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Abstract
We investigated a mid-infrared (mid-IR) dual-band absorber consisting of a continuous gold film coated with an asymmetric silicon grating. In each unit cell of the grating, there are three unequally spaced silicon strips. Numerical results reveal that the (+1, -1) planar surface plasmon polariton (SPP) waves excited by the transverse-magnetic (TM) incidence can be coupled with different Fabry-Pérot (FP) resonances and the resonant energy is dissipated to the ohmic loss. Under the normal incidence condition, the absorber provides two high-absorbance peaks at wavelengths of 3.856 µm and 4.29 µm, with the absorption bandwidths of ∼25.7 cm−1 and ∼21.5 cm−1. When changing the angle of the incidence, it is observed an interesting feature that either of the peaks does not split. The presented structure offers an approach to the design of optical components for multi-spectral control of mid-IR signals.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Perfect absorbers are very useful for a variety of applications such as filtering [1,2], photonic detection [3,4], sensing [5–7], thermal emitting [8], and modulation [9]. In particular, subwavelength surface structure based perfect absorbers have attracted great attention due to their obvious advantages of overall thin thickness and flexible spatial variation.
To achieve such absorbers, many researchers have investigated the use of metal-insulator-metal (MIM) configurations [10–15]. MIM structure absorbers usually consist of two or more metallic layers, which is advantageous for tightly confining the electromagnetic energy on resonance. However, MIM structure absorbers typically have relatively high losses and broad operating bandwidths [1], so it is hard to use them in many narrowband applications. Compared with MIM structure absorbers, metal-based dielectric grating absorbers can have much narrower operating bandwidths [16–21]. The narrow bandwidths will benefit a number of sensing applications [22,23]. Thus, this type of absorbers is very promising.
However, most of the aforementioned metal-based dielectric grating absorbers have only a single operating band, which will be disadvantageous in many multi-spectral applications. For example, in mid-IR spectroscopy applications, absorbers with dual or multiple operating bands are particularly desirable, because we can use them to simultaneously monitor multiple spectral fingerprint regions of different chemical or biological moieties [12].
In this study, we investigated a gold film based asymmetric silicon grating structure to realize a dual- and narrow-band absorber. The grating was constructed by utilizing three unequally spaced silicon strips in each unit cell. This asymmetric configuration enables the absorber support horizontal FP resonances. The (+1, -1) planar SPP waves excited by a TM-polarized incidence can be coupled with different FP resonances, and the resonant energy is dissipated to the ohmic loss, thus generating two absorption peaks. When changing the angle of incidence, either of the two absorption peaks does not split. This is different from typical cases, where a peak at normal incidence usually splits at oblique incidence. Moreover, the influences of the geometric parameters on the performance of the absorber were discussed briefly. Although only numerical results were presented, our absorbers could be potentially compatible with various low-cost, flexible, and efficient fabrication technologies such as complementary metal oxide semiconductor (CMOS) technology [24], nanoimprint lithography [25], digital-mask projective lithography [26], and digital micromirror devices based multistep lithography [27].
2. Designed structure and performance
Figure 1(a) shows the proposed dual- and narrow-band absorber. It consists of a silicon grating on the stack of a gold film and a quartz substrate. The incident light is a traverse-magnetic (TM) plane wave, whose polarization is perpendicular to the grating lines. The absorber has a period of $\Lambda $. In each unit cell, there are three silicon strips. Figure 1(b) illustrates a single unit cell of the absorber. It is shown that the center-to-center distances between two adjacent silicon strips are different (i.e., ${d_{1}}$ and ${d_{2}}$). The silicon strips have the same width (i.e., ${w_{s}}$) and the same height (i.e., ${h_{s}}$). The thickness of the gold film is ${h_{g}}$.
Fig. 1. (a) Schematic view of the proposed dual- and narrow-band absorber. (b) Cross-sectional view of the unit cell.
To simulate the performance of the absorber, a finite-difference time-domain (FDTD) method was used. In the simulations, optical parameters of silicon and gold were taken from [28]. At normal incidence, the calculated reflection, transmission, and absorption spectra are shown in Fig. 2. The geometric parameters (in microns) are: $\Lambda = 3.0$, ${w_{s}} = 0.30$, ${d_{1}} = 0.56$, ${d_{2}} = 0.88$, ${h_{s}} = 0.70$, and ${h_{g}} = 0.10$. It is clearly seen that the transmission $T(\lambda )$ is nearly zero across the 3-5 µm wavelength range. There are two narrow dips in the reflection $R(\lambda )$. According to $A(\lambda ) = 1 - R(\lambda ) - T(\lambda )$, we obtain two narrow peaks in the absorption $A(\lambda )$. One of the absorption peaks is at ${\lambda _{1}}$ = 3.856 µm, with a full-width at half-maximum (FWHM) of ∼25.7 cm−1. The other absorption peak is at ${\lambda _{2}}$ = 4.29 µm, with a FWHM of ∼21.5 cm−1. The absorbance on resonance can be higher than 0.996.
3. Physical understanding
Figures 3(a) and 3(b) show the magnetic field profiles for ${\lambda _{1}}$ = 3.856 µm and ${\lambda _{2}}$ = 4.29 µm at normal incidence. As can be seen, the magnetic fields are bonded to the gold film, indicating planar SPP resonance modes. These SPP resonance modes are excited by the orders diffracted by the silicon grating. The excitations should satisfy the wavevector matching condition [29]:
where ${\beta _{\parallel} }$ and ${k_{\parallel} }$ are the in-plane wavevectors of the SPP mode and incident light, i is the index of diffraction orders. In our structure, the (+1) and (-1) diffraction orders need to be under consideration, so there is:Fig. 3. (a) Self-normalized magnetic field profile for ${\lambda _{1}}$ = 3.856 µm. (b) Self-normalized magnetic field profile for ${\lambda _{2}}$ = 4.29 µm. (c) Reflection spectra versus the incident angle. The horizontal dashed lines correspond to incident angles of 3.2° (the lower) and 8.8° (the upper). (d) Illustration of the (+1) plasmonic mode based on geometric optics. (e) Illustration of the (-1) plasmonic mode based on geometric optics.
According to Eqs. (2) and (3), for a usual grating, there is typically ${\lambda ^{( + 1)}} = {\lambda ^{( - 1)}}$ at normal incidence. However, owing to the asymmetric grating, there will be ${\lambda ^{( + 1)}} \ne {\lambda ^{( - 1)}}$ at normal incidence in our case. In the following, we will show this.
We first consider the case where the incident angle $\theta $ = 0. In our structure, the effective width of the silicon strips, ${n_{\textrm{Si}}}{w_{s}}$ (${n_{\textrm{Si}}} \approx 3.43$), is comparable to ${{{\lambda _{1}}} \mathord{\left/ {\vphantom {{{\lambda_{1}}} 4}} \right.} 4}$ and ${{{\lambda _{2}}} \mathord{\left/ {\vphantom {{{\lambda_{2}}} 4}} \right.} 4}$. When the excited SPP waves propagate in the ± x direction, the silicon strips can reflect the waves back and forth, thus generating horizontal FP resonances [30]. The resonance wavelength is determined by the FP resonance condition:
For ${\lambda _{1}}$ = 3.856 µm, it is shown in Fig. 3(a) that there exists a FP cavity (FP1) consisting of the strips 2 and 5. This FP cavity has a geometric length of $\Lambda $, so $n_{\textrm{eff}}^{\textrm{FP1}}\Lambda = {{m{\lambda _{1}}} \mathord{\left/ {\vphantom {{m{\lambda_{1}}} 2}} \right.} 2}$. Based on the field distribution, we know that $m$ = 2. Thus, according to Eq. (4), there is:
For ${\lambda _{2}}$ = 4.29 µm, two FP cavities (FP2 and FP3) with different geometric lengths exist, as shown in Fig. 3(b). One of the FP cavities consists of the strips 1 and 3, whereas the other consists of the strips 3 and 4. Assuming that the geometric lengths of FP2 and FP3 are ${L_{2}}$ and ${L_{3}}$, respectively, there will be:Then, to identify the resonance modes associated with the peaks at ${\lambda _{1}}$ and ${\lambda _{2}}$, we investigated reflection spectra of our structure at different angles of incidence. The results are plotted in Fig. 3(c). It is observed that, as the incident angle deviates from 0°, the peak at ${\lambda _{1}}$ exhibits a blueshift, whereas the peak at ${\lambda _{2}}$ exhibits a redshift. The observed blueshift is consistent with Eq. (2), so the (+1) mode should be associated with the peak at shorter wavelength in Fig. 3(c). However, the observed redshift is consistent with Eq. (3), so the (-1) mode should be associated with the peak at longer wavelength in Fig. 3(c). At normal incidence, there are ${\lambda ^{( + 1)}}$ = 3.856 µm and ${\lambda ^{( - 1)}}$ = 4.29 µm.
For this reason, either of the peaks does not split when changing the incident angle. This is an interesting phenomenon, and is different from typical guided-mode-resonance (GMR) and surface-plasmon-resonance (SPR) cases [6,31]. The results in Fig. 3(c) imply that the two absorption peaks can be tuned by rotating our structure with respect to the incidence. When $\theta $ < 3.2°, the intensity extinction on resonance is higher than 20 dB. When $\theta $ < 8.8°, the intensity extinction on resonance is still higher than 10 dB.
Finally, for a given incident angle $\theta $, the couplings between the incident light and the resonance modes are illustrated in Figs. 3(d) and 3(e) based on geometric optics. The incident light is diffracted by the silicon grating into (±1) orders. The (+1) diffraction order excites a SPP wave propagating in the + x direction, which is coupled with the FP resonance FP1, as shown in Fig. 3(d). However, the (-1) diffraction order excites a SPP wave propagating in the –x direction, which is coupled with the two FP resonances FP2 and FP3, as shown in Fig. 3(e). According to Eqs. (5) and (6), these FP resonances have different resonance wavelengths. Thus, our structure can provide two absorption peaks.
We should note that, in Fig. 3(d), the horizontal FP resonances between the inner silicon strip (i.e., strip 2) and the outer silicon strips (i.e., strips 1 and 3) are not excited. It can be understood as follows. The gaps between the inner silicon strip and the outer silicon strips is relatively narrow. In the investigated wavelength range, if these FP resonances were excited, they should satisfy similar conditions to Eq. (6). In this case, there will be three FP resonances in each unit cell, and the effective cavity length of each FP resonance is equal to half the resonance wavelength. However, the resonance modes in our structure is the coupled modes of SPP waves and FP resonances. Since the phase change cannot satisfy the SPP waves, the above situation is impossible.
The mechanisms of resonance absorption can be understood based on Fig. 4. For the resonance wavelength ${\lambda ^{( + 1)}}$ = 3.856 µm, Fig. 4(a) shows that the electric field is mainly confined in the left silicon slit. The displacement current in the gold film is strong. Thus, the resonant energy is dissipated as the ohmic loss, as shown in Fig. 4(b). For the resonance wavelength ${\lambda ^{( - 1)}}$ = 4.29 µm, similar phenomena are seen and the resonant energy is also dissipated as the ohmic loss, as shown in Figs. 4(c) and 4(d).
Fig. 4. (a) Self-normalized electric field (color map) and displacement current (color arrow) profiles for ${\lambda ^{( + 1)}}$ = 3.856 µm. (b) Energy dissipation profiles (in W/m3) for ${\lambda ^{( + 1)}}$ = 3.856 µm. (c) and (d) are the same as (a) and (b), but are for ${\lambda ^{( - 1)}}$ = 4.29 µm.
Moreover, in Fig. 4(d), the ohmic loss in the gold film between the strips 1 and 3 is continuous, while the energy loss at the strips 1 and 3 is discontinuous. The observed continuity of the ohmic loss is because the resonant energy should be dissipated in the cavities FP2 and FP3, as shown in Fig. 3(e). The observed discontinuities of the ohmic loss are because the strips 1 and 3 function as FP reflectors. Although there is the ohmic loss in the gold film between the inner silicon strip (i.e., strip 2) and the outer silicon strips (i.e., strips 1 and 3), the horizontal FP resonances between the inner silicon strip and the outer silicon strip are not excited.
Additional understanding of the two absorption peaks can be gleaned from the optical constants of our structure. Figure 5 shows the calculated $\varepsilon $ and $\mu $ under the normal incidence condition, which were obtained by means of a retrieving method [32]. As can be observed, either ${\mathop{\rm Re}\nolimits} (\varepsilon )$ or ${\mathop{\rm Re}\nolimits} (\mu )$ is negative across the 3-5 µm wavelength range. This indicates that there is no transmission in this spectral region. Moreover, both ${\mathop{\rm Re}\nolimits} (\varepsilon )$ and ${\mathop{\rm Re}\nolimits} (\mu )$ cross zero at a wavelength of 3.856 µm (or 4.29 µm), which indicates zero reflection at this wavelength [9]. As a result, the absorption at a wavelength of 3.856 µm (or 4.29 µm) is maximized.
Fig. 5. Retrieved optical constants for the dual- and narrow-band absorber. The vertical dashed lines represent the wavelengths of 3.856 µm and 4.29 µm.
4. Discussion
The distances between the silicon strips can affect the performance of the absorber. Figure 6 shows the simulated reflection spectra when independently changing ${{{d_{1}}} \mathord{\left/ {\vphantom {{{d_{1}}} {{d_{2}}}}} \right.} {{d_{2}}}}$, ${d_{1}}$, or ${d_{2}}$. As is seen in Fig. 6(a), if ${{{d_{1}}} \mathord{\left/ {\vphantom {{{d_{1}}} {{d_{2}}}}} \right.} {{d_{2}}}}$ approaches 1.0, the peak 1 disappears. It is similar when ${d_{1}}$ approaches ${d_{2}}$ (Fig. 6(b)) or ${d_{2}}$ approaches ${d_{1}}$ (Fig. 6(c)). These indicate that the asymmetric configuration in each unit cell is the origin of the two peaks.
Fig. 6. (a) Reflection versus the ratio ${{{d_{1}}} \mathord{\left/ {\vphantom {{{d_{1}}} {{d_{2}}}}} \right.} {{d_{2}}}}$. Note that ${d_{1}} + {d_{2}}$ = 1.44 µm. (b) Reflection versus ${d_{1}}$. (c) Reflection versus ${d_{2}}$.
Both of the peaks exhibit slight shifts in Fig. 6(a). These are because the $n_{\textrm{eff}}^{\textrm{FP}}$ and/or L in Eqs. (5) and (6) are affected by the locations of the silicon strips. The shifts of the peaks in Fig. 6(b) are more significant than those in Figs. 6(a) and 6(c), since the effective cavity lengths are more sensitive to ${d_{1}}$. We would explain these based on Figs. 3(a) and 3(b). For the peak 1, the magnetic field in the left silicon slit is strong, so the effective index of cavity FP1 is sensitive to ${d_{1}}$. For the peak 2, the geometric lengths of the cavities FP2 and FP3 are associated with ${d_{1}}$.
It is also observed that the FWHMs of the two peaks exhibit changes. With decreased ${d_{1}}$, the electric field in the left silicon slit increases considerably, thus enlarging the displacement current and the ohmic loss in the gold film. So the peak 1 is broader at smaller ${d_{1}}$, as shown in Figs. 6(a) and 6(b). Similarly, at smaller ${d_{2}}$, as shown in Figs. 6(a) and 6(c), the slightly larger FWHM of the peak 2 can be mainly attributed to the stronger electric field in the right silicon slit.
Besides, when ${d_{1}}$ and/or ${d_{2}}$ deviate from the optimal values, the intensity extinctions of the two peaks could decrease significantly. This implies that the grating parameters affect the coupling strength between the (±1) SPP waves and the FP resonances.
Figure 7 shows the calculated reflection spectra when ${h_{s}}$ and ${w_{s}}$ are independently adjusted. In Fig. 7(a), we can observe that the absorbances at the peaks decrease with the decreased ${h_{s}}$. This is because a small ${h_{s}}$ weakens the FP resonances (Fig. 3), thus reducing the energy dissipation. Both of the peaks exhibit redshifts as ${h_{s}}$ increases, which results from the increased $n_{\textrm{eff}}^{\textrm{FP}}$ in Eqs. (5) and (6). However, the two peaks are separated from each other with the increased ${h_{s}}$. This is because the roles of the silicon strips are different in the FP cavities. The results in Fig. 7(a) suggest that we can tune the absorption bands by adjusting the grating thickness.
When changing ${w_{s}}$, similar phenomena are shown in Fig. 7(b) and can be understood based on the above analysis. The FWHMs of the two peaks increase significantly with increased ${w_{s}}$, which mainly results from the increased ohmic loss. It is worth noting that ${w_{s}}$ plays an important role in generating the two peaks. Since each of the silicon strips functions as a reflector (see Fig. 3), the widths of them are surely crucial. Too small/large ${w_{s}}$ could weaken the horizontal FP resonances and lower the peaks quickly.
In addition, we investigated the spectral response of our structure when adjusting the polarization angle of the incidence, and the results are shown in Fig. 8(a). It can be observed that the intensity extinctions of the two peaks decrease with increased polarization angle. This is expected, because the present grating is one-dimensional.
Fig. 8. (a) Reflection as a function of the incident polarization angle. TM-polarized incidence corresponds to a polarization angle of 0°. (b) Phase distribution at z = 0.4 µm for the TE excited peak 1’. Inset shows electric field distribution for the TE excited peak 1’. (c) The same as (b) but for the TE excited peak 2’.
Interestingly, when the incidence is a transverse-electric (TE) plane wave (corresponding to a polarization angle of 90°), two new peaks appear. The new peaks are attributed to phase resonances [22]. To illustrate this, Figs. 8(b) and 8(c) show the electric field and phase distributions at the two peaks 1’ and 2’, respectively. It can be observed that, in each unit cell, the phase difference is $\pi $ and the Ey is opposite. This phase configuration leads to destructive interference in the far field, thus generating the two peaks 1’ and 2’.
5. Conclusion
We have designed and numerically investigated a dual- and narrow-band absorber. It is enabled by placing an asymmetric silicon grating on top of a continuous gold film. According to the FDTD simulations, the designed structure provides two absorption peaks at wavelengths of 3.856 µm and 4.29 µm with the absorbances of >0.996 at normal incidence. The two peaks have FWHMs of ∼25.7 cm−1 and ∼21.5 cm−1, respectively. It is demonstrated that the structure can support horizontal FP resonances. The excited planar SPP waves can be coupled with the FP resonances with different effective lengths, and then dissipate the energy to ohmic loss. Thus, the (+1, -1) modes have different resonance wavelengths. For this reason, a unique feature is seen that the peaks do not split at oblique incidence. As the incident angle increases, the peak at shorter/longer wavelength exhibits a blue/red shift. At an incident angle of <3.2°, the intensity extinctions of the peaks can be >20 dB. At an incident angle of <8.8°, the intensity extinctions of the peaks can still be >10 dB. These results imply that the two absorption bands can be tuned by rotating the absorber with respect to the incidence. In addition, it is shown that the absorption features can also be tuned flexibly by adjusting the geometric parameters. The proposed absorber will be useful for a variety of multi-spectral applications such as filtering, photonic detection, spectroscopic sensing, etc.
Funding
National Natural Science Foundation of China (60907003, 61671455, 61805278); Program for New Century Excellent Talents in University (NCET-12-0142); China Postdoctoral Science Foundation (2018M633704).
Disclosures
The authors declare no conflicts of interest.
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