the 20 μm structure is almost 90% of the asymptote temperature. This indicates that our absorbers with a complex geometric shape has good small-size absorption performance, which is attributed to the strong local field capability of PMAs. To analyze the absorption performance of smaller finite-size structures, we proceed by analyzing their absorption cross-section (See Appendix D for more details). Figure 5(e) plots the simulated absorption cross-section for various sizes of finite PMAs arrays ranging from 1 × 1 to 10 × 10. The results show that when the array size is larger than 4 × 4 (the corresponding dimension is about 6 μm × 6 μm), the average absorption cross- section ${\mathrm{\sigma}_{\textrm{ave}}}$ gradually stabilizes and the maximum value converges to the geometric cross-section ${\mathrm{\sigma}_{\textrm{geo}}}$ (∼ 2.16 μm² as shown by the dotted line in Fig. 5(e)). Here, the ${\mathrm{\sigma}_{\textrm{ave}}}$ is calculated by dividing the total absorption cross-section of the array by the number of unit cells in the array. For the case of only one independent PMA, although the two coupled modes are detuned, the ${\mathrm{\sigma}_{\textrm{ave}}}$ is much larger than the ${\mathrm{\sigma}_{\textrm{geo}}}$. This shows that the absorption performance of our absorber neither origin from the multi-period comprehensive effect nor from the coupling of adjacent units, but from the electromagnetic properties of the isolated absorber itself.

 

Fig. 5. (a) A group of fabricated PMAs based on the MLA with array sizes ranging from 5 μm × 5 μm to 150 μm × 150 μm are characterized using a thermal imaging microscope. Scale bar: 200 μm. The SEM image of the meander line antenna ((b) and (c)). The side lengths of (b) is 5 μm, and the side lengths of (c) is 15 μm. (d) The measured temperatures of the MLA based PMA as a function of the array size. The inset shows the measurement setup. (e) The calculated absorption cross-section spectra of various finite-size PMAs.

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In a more practical scenario, each pixel of an infrared focal plane array is integrated with a finite-sized PMA, as shown by Fig. 1(c). In this situation, the PMAs form a periodic array and there is an air gap between the neighboring PMAs. Figure 6(a) shows the unit cell used to simulate such a periodic array of isolated PMAs. Here L_air represents half the size of the air gap and L_air = 50 nm corresponds to a 100 nm air gap between the neighboring PMAs. Figure 6(b) shows the impact of L_air on the spectral absorption of a periodic PMA with 2 × 2 MLAs. When L_air is increased from 0 nm to 100 nm, the absorption peak M₁ in the 11 μm – 12 μm range is not affected too much but the absorption peak M₃ in the 13 μm – 14 μm range is significantly reduced. This phenomenon can be understood by the Fabry-Perot resonance model. The existence of the air gap reduces the ${n_{\textrm{eff}}}$ of the sub-wavelength metallic waveguide, thereby detuning the resonance wavelength of plasmon mode and the phonon mode. Therefore, the impact of the air gap can be mitigated by tuning the size of the structure which is equivalent to increasing the resonance length ${L_\textrm{r}}$. For example, when L_air = 50 nm, the reduced absorption peak M₃ can be increased by scaling up the relevant parameters of the MLA based PMA (excluding t₁, t₂, and t₃) and the side length of the unit cell by a factor of 1.2, as shown in Fig. 6(c). The resulting side length of the unit cell is only 3.734 μm and other relevant parameters are: P = 1.764 μm, Ratio = 0.9, g = 462 nm, W = 126 nm, L = 194.88 nm, d₁ = d₂ = d₃ = 117.6 nm, t₁ = 50 nm, t₂ = 600 nm and t₃ = 100 nm. The spectral absorption can be further improved by using a larger finite-sized antenna array. Figure 6(d) presents the schematic diagram of the PMA integrated microbolometer. The absorber comprises a SiO₂ layer sandwiched between an array of gold MLA antennas and a gold backplate. There is a 20 nm thick Si₃N₄ film under the absorber, followed by a 20 nm thick vanadium oxide (VO_x) thermistor layer. The thin silicon nitride layer serves as the electrical insulation layer and also delivers the generated heat from the absorber to the thermistor layer. All these structures are suspended by a 250-nm-thick Si₃N₄ micro-bridge, which not only provides mechanical support but also thermally isolates the thermistor layer from the substrate. The legs of the micro-bridge are assumed to be connected to a silicon substrate with a fixed temperature of 293.15 K. The two legs are assumed to be 2 μm-long, and the side lengths of the square cross-section of the legs are 200 nm. The thermal analysis is conducted by DEVICE - a multiphysics simulator from Lumerical Inc. At resonant wavelengths, the incident light is trapped/absorbed in the MIM structure. The absorbed optical energy is eventually dissipated as heat that elevates the temperature of the microbolometer. So the MIM absorber as a whole is regarded as the heat source in the simulation. We first carried out an optical simulation to find out the profile of absorbed optical power in the absorber. The input optical power is set to be 10 nw. The profile of absorbed optical power is then used as the heat source in the subsequent thermal analysis to calculate the temperature change in the thermistor layer. In the thermal analysis, the thermal radiation and thermal convection are ignored. Since the absorbed power is relatively small, as we can see from Fig. 6(e), the resulting temperature change in the microbolometer is minimal and is almost uniform in the thermistor layer. The average temperature rise of the VO_x layer is 72.32 mK. To determine the temperature response of the microbolometer, we apply a time-domain gate function to turn the heat source on at t = 100 μs and off at t = 500 μs. Figure 6(f) shows the temperature response of the thermistor. The simulated thermal response time of the microbolometer is found to be 24.11 μs.

 

Fig. 6. (a) The unit cell used to simulate the finite size MLAs array with air gap on the four sides (b) The spectral absorption of the 2 × 2 MLAs array as a function of L_air. (c) The spectral absorption of the MLA based PMA with P = 1.47 μm, Ratio = 0.9, g = 385 nm, W = 105 nm, L = 162.4 nm, d₁ = d₂ = d₃ = 98 nm and the PMA with enlarged antennas: P = 1.764 μm, Ratio = 0.9, g = 462 nm, W = 126 nm, L = 194.88 nm, d₁ = d₂ = d₃ = 117.6 nm. (d) The thermal model of a PMA integrated microbolometer. (e) The steady-state temperature distribution across the bolometer upon infrared radiation. (f) The transient temperature response of the thermistor.

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3. Methods

Numerical Simulation and Analysis. The periodic structure is studied by simulating a unit cell with Bloch boundary conditions applied at the x- and y- boundaries and perfectly matched layers (PMLs) applied at the z-boundaries. A plane wave source is used to excite the structure, and a power monitor is used to collect the reflected waves. The complex dielectric constants of gold (Au) and SiO₂ are obtained from [38]. The simulation time is 2000 fs and the convergence criteria were set to be with auto shutoff min of 1e-5. The coefficient numbers for silicon dioxide was 10 and the root-mean-square (RMS) errors of the approximation is 0.0674. The coefficients number for Au fitting is 5 with RMS error of the approximation to be 0.0214. The cross-section of the electric field and magnetic field distribution was detected by a 2D field profile monitors in x–y plane and x–z plane, respectively.

Fabrication. The substrate is a single-sided polished 500 μm silicon. First, a 10 nm titanium adhesion layer was evaporated on the substrate, followed by a 100 nm gold film, which serves as the MIM structure’s metal backplate. After that, a layer of 500 nm silica is deposited on the gold layer as the dielectric spacer by plasma-enhanced chemical vapor deposition (PECVD). Then, a layer of e-beam resist (PMMA AR-P 679.04 950K) was spin coated and then exposed by electron beam lithography (EBL) according to the designed patterns of the nanoantenna array. After exposure, a standard lift-off process is used to complete the pattern transfer.

4. Conclusions

To conclude, we presented a comprehensive study of an infrared plasmonic metamaterial absorber constructed from an array of deep sub-wavelength nanoantennas atop a dielectric spacer and a gold backplate. The dispersion caused by the vibrational modes in the silicon dioxide spacer leads to a broadened high spectral absorption from 11 μm to 14 μm and enhanced absorption at 8 μm. Spectral anticrossing with an energy splitting proportional to the coupling strength is observed when the LSPR is spectrally aligned with the phonon mode at λ = 12.5 μm. Numerical simulation results reveal that the optical near-fields are more confined around the MLA that attribute to the excitation of slow SPP strip mode. The high spectral absorption at the ENP₂ can maintain with an incident angle from 0° to 40°. For oblique TM-wave incidence, a spectral splitting at the ENZ region due to the strong coupling between plasmon mode and Berreman mode is observed. We also evaluated the absorption performances of a periodic array of the finite-sized PMAs with an air gap between the neighboring PMAs. Such a small PMA can adapt to the pixels of infrared FPAs as small as 5 μm. Compared with conventional Fabry-Perot absorbers, PMAs have a unique advantage because they allow each pixel in the FPA to independently resolve the parameters of the incident electromagnetic wave such as wavelength, polarization state and incident angle. Our approach of minimizing the antenna footprint without comprising the absorber performances may hold great promise for realizing deep subwavelength pixel infrared FPAs with enhanced performances and expanded functionalities.

Appendix A: details about the distribution of free charge density

 

Fig. 7. Distribution of free charge density. The free charge distribution of MLA at 11.88 μm excited by x-direction polarized incident light.

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Appendix B: details about the Lorentzian line shape fitting of the absorption spectrum of the uncoupled metamaterial absorber

The uncoupled metamaterial absorber’s absorption spectrum can be analytically described by a Lorentzian line shape shown in Fig. 8(a).

$${\alpha _{\textrm{MM}}} = \frac{{A{\gamma _{\textrm{MM}}}}}{{{{(\omega - {\omega _{\textrm{MM}}})}^2}\textrm{ + }\gamma _{\textrm{MM}}^2}}$$

And the ${\gamma _{\textrm{MM}}}$ is calculated to be 11.8 meV. Based on the same process, ${\gamma _{\textrm{ph}}}$ = 4.7 meV can be obtained. Here, the permittivity of silicon dioxide used in this simulation is from the Lorentz model in [6] with the second oscillator (at the ENP₂) removed. The dielectric constant with or without phonon at the ENP₂ is plotted in Fig. 8(b).

 

Fig. 8. (a) Lorentzian line shape fitting of the absorption spectrum of the uncoupled metamaterial absorber. (b) The dielectric constant of silica with or without phonon at the ENP₂.

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Appendix C: details about the strong coupling between the LSPR mode and Berreman mode

As shown in Fig. 9(a), we plot the simulated absorption spectra of the PMA as a function of the scale factor for TM polarization at 45 degrees incidence. The anti-crossing phenomenon can be observed, so we believe that there is a strong coupling effect between the LSRP mode and the Berreman mode.

 

Fig. 9. The simulated absorption spectra of the PMA as a function of the scale factor for TM polarization at 45 degrees incidence.

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Appendix D: details about the simulation of the absorption cross-section

Here we take a 2 × 2 isolated absorber arrays to show the simulation method of the absorption cross-section. The dimension of the absorption cross-section analysis group is equal to 2$\cdot $P. The Total-field Scattered-field (TFSF) Sources is slightly larger than the analysis group and is entirely located inside the simulation region. The boundary conditions of the simulation region are all set to PMLs. The incident light is polarized in the x-direction. The analysis group calculated the total absorption cross-section of the 2 × 2 arrays and then divided by 4 to get the average absorption cross-section, as shown in Fig. 5(e). The magnetic field distribution in Fig. 10(c) shows two magnetic dipoles, indicating that the absorbers work independently.

 

Fig. 10. (a) Perspective view of the numerical simulation software. (b) Schematic diagram of the location of the simulation region, TFSF, absorption cross-section analysis group, and the structure. (c) The local magnetic field intensity |H| in the x–z cut plane (as shown in the blue dashed box in Fig. 10(a)) of the PMA at resonance wavelength.

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Funding

National Key Research and Development Program of China (2019YFB2005700); National Natural Science Foundation of China (11774112, 11604110); Fundamental Research Initiative Funds for Huazhong University of Science and Technology (2017KFYXJJ031, 2018KFYYXJJ052, 2019KFYRCPY122).

Acknowledgments

We thank Li Pan engineer in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for the support in PECVD fabrication. We thank Zeng Tiantian engineer in the Huazhong University of Science & Technology Analytical & Testing Center for the support in FTIR test. We thank the technical support from Experiment Center for Advanced Manufacturing and Technology in School of Mechanical Science & Engineering of HUST.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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