1. Introduction

Metal–insulator–metal (MIM) based infrared (IR) perfect absorbers—a type of artificial material composed of arrays of subwavelength structures—can manipulate electromagnetic waves to exhibit extraordinary light absorption performance [1–5]. The MIM structure can couple with the electric and magnetic components of the incident wave, by matching it’s impedance to free space, to perfectly absorb the light with a specific wavelength [6]. The MIM-based IR dual-band perfect absorbers have proven promising in many expanding fields such as refractive index sensing, absorption spectroscopy, spectroscopic chemical fingerprinting, etc [2,7–11].

The geometry of the subwavelength metal structure on top of an MIM-based IR perfect absorber is multitudinous, as an ellipse [12], a rod [11], a square [9], a cross [6,13], etc. The cross-structure is a type of electric ring resonator that can interact strongly with the electric component and negligibly with the magnetic component of the incident electromagnetic wave. Nevertheless, by connecting the cross-structure to a metallic ground plane, an antiparallel current can be generated, owing to strong coupling of the cross-structure and ground plane to the magnetic component of the incident electromagnetic wave. Consequently, unity absorption can be achieved at a specific frequency in the cross-shaped MIM infrared perfect absorber (CS-MIM-IPA) [2]. Sungho Kang et al. demonstrated that the CS-MIM-IPA has the advantage of achieving near-unity absorption, independent of incident angle and polarization of the impinging radiation [8]. Kai Chen et al. utilized asymmetric cross structures to accomplish a dual-band perfect absorber [10]. Moreover, these two resonant bands can be readily, or even independently, tuned throughout the mid-IR wavelength range, owing to the independent spectral modulation by two asymmetric arms of the cross-structure [14]. Further, Xianliang Liu reported the development of a spatially dependent metamaterial perfect IR absorber using a cross-shaped MIM structure [6]. In the following year, Liu further demonstrated the development of selective thermal emitters based on cross-shaped MIM metamaterial absorbers consisting of differently scaled cross structures, thereby introducing the great flexibility of metamaterials for tailoring blackbody emission [15]. The above-mentioned studies indicate that the feasibility of employing cross-structures to customize highly efficient MIM metamaterials for various applications have been widely investigated in the recent years [16]. Currently, independent control of the dual-absorption bands of the CS-MIM-IPA structure is still heavily discussed. For dual-band perfect absorbers, independent control of the absorption peaks allows for the design of customized metamaterials to meet various applications and requirements. More importantly, a detailed analysis of the influence of the structural parameters from the aspects of structure size, array size et al., on the performance of perfect absorber and the related underlying mechanism, are of great importance for practical applications and further development of metamaterial devices. However, such studies are still, to the best of our knowledge, insufficient [6,8,10,14].

Here, we demonstrate independent tunable dual-absorption bands CS-MIM-IPA structure. Active modulation of the surface plasmon polaritons mode (SPP mode, with narrow linewidth) and localized surface plasmon mode (LSP mode, with broad linewidth) had be achieved. The results show that the peak position of the LSP mode and SPP mode are dominated by the arm length and the period size, respectively. The parallel arm controls the resonant wavelength of the LSP modes. The perpendicular arm has negligible influence on the resonant wavelength of the SPP modes, while it has a noticeable influence on that of the LSP modes at the beginning of the perpendicular arms. Furthermore, the role of plasmon coupling effects and space ratio of the cross-structure in balancing the absorption intensity of the LSP modes had been investigated.

2. Methods

The simulation was performed using finite difference time domain (FDTD) simulations (FDTD Solutions, Lumerical Inc.). A schematic of the cross-shaped MIM absorber, which was composed of an Au reflector, cross arrays on top, and a dielectric layer in between, is shown in Fig. 1(a). The cross-structure is composed of four arms (with Lx and Ly lengths), whose axes are along the x- and y-axis, respectively. A circular configuration on the corner of each arm was set with a radius of 100 nm. The thickness of the Au cross-structure was 150 nm, and that of the SiO₂ dielectric layer and Au plane was 200 nm and 100 nm, respectively. As the Au plane was thicker than the penetration depth of the incident IR light, the transmission of the CS-MIM-IPA can be considered as zero, and the wavelength-dependent absorption of the structure can be directly obtained by the formula:

 

Fig. 1. Schematic representation and optical response of CS-MIM-IPA. (a) Schematic representation of CS-MIM–IPA. The blue and pink arrows indicate the light illumination direction (along the backward direction of z-axis) and the electric field polarization direction (along the x-axis), respectively. The black dotted line represents the shadow of the near-field monitor, in x-z plane, upon the cross-structure that is in the middle of the Ly arms. The orange dotted line represents the location of the extracted near-field profile of SPP (shown in Fig. 2(c). (b) Absorption spectrum of the CS-MIM-IPA with Lx = Ly = 0.6 μm and Px = Py = 3.6 μm. (c) and (d) Near-field distribution (bottom panel) and Ez component of the electric field distribution (upper panel) in x-z view with the excitation wavelengths of 4595 nm and 3652 nm, which are labeled by blue and red circles in (b), (c), and (d), respectively. The golden dotted rectangles are for guiding the eyes to the location of the cross-structure. The length of the white bar shown in (c) is equivalent to 500 nm.

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The refractive index of Au was taken from the experimental data recorded by Johnson and Christy [17]. A plane wave source was used to normally illuminate the structure along the z-axis. Period boundaries were applied along the x and y axes, and perfectly matched layer (PML) boundaries were used in the z-direction to terminate the simulation area. An override mesh size of 10 × 10 × 10 nm³ over the Au structure and Au plane was used to obtain accurate optical response of the CS-MIM-IPA structure.

3. Results and discussions

The constitutive parameters correspond to the length of the parallel arm of the cross-structure (indicated as Lx, whose direction is along the polarization direction of light); length of the perpendicular arm of the cross-structure (indicated as Ly, whose direction is perpendicular to the polarization direction of light); period of the cross-structure elements in the parallel (denoted by Px) and perpendicular directions (denoted by Py). The absorption spectrum of the CS-MIM-IPA structure, with Lx = Ly = 0.6 μm and Px = Py = 3.6 μm, is shown in Fig. 1(b). Two absorption peaks located at 3.7 μm and 4.5 μm with absorption rates of 95.5% and 95.3% corresponding to the SPP and LSP modes can be observed, respectively. Note that the linewidth of the LSP mode (at 4.57 μm, indicated by a red circle) is much broader than that of the SPP mode (at 3.7 μm, indicated by a blue circle). This can be attributed to the stronger ohmic loss and radiation damping of the LSP modes [6]. Further, the LSP mode results from the excitation of the LSP in each cross element and was accompanied by an electric field that was mainly concentrated in a small region near the Au structure (as shown in the upper panel of Fig. 1(c)). Accordingly, the LSP modes, generally, accompany a broad linewidth (270 nm full width at half maximum in this case). In contrast, the SPP modes resulted from the excitation of SPPs between each cross array was mainly located in the vacuum area (as shown in the upper panel of Fig. 1(d)) [18]. Therefore, as the SPPs are excited at the metal/vacuum interface, this ohmic loss associated with this mode decreases. Moreover, due to the non-radiative character of the SPP modes, nearly no radiation damping, the SPP modes give rise to a narrow linewidth compared to the LSP modes [19].

The absorption spectra of CS-MIM-IPA with variation of Lx from 0 nm (corresponding to a rod oriented parallel to the y-axis) to 650 nm are shown in Fig. 2. Two different frequency regimes are considered: the resonant frequency of the LSP mode higher (regime 1, f_LSP> f_SPP, shown in Fig. 2(a)) and lower (regime 2, f_LSP< f_SPP, shown in Fig. 2(b)) than that of the SPP mode. Figure 2(a) shows that LSP modes with broader linewidths were observed at a wavelength of approximately 3.00 μm with an Lx of 300 nm (shown by the green curve), which then notably redshifted, as indicated by the black dotted arrow in Fig. 2(a). Note that no LSP peak can be seen when the Lx is 0 nm (rod), 100 nm, and 200 nm. This is because the corresponding LSP peak wavelengths are beyond the spectral range considered here. The SPP mode observed in the blue curve in Fig. 2(a) corresponding to an Lx of 200 nm became stronger and slightly redshifted as Lx was further increased to 350 nm (as indicated by the red dotted arrow). Furthermore, an anomalous spectral profile that includes two peaks, located at approximately 3.60 μm and 3.75 μm with no distinct linewidth difference, can be observed at 410 nm Lx. This spectrum profile results from a coupling between the LSP and SPP modes, due to spectral overlapping between them, and does not distinctly correspond to the LSP and SPP modes [18]. Note that, the variation interval of Lx, as shown in Fig. 2(a), was not equal. This is because we wanted to observe the appearance of the SPP and LSP modes (for the case of Lx equal to 200 nm and 300 nm, respectively) and their variation trends, simultaneously. If Lx varied at constant intervals, the case for 350 nm Lx would have been replaced by 400 nm, which would have corresponded to a coupling situation and induced spectral indistinguishability between the SPP and LSP modes. Moreover, it should be noted that the absorption peak of the SPP mode at 350 nm Lx has negligible divergence over the red dotted arrow. This reveals that Lx has only a slight influence on the resonant wavelength of the SPP modes in regime 1.

 

Fig. 2. Absorption spectra of the cross-shaped MIM IPA structure with the variation of parallel arm length (Lx) from 0 to 410 nm (a) and from 470 nm to 650 nm (b). The black and red dotted arrows indicate the peak position of LSP and SPP modes. (c) Near-field profile of SPP modes along x-direction with Lx of 470 and 650 nm (The monitor was located at the position shown by the orange dot line in Fig. 1 (a)) . (d) and (e) show the Ez component distribution, in x-z plane, of two different SPP modes, which is marked by blue and red circles in (a) and (b), respectively.

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With further increase in Lx to 470 nm, the LSP and SPP modes spectrally separated and two peaks with distinct linewidths were observed again, as shown in Fig. 2(b) (located in regime 2). The absorption peak wavelength of LSP modes monotonously redshifted from 3.9 μm to 4.7 μm, as indicated by the black dotted arrow, with Lx increasing from 470 nm to 650 nm. However, the peak wavelength of SPP modes did show stationary, as indicated by the red dotted arrow. The near-field distribution profiles of the SPP modes at Lx = 470 nm and 650 nm, obtained by a linear near-field monitor located in the middle of two cross-structure elements (marked by a golden dotted line in Fig. 1 (a)), are shown in Fig. 2(c). It can be seen that the two nodes and the antinode of the SPP show perfect spatial overlapping, which indicates that the resonant wavelength of the SPP modes does not vary in regime 2.

It can further be observed that the increase in Lx has an influence on the resonant wavelength of the SPP mode in regime 1 (shown in Fig. 2(a)) and nearly no influence in regime 2 (shown in Fig. 2(b)). The different impact of Lx variation on the resonant wavelength of the SPP modes in these two frequency regimes can be attributed to the electron reservoir effects [14,20]. Specifically, a plasmon mode with a higher resonant frequency can support the oscillation of the mode with lower resonant frequency; however, it cannot work with a lower resonant frequency. With the increase in Lx, the resonant wavelength of the LSP mode undergoes redshift. In regime 1 (f_LSP> f_SPP), the corresponding electrons of the LSP mode can participate in the oscillation of the SPP mode. As a result, the resonant wavelength variation of the LSP mode can influence the SPP mode and result in a slight redshift the resonant wavelength of the SPP modes. In regime 2 (f_LSP< f_SPP), however, the electrons corresponding to the LSP mode can no longer follow the oscillation of the SPP mode; therefore, the increase in Lx does not influence the resonant wavelength of the SPP modes anymore.

This conclusion is further supported by the Ez component of the near-field distribution. The Ez component distribution under 3.71 μm excitation with Lx = 350 nm (marked by blue circle in Fig. 2(a)) and under 3.65 μm excitation with Lx = 650 nm (marked by red circle in Fig. 2(b)) are shown in Fig. 2(d)) and (e), respectively. Figure 2(d) shows that the intensity of the LSP mode (which is strongly localized within the dielectric layer, as labeled by olive arrows), is highly enhanced and its phase is the same as that of the SPP mode (labeled by orange arrows). Moreover, we found that the excitation position of SPP in Fig. 2(d) is located at the interface between the dielectric layer and vacuum, and a strong coupling between the LSP and SPP modes can be seen (as labeled by the white dotted ellipse).

In contrast, as shown in Fig. 2(e), the intensity of the LSP mode within the dielectric layer is extremely weak, and the phases between the LSP and SPP modes are opposite to each other. The SPP excitation position is mainly localized in the upper surface of the cross-structure, and no interaction between the LSP and SPP modes can be seen. By comparing Figs. 2(d) and 2(e), we can observe a migration of the SPP excitation from the bottom of the Au/ITO interface (in regime 1) to the top of the Au/vacuum interface (in regime 2) of the cross-structure. The near-field distribution further sustains our inference that in different frequency regimes the influence of Lx variation on the optical response of the SPP mode is different.

Next, we changed Ly from 0 nm (a rod with main axis parallel to x-axis) to 500 nm in steps of 100 nm. The corresponding absorption spectra are shown in Fig. 3. It was found that the resonant wavelength of the LSP mode displayed a non-monotonic blueshift over the range of Ly from 0 to 500 nm, as indicated by the black dotted arrow. To present the variation of LSP modes more clearly, the peak position related to Ly is shown in the inset in Fig. 3(a). It was observed that the peak position represented a non-monotonic relation with Ly: it first strongly blue shifted from approximately 4.75 μm to 4.60 μm with Ly changing from 0 to 200 nm and then, gradually blue shifted with Ly changing from 200 nm to 500 nm. In short, Ly presents an obvious influence on the resonant wavelength of the LSP modes at the beginning of their emergence, and then, this influence becomes weaker with the increase in Ly.

 

Fig. 3. Absorption spectra and Ez component distribution of CS-MIM-IPA with the variation of Ly. (a) Absorption spectra of CS-MIM-IPA with the variation of Ly from 0 nm to 500 nm with an interval of 100 nm. Lx is kept within 600 nm. The red and black dotted arrows represent the variation trends of SPP and LSP modes, respectively. The inset in (a) displays the peak position of LSP modes, corresponding to Ly, in different perpendicular arm materials: black rectangles for Au, blue circles for silica, and green triangles for silicon (connecting lines have been drawn to guide the eye). (b) to (d) show the Ez component distribution of the cross elements excited by the resonant wavelengths of corresponding LSP modes with Ly of 0 nm, 100 nm, 200 nm, and 500 nm, respectively. The insets in (b) to (e) display the enlarged images of the perpendicular and parallel arms. The olive arrows indicate the position with maximum electric field density in the perpendicular arms.

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The resonant wavelength variation of the LSP modes with Ly can be attributed to the decrease in the repelling force against the oscillating electrons, which support the LSP mode of the parallel arms with the increase in Ly. It is known that a decrease in the repelling forces in an isolated nanostructure will undoubtedly result in a blueshift of the LSP resonant wavelength [19]. Therefore, Ez component distribution of the cross structures is plotted to ascertain the influence of the free electron induced repelling the force on the LSP modes, as shown in Fig. 3(c) and 3(e). Figure 3(c) displays the Ez component distribution of the cross structures, in x-y view, with Ly of 100 nm. Note that additional charges, which are same as in the corresponding parallel arms (shown by the olive arrow in the enlarged view images in Fig. 3(c)), appear along the transverse axis of the perpendicular arms. With further increase in Ly to 200 nm and 500 nm, the apex, which has the maximum charge density in the perpendicular arm (shown by the olive arrows in Fig. 3(d) and 3(e), respectively), shifts away from the parallel arms. Moreover, we observed a decrease in the maximum near-field intensity on the apex of the perpendicular arms as Ly increased. Both of these result in weakening of the repulsive force against the oscillating charges in the parallel arms. Therefore, when Ly was between 200 and 500 nm, a gradual blueshift variation trend was observed.

To further demonstrate the role of the free electrons in the perpendicular arms on the resonant wavelength of the LSP modes, we replaced the perpendicular arms’ material with silica and silicon. The corresponding LSP peak position related to Ly is shown in the inset of Fig. 3(a) by the blue circles and green triangles (connecting lines have been drawn to guide the eye), respectively. The results show that as the silica arm length changed from 100 nm to 500 nm, the LSP peak wavelength varied from approximately 4.741 μm to 4.745 μm (equivalent to a variation of 4 nm). Further, when silicon was used as the perpendicular arm material and Ly was changed from 100 nm to 500 nm, the LSP peak wavelength varied from approximately 4.752 μm to 4.766 μm (equivalent to a variation of 14 nm). For Au, the variation reached approximately 200 nm. These results further demonstrate the roles of free electrons in the perpendicular arms and the influence of the repulsive force on the LSP modes.

Figure 3(a) further shows that the perpendicular arms have nearly no influence on the resonant wavelength of the SPP modes, as indicated by the red dotted arrow. This observation can be explained by the fact that the SPP modes are resulting from the coupling between the elements among the periodic structures, and the perpendicular arms locates in the node position of the SPP modes (as shown by the near-field distribution in Fig. 4(d)).

 

Fig. 4. Absorption spectra and near-field distribution of CS-MIM-IPA with the variation of period size within cross-shaped elements. Absorption spectra of CS-MIM-IPA with the variation of Px from 3.0 μm to 3.8 μm (a) and of Py from 3.0 μm to 5.0 μm (b). When we varied Px, the size of Py was fitted as 3.8 μm and vice versa. The red and black dotted arrows represent the variation trends of SPP and LSP modes, respectively. The insets in (a) and (b) display the maximum absorption of SPP modes (black rectangular data points) and LSP modes (red circular data points) related with Px and Py, respectively. Figure 4(c) and (d) display near-field distribution, in x-y view, of the resonant SPP modes at 3.0 μm and 3.7 μm wavelengths, respectively, (labeled by yellow and red circles in (a)) with Py of 5.0 μm. Figure 4(e) and (f) display the near field distribution of Ez component at the wavelength of 3.0 μm (e) and 4.5 μm (f).

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In the previous discussions, it was noted that Lx and Ly can considerably influence the resonant wavelength of the LSP mode. As the SPP mode is strongly related to the coupling among each cross-shaped element, period of the cross-shaped elements can be used to control the SPP modes.

We further varied period of cross-shaped elements and the influences on the optical responses of CS-MIM-IPA can be observed in Fig. 4. With Px varied from 3.0 μm to 3.8 μm, the resonant wavelength peaks of the SPP modes monotonously redshifted, as labeled by the red dotted arrow in Fig. 4(a). Moreover, nearly no influence on the resonant wavelength of the SPP mode can be observed with Py varying (as indicated by the red arrows in Fig. 4(b)). However, an obvious change in the maximum absorption intensity of the SPP modes for both the cases (Px and Py variation) can be observed. By observing the maximum absorption peak intensity at different periods, the period size dependency of the absorption peak intensity can be obtained, as indicated by the black rectangles (connecting line has been drawn to guide the eye) in the insets of Fig. 4(a) and 4(b).

The result shows that, with Px varying from 3.0 μm to 3.6 μm (equal to Py), the maximum absorbance of the SPP modes changes from approximately 60% to more than 99%, and then, decreases to 96% with Px of 3.8 μm, as shown in the inset of Fig. 4(a). Afterwards, when we changed Py, the maximum absorbance of the SPP modes changed from approximately 70% to more than 95% as Py increased from 3.0 μm to 3.6 μm (equal to Px) and then, sharply decreased to 60% with a Py of 3.8 μm, as shown in the inset of Fig. 4(b). The maximum absorption trend of the SPP mode in both cases was similar. It should be noted that we only increased Px to 3.8 μm because the resonant wavelength of SPP modes would redshift (be close to that of LSP mode) and result in a coupling between the LSP and SPP modes with relatively large Px. This coupling induces an irregular profile (as shown by the blue line in Fig. 1(a)), and the peak intensity in this case cannot be used to assess the intensity variation trends. As the resonant wavelength of the SPP and LSP modes nearly fix with the variation of Py, we can further expand the evaluated period size of Py. It shows that the absorption peak intensity of the SPP modes of the MIM structure gradually decreases with further increase in Py over the range from 3.8 μm to 5.0 μm. Further, it is worth noting that the maximum absorption peak intensity of the SPP modes is obtained with a Px (Py) of 3.6 μm, which is equal to Py (Px). In other words, maximum absorption for the SPP modes is achieved when the period size in both x- and y-direction remains same. In addition, we investigated the absorption response of the absorber at different length of parallel arms keeping Px = Py, and the result is not shown here. It was found that the absorption intensities of SPP and LSP peaks can maintain near-unity with the increase of parallel arms from 3.6 μm to 4.2 μm. Specifically, the absorption of the SPP band was almost larger than 99%, and the LSP band raised from 96% (Px = Py = 3.6 μm) to 99.9% (Px = Py = 4.2 μm). This result further supports our previous conclusion that the highest absorption is achieved with Px being equal to Py.

The relationship between the maximum absorption trend of the SPP mode and period size can be explained as follows. It is known that SPP is strongly related to the coupling among the structural elements of the MIM-IPA [11]. As the SPP is excited along the x-direction, a variation in Px induces a grating constant change and will undoubtedly change the coupling wavelength of the SPP modes. Moreover, the space between two cross-structure elements in the y-direction acts similar to a resonant oscillator that can, to some degree, modulate the oscillation of the SPPs. This hypothesis is supported by the absorption profile shown by the purple curves in Fig. 4(b), where a lesser intense peak (denoted as P3) is observed at approximately 3.0 μm with the increase of Py to 5.0 μm. Figure 4(c) shows the corresponding near-field distribution of the P3 mode which is analogous to standing wave generated along y direction. From these results, it can be inferred that the SPP will be influenced by the period size not only in the parallel arm direction, but also in the perpendicular arm direction as well.

Figure 4(a) and 4(b) show that the period size, in both x- and y-direction, has nearly no influence on the resonant wavelength of the LSP modes. However, an influence on the LSP mode’s absorption intensity can be observed. The maximum absorption of the LSP mode, corresponding to Px and Py, is displayed by the rectangular data points (connecting line has been drawn to guide the eye) in the insets of Fig. 4(a) and (b). It clearly shows that with Px varying from 3.0 μm to 3.8 μm, the maximum absorptivity increases approximately from 90% to 98%. When Py is increased from 3.0 μm to 4.8 μm, the maximum absorptivity increases approximately from 90% to 99% and then, sharply decreases to 50% with a Py of 5.0 μm.

The enhancement of the absorption intensity of the LSP modes with an increase in the period size can be attributed to a decrease in the plasmon coupling between the elements [20]. Although LSP is a highly confined electromagnetic mode, some recent studies have demonstrated that the LSP supported by the structures will couple with each other through plasmon coupling [21] or grating effects [22], even though the distance between each element is in a range much larger than the near-field coupling limits (generally, of the order of tens of nanometers). Moreover, this type of coupling can sometimes result in a small near-field enhancement and shorter dephasing time (corresponding to stronger damping) compared with the isolated structures, owing to a faster radiative decay rate [21]. In our case, as the period size increased from 3.0 μm to 4.8 μm, the damping of the LSP modes reduced because of the decrease in the LSP’s coupling among the cross-structure elements, which resulted in an increase in the absorption intensity. To reveal the mechanism of the sharp decrease in the maximum absorption of the LSP mode with a Py of 5.0 μm, we further extracted the near field distributions of Ez component corresponding to P3 (3.0 μm) and LSP (4.5 μm) as shown in Fig. 4(e) and 4(f), respectively. Figure 4(e) shows that the phase of Ez component at the two parallel arms along negative and positive direction of x-axis are positive and negative, respectively, at the wavelength of 3.0 μm. It is opposite to the case at the wavelength of 4.5 μm corresponding to the excitation of LSP, as shown in Fig. 4(f). Therefore, we can inferr that the excitation of P3 mode inhibits the excitation of LSP and result in a dramatic decrease of the absorption amplitude at Py = 5 μm. Moreover, we speculate that this decrease in the absorption intensity may also a consequence of the decreasing space ratio of the cross-structure in the whole CS-MIM-IPA with the increasing Py. As discussed in the previous sections, the increase in Py induces a stronger LSP and enhances the absorption due to reduced damping. Simultaneously, the space ratio without the Au cross-structure will increase as well, and it will decrease the absorption of the entire structure to some extent. For Py varying from 3.0 μm to 4.8 μm, the decreased plasmon coupling effects are dominant and with a further increase of Py to 5.0 μm, the decrease in the space ratio of the cross-structure in the whole structure becomes dominant.

Q factor plays an important role in the application of plasmon devices in sensing and spectroscopy. We also presented Q factors of the MIM absorbers under different conditions (with the variation of Lx, Ly, Px and Py, respectively). Q factors are extracted according to the following formula [23] Q = λres/FWHM_λres and the results are shown in Fig. 5. It can be seen that Q factor of LSP peaks is always around 15. Note that, Q factor of the LSP increases to around 23 with Lx = 470 nm as shown in Fig. 5(a). The increase of Q factor is attributed to a compression to peak width of LSP due to the strong coupling between LSP and SPP (as shown in Fig. 2(b)). It can be seen from Fig. 5 that Q factor of SPP peaks are nearly 10-20 times higher than that of LSP. Consequently, we will mainly discuss the influence of structural parameter on Q factor of SPP in the following. As shown in Fig. 5(a), Q factors of SPP are nearly the same (around 150) with Lx = 470 nm and 530 nm and then enhanced to around 300 with Lx = 650 nm. The relative lower Q factor with Lx = 470 nm and 530 nm results from the coupling between SPP and LSP that broadens the bandwidth of SPP as shown in Fig. 2(b). With further increase of Lx, the resonant wavelength of LSP redshift and accordingly the coupling between SPP and LSP weakens significantly. When Lx = 650 nm, Q factor of SPP reaches a maximum of about 310. The result shows that Q factor of SPP will increases as the resonant wavelength of LSP being away from the one of SPP. Q factor related with Ly is shown in Fig. 5(b). It shows that Q factor gradually decreases (from 330 to 250) with Ly increasing from 0 nm to 200 nm. By comparing with Fig. 3(a), we can demonstrate that Q factor of SPP will decrease as the LSP peak and SPP peak approach each other. This result is consistent with the variation rule obtained from Fig. 5(a). As shown in Fig. 5(c), Q factor gradually increases as Px increases from 3 μm to 3.6 μm, and suddenly decreases with Px = 3.8 μm. We attributed the sudden decrease of the Q factor to the coupling between SPP and LSP (as shown in Fig. 4(a)) that leads to the reduction of SPP strength and broadening of its bandwidth that significantly reduces the Q factor. Figure 5(d) shows Q factor at different Py. With Py increases from 3 μm to 5 μm, the Q factor increases first and then becomes stable. We speculate this result to the fact that SPP intensity gradually increases with Py increases to around 3.8 μm (as shown in the illustration in Fig. 4(b)). Subsequently, the intensity of SPP decreases, that will generally reduce Q factor. Meanwhile, the resonant wavelength of LSP, however, gradually moving away from the one of SPP that corresponding to the enhancement of Q factor as mentioned in the previous. The combination of these two processes resulted in the nearly unvaried Q factor for Py = 4 μm and Py = 5 μm.

 

Fig. 5. Q factor of MIM perfect absorber with the variation of Lx (a), Ly (b), Px (c) and Py (d). The Q factors are extracted from Fig. 2(b), Fig. 3(a), Fig. 4(a) and Fig. 4(b), respectively.

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In addition to simulation, some analytical models such as transmission-line model and resistor–inductor–capacitor circuit model have been used to predict the resonance wavelength, absorption and spectral bandwidth of the perfect absorbers [8,16,24,25]. More attention is needed to a model which is suitable for the asymmetric cross structure involved in this paper in the following work. Note that, despite we did not conduct experiment, the structural parameters involved in this paper can meet the requirements of sample fabrication [6,8].

4. Conclusion

We investigated an independent control of the dual-absorption bands of the CS-MIM-IPA structure by modifying the constitutive parameters of CS-MIM-IPA (including Lx and Ly and period of the cross-structure elements). The results show that the peak position of the LSP mode and SPP mode are dominated by the arm length and the period size, respectively. Specifically, we observed that the increase in Ly resulted in a non-monotonous redshift of the LSP modes due to the Coulomb repulsion effects. The variation of the period size will exclusively change the peak position dominated by SPP modes. Furthermore, it is found that the period variation could change the absorption intensity of both the SPP and LSP modes. With the period size increasing, the absorption intensity of the LSP modes firstly increased (where the LSP coupling effect is dominant), and then, sharply decreased (where the space ratio of the cross-structure is dominant). This clearly reflects the role of LSP coupling effects and space ratio of the cross-structure in balancing the absorption intensity of the LSP modes. A strong connection between the LSP and SPP modes due to the electron reservoir effects had been demonstrated. In addition, temperature-sensitive VO₂ materials [26], graphene [27] and 2D atomic layer materials [28] may also good candidates for customized control of the performance of the perfect absorber due to the fact that the combination of these materials with MIM-perfect absorber can strongly influence the plasmon resonance [29]. Our investigations revealed the role of coupling effects between LSP and SPP on the absorption of CS-MIM-IPA and may provide deeper insights into the underlying mechanisms of the spectral modulation of the CS-MIM-IPA [30–34].