Multi-Peak Narrowband Perfect Absorber Based on the Strong Coupling Between Fabry–Perot Mode and SPP Waveguide Mode

Abstract

Plasmonic- or metamaterial-based multi-narrowband perfect absorbers hold significant potential applications in filtering, photodetection, and spectroscopic sensing. However, it is rather challenging to realize multi-peak and narrowband absorption simultaneously only using plasmonic metallic materials due to the single or dual resonance and large optical losses in the metallic nanostructure. Here, we numerically demonstrate a new multi-narrowband perfect absorber based on the strong coupling between the Fabry–Perot cavity modes and the surface plasmon polariton waveguide modes in a nanostructure consisting of periodic Ag grating and Ag film separated by a SiO₂ waveguide layer. Six absorption peaks, an ultranarrow absorption resonance with FWHM as narrow as 8 nm, and an absorption peak amplitude surpassing 95% have been achieved. Furthermore, the optical properties of the designed nanostructures can be precisely tuned by modulating the grating period, slit width, height, as well as the thickness and refractive index of the waveguide layer. This approach establishes a versatile platform for designing high performance multi-narrowband absorbers, with promising applications in optical filters, nonlinear optics, and biosensors.

1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along the interface between a metal and a dielectric medium, which result from the coupling between optical fields and collective electron oscillations at the metal/dielectric interface. Noble metals like Cu, Ag, and Au are particularly effective at supporting SPP excitation within the visible wavelength band, as their performance is highly dependent on microstructural properties such as composition, shape, and size. Consequently, the excitation wavelength of SPPs can be precisely tuned by altering the metal’s microstructure through different micro/nanofabrication technology [1,2], thereby providing an effective method for investigating plasmonic and metamaterial electromagnetic absorbers. Plasmonic or metamaterial perfect absorbers have attracted wide attention due to their significance in science and practical applications, such as thermal emitters [3], heat-assisted magnetic recording [4], solar steam generation [5], biosensors [6], and hot electron-based photodetection [7,8]. Over the past decade, numerous plasmonics or metamaterial perfect absorbers based on different metallic nanostructures have been extensively investigated theoretically and experimentally [9,10,11,12]. For example, the metal–insulator–metal (MIM) structure is advantageous for tightly confining the electromagnetic field on resonance [10]. Nonetheless, such plasmonic metamaterials typically exhibit broad absorption bandwidths due to strong radiative damping and intrinsic metal losses. This characteristic severely impedes their applications in color filters, thermal radiation tailoring, and sensors, where ultra-narrowband spectral response is essential [13,14].

To solve this problem, the mechanism of coupling plasmonic mode with plasmonic mode or photonic mode (Fabry–Perot mode, cavity mode, waveguide mode) was proposed to realize the narrowband perfect absorber. For example, Koray Aydin et al. demonstrated an ultra-narrowband absorber based on the surface lattice resonances of Au-nanoring and the nanowire arrays reflecting Au metallic film substrate [15]. Ye et al. realized the double narrowband resonances through the plasmonic mode coupling between the localized surface plasmon resonance (LSPR) mode of the Au-nanoring array and the cavity modes of the Au–SiO₁–Au structure [16]. Chen et al. achieved an ultra-narrowband perfect absorber with significant electric field enhancement through the strong interaction between the magnetic plasmon in metallic split-ring resonators and the optical cavity modes of Fabry–Perot (FP) cavity [17]. Although there have been many research publications about utilizing the electromagnetic mode coupling mechanism to achieve narrowband perfect absorption mentioned above, there are few results related to the Fabry–Perot modes in the grating slit and the SPP waveguide mode in the dielectric layer. In addition, due to the dependence on the excitation of plasmonic or optical resonances, most of the proposed metamaterial absorbers only have one or two resonance wavelengths other than multi-wavelengths, which greatly limits its application in which multiband resonances are necessary [18,19,20,21], so it is important to study and design multi-narrowband metamaterial perfect absorbers.

In this paper, we proposed and numerically demonstrated a new multi-narrowband perfect absorber based on the strong coupling of the Fabry–Perot cavity resonance mode and the SPP waveguide mode in the Ag periodic grating/SiO₂ spacer/Ag film structure. Through systematic simulations, we demonstrated the multi-narrowband absorber with six absorption peaks and an ultra-narrow absorption bandwidth of 8 nm with peak absorption exceeding 95%. A comprehensive investigation of the spectral characteristics reveals the coupling mechanism between FP mode and waveguide modes by varying key structural parameters, including Ag-grating height, period, and slit width. Furthermore, the effect of the thickness and refractive index of dielectric spacer on the optical properties were also investigated. Our findings offer a robust platform for designing high performance multi-narrowband absorbers, with promising applications in color filter, thermophotovoltaic narrowband emitter, and plasmonic biosensing technology.

2. Modeling and Simulation

Figure 1a shows the schematic of the proposed nanostructure, in which a dielectric spacer waveguide layer is inserted between the Ag gratings and the Ag film, where h indicates grating height, w is the slit width, H and n_d are the thickness and refractive index of spacer (here is SiO₂), respectively, P is the grating period, and t₁ is the thickness of Ag film (unless otherwise specified, t₁ is fixed at 200 nm). This nanostructure can be fabricated by using a combination of electron beam lithography and a subsequent lift-off process [22,23]. The real specific area of the nanostructure is determined by how large area is needed for application scenarios. We calculated the optical properties of the nanostructure with the finite-difference time-domain (FDTD) method [24,25]. To realize high precision, the nanostructure was assumed to be infinitely long in y direction, so we built a 2D model and used one period of the nanostructure in the following simulation; the periodic boundary condition was set in ±x direction and perfectly matched layers (PMLs) was set in ±z direction under normal TM-polarized incidence, and the spatial mesh grids are set as ∆x = ∆z = 2 nm, respectively. All absorption spectra were normalized to the incident light power. The optical permittivity data of silver were sourced from Palik [26]. The nanostructure was illuminated with normally incident light in an air environment. In the real experiment, the environment (such as temperature, air pressure, and humidity) change will affect the refractive index of air. Here we fixed the refractive index of air at 1.0.

3. Results

Figure 1b presents absorption spectra of the proposed nanostructure and the reference periodic Ag grating structure with P = 500 nm, w = 100 nm, H = 400 nm, and h = 400 nm. Owing to the opaque Ag film, the transmission channel is canceled and we can obtain the absorption A by A = 1 − R. Six obvious absorption peaks and a small absorption peak at λ₀ = 519 nm are observed for the proposed nanostructure. The absorption A is high at 81%, 95.4%, 98.5%, 80.2%, 92.8%, 54.6% for λ₁ (500 nm), λ₂ (591 nm), λ₃ (676 nm), λ₄ (716 nm), λ₅ (792 nm), λ₆ (1147 nm), respectively. And the bandwidth values of these absorption peaks at λ₁, λ₂, λ₃, λ₄, λ₅ and λ₆ are 4 nm, 3 nm, 8 nm, 18 nm, 8 nm, and 60 nm, respectively. In contrast, the reference Ag grating without SiO₂ spacer (H = 0 nm) shows only one dominant peak at 771 nm and a weaker peak at λ₀ = 519 nm. This comparison clearly demonstrates that introducing SiO₂ waveguide layer between the Ag grating and Ag film enables the multi-narrowband perfect absorption. In addition, due to the coupling of the Fabry–Perot resonance mode and waveguide mode, a Fano-like resonance with an asymmetric line shape can be clearly observed at λ₃ = 676 nm and λ₄ = 716 nm in Figure 1b. Multiband absorbers proposed by other researchers in recent years were compared to evaluate the performance of the proposed nanostructures [23,27,28,29]. The results are summarized in

Table 1. Result of proposed perfect absorber compared with other multiband absorbers.

Reference	Number of Peaks	Maximum Peak Absorption	FWHM (Full-Width at Half-Maximum)	Wavelength
[27]	4	98.5%	~5 nm	2200–2400 nm
[28]	5	85.7%	/	5–100 um
[29]	5	99.3%	15 nm	800–2000 nm
[23]	5	99.9%	5 nm	750–3000 nm
Proposed	6	98.5%	8 nm	450–1200 nm

.

The influence of grating height h on the absorption spectrum of the proposed nanostructure and the reference grating is shown in Figure 2a,b, respectively. The slit supports the Fabry–Perot cavity resonance mode when the grating height h satisfies the resonance condition [30]. So, the absorption is greatly enhanced when Fabry–Perot resonance is excited as shown in Figure 2b. The black dashed lines correspond to Fabry–Perot resonance modes of different orders, which increase with the grating height. In contrast, the absorption spectrum of the proposed nanostructure (Figure 2a) not only exhibits the characteristic of Fabry–Perot modes, but also possesses two additional higher absorption bands (the vertical dashed lines). Moreover, compared to reference grating, the absorption peaks associated with Fabry–Perot resonance of Figure 2a show a difference depending on the metallic grating height h, and this behavior can be ascribed to the different phases obtained at the termination of the metallic slits (SiO₂ dielectric layer) [31].

Furthermore, the six absorption peaks with h = 400 nm from left to right in Figure 1b are denoted by P₁, P₂, P₃, P₄, P₅, and P₆, respectively. The wavelength of P₄ and P₅ remains constant with the increased grating height h, suggesting that these peaks are independent of the electromagnetic field distribution within the metal slits. In other words, the appearance of peak P₄ and P₅ has no relation with the cavity mode inside the metallic slits and the specific mechanism will be discussed later through the field distribution. Although peak P₁ (500 nm) also remains constant with the increased grating thickness, the mechanism is not same as that of P₄ and P₅. Herein, the absorption peak (P₁) is caused by the Wood Rayleigh anomaly, which is mainly determined by the period of the grating [32].

Figure 2a reveals an additional interesting aspect of the Fabry–Perot mode and the waveguide mode. As grating thickness h increases, the absorption peak (caused by Fabry–Perot mode) red-shifts, while the absorption peaks caused by the waveguide mode almost remain constant. The anti-crossing phenomenon takes place when the Fabry–Perot modes red-shift and interact with the SPP waveguide modes. To observe the anti-crossing behavior between the Fabry–Perot mode and waveguide mode more intuitively, Figure 2c,d displays the absorption spectra as the grating thickness increases from 280 nm to 600 nm. Apparently, as the height of the Ag grating increases, the absorption peak caused by the SPP waveguide mode (waveguide mode 1 and 2) kept nearly constant (the horizontal black dash line), while the wavelength of Fabry–Perot cavity mode (inclined black dash line) red-shifted and interacted with the waveguide mode. When the grating thickness reaches 480 nm, the Fabry–Perot cavity mode and SPP waveguide mode exhibits a repulsion behavior. For the spectrum of h = 520 nm, the Fabry–Perot cavity resonance occurs at λ = 830 nm, which is longer than that of SPP mode (λ = 792 nm). This simulation result clearly indicates the anti-crossing behavior in the proposed nanostructure, demonstrating the strong mode coupling between the Fabry–Perot cavity mode and the SPP waveguide mode.

To further understand the physical origin of the multiple narrowband absorption peaks and the Fano-like resonance with an asymmetric line-shape of the proposed nanostructure, we calculated the magnetic field distribution pattern of the different absorption peak wavelength (P₁, P₂, P₃, P₄, P₅, and P₆) with grating thicknesses of 300 nm and 400 nm (the structure parameter are P = 500 nm, w = 100 nm, and H = 400 nm), respectively. As mentioned above, the peak P₁ is caused by the Wood Rayleigh anomaly, so the field distribution of peak P₁ is not shown here. As shown in the first row of Figure 3 (h = 300 nm), the second order, first order and first order vertical FP cavity mode are excited in the grating slit at peak P₂, P₃, and P₆, respectively. For peaks P₄ and P₅, the magnetic field is mainly concentrated at the Ag-grating/SiO₂ interface or the interface between the SiO₂/Ag film, showing the characteristic of SPPs along the x direction, which is also regarded as the waveguide mode in the dielectric waveguide on Ag film. Under the condition of h = 400 nm, the peak wavelength and field distribution pattern of P₅ almost remain unchanged. Peaks P₂ and P₆ redshift with the increased grating thickness and do not couple with the other mode, so the field pattern is also same as that of h = 300 nm. But for the peak P₃, the cavity resonance red-shifts and interacts with the waveguide mode at P₄, so the field pattern experiences a big change, as shown in Figure 3g,h. Therefore, it is convenient to adjust the mode coupling between the Fabry–Perot mode and the SPP waveguide mode and realize the multi-narrowband absorption by tuning the grating height h.

In order to further understand the characteristics of these narrowband absorption peaks and the anti-crossing behavior, we have also systematically investigated the effects of geometric parameters on the optical properties of the proposed nanostructures in Figure 4 by individually changing H, w, n_d, or P from the base values given in Figure 1 (P = 500 nm, w = 100 nm, H = 400 nm, h = 400 nm, n_d = 1.5). The effect of SiO₂ waveguide thickness on the absorption is shown in Figure 4a, and the value of absorption peak increases with the increased SiO₂ film thickness H, which can be attributed to the illustration that the thicker dielectric layer can support more waveguide modes [33]. The SiO₂ thickness H increases from 200 nm to 600 nm, and the absorption peak increases from five to eight (short dash circle in Figure 4a).

The effect of slit width w on the absorption spectra of the nanostructures with parameters fixed at h = 400 nm, P = 500 nm, H = 400 nm, and n_d = 1.5 under TM-polarized light normal incident is shown in Figure 4b. The peak wavelength of P₁, P₄, and P₅ remains almost constant with the increased slit width. As described above, the absorption peak P₁ is caused by the Wood Rayleigh anomaly, so it is independent of the slit width. Peak P₄ and P₅ are caused by the SPP waveguide mode, and therefore their resonance wavelengths are also independent of the slit width. However, the P₂, P₃, and P₆ are mainly induced by the cavity resonance in the Ag-grating slit, which causes the peak wavelength to be strongly dependent on the slit width and blue-shift with the increased slit width, which matches well with the previous theory [32]. In addition, with the increased slit width, peak P₄ generates an anti-crossing with peak P₃, so the Fano-type resonance wavelength can also tailored by adjusting the slit width.

Figure 4c presents the effect of the refractive index n_d of the waveguide layer on the absorption spectra of the proposed nanostructures with w = 100 nm, t = 400 nm, P = 500 nm, and H = 400 nm. Except P₁, the absorption peaks (P₂, P₃, P₄, P₅, P₆) all have an obvious red-shift with the increased refractive index n_d. For P₂, P₃, and P₆, the red-shifts are caused by the different phase changes at the termination of the slit. For P₄ and P₅, the SPP waveguide mode is sensitive to the dielectric environment [34]. In addition, when the index grows up to 1.6, new absorption peaks (labeled as m = 1, m = 2, m = 3) arise in the short wavelength region. The mechanism is similar to that of the new absorption peaks induced by the increased thickness of waveguide layer in Figure 3a. According to SPP waveguide theory [34], the number of transmission modes in the waveguide is strongly dependent on the thickness and refractive index of the waveguide. In addition, when the P₂ mode red-shifts with the increased refractive index, it anti-crosses with the higher order waveguide mode (which is labeled as m = 1).

Figure 4d shows the influence of grating period P on the absorption spectra of the proposed nanostructure when it increases from 500 nm to 800 nm. The resonant wavelength of the Fabry–Perot mode at 591 nm (P₂) and 676 nm (P₃) only slightly shift (even unchanged for P₃) with the change in period P, except for the region (larger than 650 nm) of coupling with the Wood–Rayleigh anomaly mode (white dash line label as n = 1). When the Fabry–Perot cavity modes couple with the Wood–Rayleigh anomaly mode, the resonance bandwidth drastically decreases. The resonance peaks at λ₄ = 716 nm (P₄) and λ₅ = 792 nm (P₅) are caused by the first order SPP mode at the Ag-grating/SiO₂ interface and SiO₂/Ag film interface, respectively. So, these modes possess the characteristic of the SPP mode, and the absorption peaks red-shift with the increased period P.

In addition, with the increased period P, higher-order SPP waveguide modes occur, and the dash lines labeled by n = 2 and n = 4 respond to the second order SPP mode and third-order SPP mode at the SiO₂/Ag film interface, respectively. The white dash line labeled as n = 3 responds to the second order SPP mode propagating along the Ag-grating/SiO₂ interface. As mentioned above, the peak P₆ is caused by the Fabry–Perot cavity mode in the grating slit, so it is original and did not vary with the period P, but with the increased period, the wavelength of P₅ red-shifts and couples with P₆, so peak P₆ will red-shift with the increased period P. Therefore, the resonance absorption behavior of the proposed nanostructure can be adjusted by selecting suitable structural parameters. In addition, it has to be noted that the period P, grating height H, and dielectric thickness h have a big influence on the optical properties, and the slit width w has a small effect on the optical properties; therefore, in the fabrication process, the period P, grating height H, and dielectric thickness h should be precisely controlled.

The influence of oblique incident light on the absorption spectra of the nanostructure (P = 500 nm, w = 100 nm, H = 400 nm, h = 400 nm) was also investigated as shown in Figure 5. The peaks P₄ and P₅ at normal incidence split into two absorption peak bands (but still kept the narrowband) when the incident angle increased from 0 to 30 degree. As mentioned above, the peaks P₄ and P₅ are caused by the excitation of SPP (P₄, P₅). At oblique incidence, the two split absorption peak bands correspond to the excitation of two SPPs with opposite wave vectors in x direction of propagation on the Ag/SiO₂ interface. In contrast, the Fabry–Pérot (FP) cavity resonance is inherently angle-independent. Consequently, the wavelength positions of peaks P₂, P₃, and P₆ relate to the FP cavity mode within the grating slit, which remains nearly constant for incident angles up to 8°. However, at larger angles (>8°), the split SPP modes interact with the FP cavity mode, inducing strong coupling between the two [35]. This hybridization results in a mixed mode, exhibiting characteristics of both resonances, thereby causing the FP cavity mode to shift with the incident angle.

To deeply elucidate the physical mechanism of the excitation of the two SPPs at the Ag/SiO₂ interface, Figure 5b,c shows the distribution of the real part of the electric field (Ey) and the magnetic field (Hz) at incident angles of 10° for wavelengths of 723 nm and 875 nm, respectively. Evidently, electromagnetic fields are strongly localized at the SiO₂ waveguide dielectric/Ag film interface. An exponential decay of the electric field (Ey) along the z-direction is observed. While the spatial distribution of Ey is similar for both wavelengths (723 nm and 875 nm), the spatial distribution of Hz exhibits opposite profiles. According to the fundamental properties of electromagnetic plane waves, the components kx, Ey, and Hz satisfy the right-hand rule, where kx represents the wave vector of the SPPs at the SiO₂ waveguide/Ag interface along the x-direction. Therefore, we conclude that the SPPs at the SiO₂ waveguide/Ag interface for 723 nm and 875 nm propagate in opposite directions along x. This confirms that the two excited SPP modes possess opposite wave vectors in the x-direction. In summary, the splitting of absorption resonances (modes P₄ and P₅) with the incident angle, as observed in the SPP modes, demonstrates that our theoretical explanations are in excellent quantitative agreement with the FDTD simulation results. It should be noted that the proposed nanostructure consists of one-dimensional grating, so the optical properties would be sensitive to the polarization state of incident light. In the future, we can realize the polarization-insensitive multi-narrowband perfect absorber by designing the 2D grating or nanopillar array (distributed in quadrangle or orthohexagnal) [29,36] on the top of the nanostructure.

4. Conclusions

In summary, a new multi-narrowband perfect absorber consisting of periodic Ag-grating and Ag film separated by a SiO₂ waveguide layer has been proposed and investigated. Six ultrasharp absorption resonance with a minimum bandwidth as narrow as 8 nm and an absorption peak amplitude surpassing 95% were obtained at normal light incidence. Numerical simulations demonstrate that the multi-narrowband absorption arises from the Fabry–Perot resonance in the slit coupling with the propagating SPP waveguide mode at the SiO₂/Ag-grating or Ag film interface. Moreover, the simulation results imply that the absorption properties are sensitive to structural parameters and the refractive index of waveguide layer, indicating the spectra tunability and selectivity of the proposed nanostructure. Those findings may offer valuable insights for the designing of multi-narrowband perfect absorbers, which could easily find significant applications in filters, nonlinear optics, and biosensors, where multi-ultranarrow band perfect absorption is necessary.