Suppressing the unwanted resonance mode in a metal-insulator-metal structure using fine-structured gratings

Xin He; Jinliang Jie; Junbo Yang; Ying Chen; Yunxin Han; Sen Zhang

doi:10.1364/OE.27.015298

1. Introduction

Resonances in subwavelength periodic structures have been studied extensively over the past decade. The excited resonance modes can be either plasmonic or photonic, which affect transmission, reflection, and absorption features of a structure [1,2]. By manipulating the excited resonance modes, a large variety of useful devices have been achieved, such as filters [3–11], selective emitters [12–14], absorbers [15–18], and modulators [19,20].

Typically, there are multiple spectral peaks/dips in the transmission or reflection spectrum, because multiple resonance modes can be excited according to the wavevector matching condition. This has been shown in many broadband or multi-spectral materials [21] and components [22–25]. However, the existence of multiple peaks/dips could be very disadvantageous for many applications requiring narrow operating bandwidth. For example, in high-resolution spectroscopic sensing and filtering, the unwanted spectral peaks/dips will significantly increase the background complexity and decrease the accuracy.

Most of previous studies have tried their best to design a structure and obtain a spectral response peak/dip with desired linewidth. However, there is little research on how to selectively suppress the unwanted peaks/dips. For example, Zhong et al. proposed a dielectric grating structure with an ultra-narrow transmission dip in the mid-infrared region, but two weaker side dips were shown [26]. Zhang et al. presented a gold grating structure with a narrow main peak in the near-infrared region, but a weaker side peak was shown [27]. Wang et al. proposed a hybrid metal-dielectric structure with single reflection peak across the 1-5 μm wavelength range [28].

Our attention is focused on ultra-narrowband mid-infrared (mid-IR) notch filters, since they are very useful for many imaging or detection applications [26]. To achieve this, it is very convenient to employ MIM structures because they have been widely used to realize perfect absorption. However, MIM structures in the literature generally have low Q-factors (<100) owing to the intrinsic loss of metals. If they are used in the mid-IR, the low Q-factors could lead to a large operating bandwidth. This is disadvantageous for narrowband applications. Moreover, as mentioned above, the suppression of the unwanted stopband is of particular important, and is a challenge.

In this work, a geometric design for suppressing the unwanted resonance mode in a MIM structure is presented. We use a low-index and thick dielectric spacer to produce high Q-factor resonances. Since usual gratings lead to the unwanted resonance mode, we propose a fine-structured grating consisting of multiple gold strips in each unit cell. These gold strips are arranged into a sub-grating, which enables the proposed grating to be dual-periodic. In comparison with that of usual gratings, the use of our grating can significantly suppress the unwanted mode at ~2.65 μm and keep the desired mode at ~3.9 μm. Thus, the designed structure shows a single and high Q-factor spectral dip over a broad mid-infrared spectral region (2-5.5 μm). Although only numerical investigations were carried out, the device shows simple in structure and easy to fabricate.

2. Design and results

Figure 1 illustrates the investigated MIM structures and their performances. In Fig. 1(a), a MIM structure consisting of an Al₂O₃ layer between a usual gold grating and a bottom gold layer is shown. The period of the structure is $Λ_{1}$ . The width of the gold strip is $w_{g}$ . The thicknesses of the grating, the Al₂O₃ layer, and the bottom gold layer are respectively $h_{g}$ , $h_{s}$ , and $h_{b}$ . Figure 1(b) shows the MIM structure with our proposed grating, where two gold strips are periodically arranged in each unit cell. In other words, there is a sub-grating in each period of this MIM structure. The period of the sub-grating is $Λ_{2}$ . The other geometric parameters are exactly the same as those in Fig. 1(a) except $w_{g}$ . For discussion purposes, we use Eq. (1) to describe the two gratings:

f_{1} = \frac{n Λ_{2}}{Λ_{1}}, f_{2} = \frac{w_{g}}{Λ_{2}}

Where

n

is a positive integer,

f_{1}

is the overall filling factor of the grating,

f_{2}

is the filling factor of the sub-grating. Obviously, when

n = 1

and

Λ_{2} = w_{g}

, the top grating is an usual grating as shown in Fig. 1(a). When

n = 2

and

Λ_{2} > w_{g}

, the top grating will be a fine-structured grating as shown in Fig. 1(b).

Fig. 1 (a) Cross-sectional view of a MIM structure with a usual grating. (b) Cross-sectional view of the MIM structure with our proposed grating. (c) Simulated reflection associated with (a). (d) Simulated reflection associated with (b). Insets in (c) and (d) show single periods of the associated MIM structures. $I_{0}$ and $I_{r}$ are the intensities of the incidence and reflection. $λ_{d}$ and $λ_{u}$ stand for the resonance wavelengths resulting from the desired and unwanted modes. Note that the investigated MIM structures have the same geometric parameters except the number and width of the gold strips in each period.

Download Full Size | PDF

Reflection spectra were numerically studied by means of a finite-difference time-domain (FDTD) method. A two-dimensional (2D) computational region was considered, where periodic boundaries were used for the structure and perfectly matched layer (PML) absorbing boundaries were employed along the line of the incidence. Optical parameters of Au and Al₂O₃ were taken from [29].

In order to obtain a desired spectral dip at ~3.9 μm, we first investigate the structure shown in Fig. 1(a). Figure 1(c) shows the calculated reflection with the following parameters: $Λ_{1}$ = 3.7 μm, $w_{g}$ = 430 nm, $h_{g}$ = 110 nm, $h_{s}$ = 1.74 μm, and $h_{b}$ = 100 nm. According to Eq. (1), there are $n = 1$ , $f_{1} = 0.116$ and $f_{2} = 1$ . A high-extinction resonance mode at 3.913 μm with a full-width at half-maximum (FWHM) linewidth of ~17 nm or ~11 cm⁻¹ is clearly observed. This mode exhibits a Q-factor of ~230, which is much higher than most of MIM structures in the literature. The ultra-narrow linewidth is advantageous for narrowband filtering. However, a notable but unwanted mode at ~2.65 μm also exists, which is disadvantages for narrowband filtering. To study if this unwanted mode can be eliminated, a parametric sweep of $w_{g}$ , $h_{g}$ , and $h_{s}$ has been made (not shown). However, the results indicate that it is always significant.

Figure 1(d) shows the calculated reflection associated with Fig. 1(b). The geometric parameters are: $n$ = 2, $Λ_{2}$ = 925 nm, $w_{g}$ = 352 nm. In this case, there are $f_{1} = 0.5$ and $f_{2} = 0.38$ according to Eq. (1). The other parameters are identical with those above. There is only a single stopband at ~3.933 μm with a FWHM linewidth of ~15 nm or ~9.7 cm⁻¹, corresponding to a Q-factor of ~262. Thus, the MIM structure with our proposed grating shows a single reflection dip at the desired wavelength and a high background reflection (>90%) over an ultra-broad spectral region (2-5.5 μm). The narrow stopband and remarkable decrease in sideband complexity would be very useful for narrowband filtering. The results suggest that the desired mode can be well kept and the unwanted mode can be significantly suppressed by using the proposed grating. Although the spectral location of the desired mode exhibits a slight redshift in comparison with that of Fig. 2(c), the Q-factor gets even higher. The redshift effect will be explained in Section 4.

Fig. 2 (a) Field profiles for the resonance mode at $λ_{d}$ associated with Fig. 1(c). (b) Field profiles for the resonance mode at $λ_{u}$ associated with Fig. 1(c). (c) Field profiles for the resonance mode at $λ_{d}$ associated with Fig. 1(d). Note that all the field profiles are self-normalized.

Download Full Size | PDF

3. Physical mechanism

At first, in order to understand the high Q-factor, the $| E |$ and $| H |$ field distributions at $λ_{d}$ and $λ_{u}$ associated with Figs. 1(c) and 1(d) are represented in Fig. 2. It is observed that a large portion of resonant energy is confined in the Al₂O₃ layer. The reason is that the Al₂O₃ layer has a relatively low refractive index (~1.7) and large thickness (1.74 μm). Moreover, the optical loss of Al₂O₃ is small in the investigated wavelength range. These lead to a relatively low loss of the resonance mode [30]. Thus, the investigated MIM structures show a high Q-factor.

It should be noted that the use of a thinner Al₂O₃ layer seems to show an almost the same linewidth as our structure, as presented in [30]. However, we would find that the Q-factor of our structure is nearly an order of magnitude larger that in [30]. In fact, using a thinner Al₂O₃ layer in our structure can also realize the desired spectral dip at ~3.9 μm. If doing so, the Q-factor will decrease significantly.

Then, we show that how the MIM structure with our grating (see Fig. 1(b)) can suppress the unwanted mode at ~2.65 μm and keep the desired mode at ~3.9 μm. Figure 3 shows the main diffracted rays in the investigated MIM structures based on geometric optics. For the MIM structure with an usual grating (see Fig. 1(a)), the TM-polarized incidence is diffracted into 5 different orders (−2, −1, 0, + 1, + 2) after passing through the top grating, as illustrated in Fig. 3(a). The in-plane wavevectors of these diffracted orders can be written as (except the 0th order):

k_{∥}^{(\pm 1)} = k \sin α \pm \frac{2 π}{Λ_{1}}

k_{∥}^{(\pm 2)} = k \sin α \pm \frac{4 π}{Λ_{1}}

where

k

and

α

are the wavevector and angle of the incidence, respectively. Resonances occur when the diffracted orders couple to the planar plasmonic modes. These processes should satisfy the wavevector matching condition:

k_{∥}^{(\pm 1)} = β_{∥} (λ^{(\pm 1)})

k_{∥}^{(\pm 2)} = β_{∥} (λ^{(\pm 2)})

where

β_{∥} (λ)

is the in-plane wavevector of the plasmonic mode excited by certain diffraction order. According to Eqs. (2-5), there are

λ^{(\pm 1)} = λ_{d}

and

λ^{(\pm 2)} = λ_{u}

at normal incidence (

α = 0

).

Fig. 3 Illustration of the main diffracted orders based on geometric optics. (a) In the case of an usual grating. (b) In the case of our proposed grating.

Download Full Size | PDF

For the MIM structure with our proposed grating (see Fig. 1(b)), the incident beam is diffracted into 3 different orders (−1, 0, + 1) after passing through the grating, as illustrated in Fig. 3(b). Only Eqs. (2) and (4) should be considered in this case. At normal incidence, the resonance wavelength is simply determined by $λ_{d} = λ^{(\pm 1)}$ .

The existence of only 3 different orders (−1, 0, + 1) can be attributed to the dual-periodic structure of our grating. Compared with an usual grating, it supports different diffraction orders [31]. There are slits with different widths in our grating, from which the diffracted rays can destructively interfere with each other. To validate this, we calculated spectral responses of the structures shown in Figs. 1(a) and 1(b) after removing the bottom gold layers. The results are shown in Fig. 4. We see that there are abrupt changes in the transmission and reflection spectra. The abrupt changes are associated with the diffraction effect of the grating. Compared with those in Fig. 4(a), a reduced number of abrupt changes in Fig. 4(b) suggests that our proposed grating supports fewer diffraction orders.

Fig. 4 Reflection and transmission features after removing the bottom gold layer. (a) In the case of an usual grating. (b) In the case of our grating. Insets show single periods of the associated structures.

Download Full Size | PDF

Furthermore, a detailed comparison between Figs. 4(a), 4(b) and Figs. 1(c), 1(d) was carried out. It is indicated that the abrupt changes marked by the red and blue rectangles in Fig. 4 are associated with the desired and unwanted modes, respectively. The abrupt change marked by the blue rectangle in Fig. 4(a), which is associated with the unwanted mode, disappears in Fig. 4(b). This implies that the unwanted mode is suppressed by using our grating. The spectral location of the abrupt change marked by the red rectangle in Fig. 4(a), which is associated with the desired mode, shows an almost unchanged property in Fig. 4(b). This implies that the desired mode can be kept by using our grating. The other abrupt changes in Fig. 4 are associated with the tiny reflection dips in Fig. 1(c) and 1(d). The blue shifts of these abrupt changes are due to the removal of the bottom gold layers.

The analysis above is consistent with the field distributions at the resonance wavelengths shown in Fig. 2, which confirms the suppression of the unwanted resonance mode based on our grating.

4. Discussion

The suppression can also be realized by using more gold strips in the sub-grating. To show this, we further increase the $n$ value in Eq. (1), and then optimize the grating parameters. In the case of each $n$ value, we just need to optimize $Λ_{2}$ and $f_{2}$ . The other structure parameters are the same as those above: $Λ_{1}$ = 3.7 μm, $h_{g}$ = 110 nm, $h_{s}$ = 1.74 μm, and $h_{b}$ = 100 nm. Figure 5 shows the calculated reflection spectra, where the results in Figs. 1(c) and 1(d) are also plotted for comparison. Table 1 lists the optimized grating parameters, where those associated with $n = 1$ and $n = 2$ are also shown. Note that simulations of the reflection for $n \geq 10$ were not carried out, because in those cases the gaps between the gold strips would be too narrow to fabricate.

Fig. 5 Reflection spectra associated with different values of $n$ . Inset shows magnified view of the desired modes.

Download Full Size | PDF

Table 1. Optimized grating parameters associated with different values of $n$ .

View Table

Compared with the case of $n = 1$ (i.e. an usual grating), the unwanted mode is observed to be significantly suppressed provided that $n > 1$ , as shown in Fig. 5. In addition, the FWHM or Q-factor of the desired mode is almost unchanged in the cases of various $n$ values. This is because the thickness of the Al₂O₃ layer is kept unchanged in these calculations. However, the spectral location of the desired mode exhibits a slight redshift as $n$ increases. The redshift can be understood as follows.

According to Eqs. (2) and (4), there is:

\frac{2 π}{Λ_{1}} = β_{∥} (λ_{d}) = \frac{2 π n_{eff}}{λ_{d}}

where

n_{eff}

is effective refractive index of the desired mode.

n_{eff}

is mainly determined by the arrangement of the gold strips because all the other parameters do not change in these calculations. The arrangement of the gold strips in each unit cell is governed by Eq. (1), based on which we obtain:

f_{1} f_{2} = \frac{n w_{g}}{Λ_{1}}

where

f_{1} f_{2}

denotes the ratio of gold in each period of the grating. In Table 1, it is clearly shown that

f_{1} f_{2}

increases as

n

increases. However, we should note that the grating layer is relatively thin in comparison the investigated MIM structure. This increase in

f_{1} f_{2}

could only lead to a small increase in

n_{eff}

, which results in the slight redshift according to Eq. (6).

Then, based on the MIM structure shown in Fig. 1(b), we studied the reflection features by independently varying the structure parameters. It must be noted that some parameters are correlated. The calculated results are shown in Fig. 6.

Fig. 6 Reflection spectra for $n$ = 2 versus the overall filling factor $f_{1}$ (a), the filling factor of the sub-grating $f_{2}$ (b), the thickness of the grating layer $h_{g}$ (c), the thickness of the Al₂O₃ layer $h_{s}$ (d), and the period of the structure $Λ_{1}$ (e). Insets show the magnified view of the desired spectral dips (I in (a), (b), and (c)) and the unwanted spectral dips (II in (a)).

Download Full Size | PDF

In Fig. 6(a), it is seen that the overall filling factor $f_{1}$ significantly affects the suppression of the unwanted resonance mode at ~2.65 μm. However, the other geometric parameters presented in Figs. 6(b)-6(e) show relatively weaker effects. In order to understand these results, we first determine the widths of the gold slits in our grating according to Eq. (1), they are:

w_{1} = (1 - \frac{1 + f_{2}}{2} f_{1}) Λ_{1}, \begin{matrix}  \end{matrix} w_{2} = \frac{1 - f_{2}}{2} f_{1} Λ_{1}

where

w_{1}

and

w_{2}

are respectively the widths of the wider and narrower slits. Based on the data in Table 1, we know that

w_{1}

is comparable to and

w_{2}

is much smaller than 2.65 μm. When

f_{1} = 0.5

, these slits result in a destructive interference of the diffracted rays. However, as

f_{1}

increases or decreases,

w_{1}

increases or decreases more quickly than

w_{2}

. The interference effect will be affected in the case of larger or smaller

f_{1}

, which enables the diffracted rays to coupe to the plasmonic mode and the unwanted spectral dip to be notable.

This effect is not so significant when adjusting the other parameters, because there are only small (Fig. 6(b) and 6(e)) or even no (Figs. 6(c) and 6(d)) changes in the widths of gold slits. However, the thickness of the Al₂O₃ layer has a distinct effect on the plasmonic modes. The change in Al₂O₃ layer thickness could enable the coupling between the plasmonic modes and the diffracted rays at other wavelengths, as shown in Fig. 6(d).

As for the desired mode, slight redshifts are observed in Figs. (a-c) when increasing $f_{1}$ , $f_{2}$ , $h_{g}$ . According to Eq. (7), independently increasing $f_{1}$ or $f_{2}$ indicates that the ratio of gold in each period of the grating increase. As a result, the effective refractive index $n_{eff}$ in Eq. (6) increase, leading to the slight redshift of the desired mode. It is similar when increasing $h_{g}$ . However, the redshifts are notable when increasing the Al₂O₃ layer thickness $h_{s}$ or the structure period $Λ_{1}$ , as shown in Figs. 6(d) and 6(e). According to Eq. (6), this is easy to understand.

The FWHM or Q-factor is seen to increase or decrease dramatically with the increase of $f_{2}$ in Fig. 6(b), whereas it is not in Fig. 6(a) or Figs. 6(c)-6(e). Based on the field distributions at-resonance shown in Fig. 2(c), we would explain that the gap between the two gold strips will decrease quickly as $f_{2}$ increases. Owing to the loss at the gold ridges, a narrower gold slits can significantly increase the loss of the desired mode. However, the increase in the other parameters would not narrow the gold slits so quickly and increase the loss of the desired mode so significantly.

In comparison with $f_{1}$ , $h_{g}$ , and $Λ_{1}$ (Figs. 6(a), 6(c) and 6(e)), it is shown that the intensity extinction is more sensitive to $f_{2}$ and $h_{s}$ (Figs. 6(b) and 6(d)). In fact, the change in each of these parameters affects the intensity extinction of the desired mode, because the desired spectral dip results from the coupling between the ( ± 1) diffraction orders and the plasmonic mode. The intensity extinction is mainly determined by the coupling strength between them. The results indicate that the filling factor of the sub-grating and the thickness of the Al₂O₃ layer thickness should be optimized carefully in order to obtain a high extinction at the desired wavelength.

In addition, we calculated the reflection spectra of our MIM structure shown in Fig. 1(b) at different angles of incidence. The results are shown in Fig. 7. Obviously, the desired spectral dip splits under oblique incidence. This can be attributed to the guided-mode resonance effect according to Eqs. (2) and (4). At oblique incidence, i.e., $α \neq 0$ , the wavevector norms of $k_{∥}^{+ 1}$ and $k_{∥}^{- 1}$ are different, resulting in two different resonance wavelengths $λ^{+ 1}$ and $λ^{- 1}$ . The phenomenon has also been shown in dielectric grating based guided-mode resonance filters [26]. Despite this, the splitting effect could be useful. The reflection features can be tuned by rotating the MIM structure with respect to the incidence. From this point of view, the results in Fig. 7 indicate that a tuning range of ~400 nm can be achieved by a 5° rotation.

Fig. 7 Simulated reflection as a function of the incident angle.

Download Full Size | PDF

5. Conclusion

In summary, we have presented that suppression of the unwanted resonance mode in a MIM structure can be achieved by designing the grating layer. The investigated MIM structure uses a low-index and relatively thick dielectric layer to realize high Q-factor resonances. Since the unwanted spectral dip at ~2.65 μm exists when using usual gratings in the MIM structure, we propose a fine-structured grating and use it to suppress the unwanted resonance mode. The proposed grating consists of multiple gold strips in each unit cell, which are arranged to form a sub-grating. Thus the grating shows a dual-period feature, which enables it to support different diffraction orders. Compared with the case of usual gratings, our FDTD simulations reveal that using the proposed grating can significantly suppress the unwanted resonance mode and keep the desired resonance mode at ~3.9 μm. By varying the various structure parameters, we carried out investigations on their influences. For suppressing the unwanted mode, it is suggested that the overall filling factor should be controlled first. For keeping the desired mode, we also need to design the filling factor of the sub-grating and the thickness of the dielectric layer carefully. Based on the design, the MIM structure shows only a single reflection dip at ~3.9 μm with ~10 cm⁻¹ linewidth and >90% background reflection across the 2-5.5 μm wavelength range. Although the MIM structure is sensitive to the angle of incidence, the design will be useful for many mid-IR applications such as narrowband filtering, selective emitting, and narrowband perfect absorption.

Funding

National Natural Science Foundation of China (NSFC) (60907003, 61671455, 61805278); Program for New Century Excellent Talents in University (NCET) (NCET-12-0142); Natural Science Foundation of Hunan Province of China (13JJ3001); China Postdoctoral Science Foundation (2018M633704).

References

1. Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014). [CrossRef]

2. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12(23), 5661–5674 (2004). [CrossRef] [PubMed]

3. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. 23(9), 700–702 (1998). [CrossRef] [PubMed]

4. W. Liu, Z. Lai, H. Guo, and Y. Liu, “Guided-mode resonance filters with shallow grating,” Opt. Lett. 35(6), 865–867 (2010). [CrossRef] [PubMed]

5. J.-N. Liu, M. V. Schulmerich, R. Bhargava, and B. T. Cunningham, “Optimally designed narrowband guided-mode resonance reflectance filters for mid-infrared spectroscopy,” Opt. Express 19(24), 24182–24197 (2011). [CrossRef] [PubMed]

6. E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J.-L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1D to 2D structures,” Opt. Express 20(12), 13082–13090 (2012). [CrossRef] [PubMed]

7. M. N. Abbas, C.-W. Cheng, Y.-C. Chang, and M. H. Shih, “An omni-directional mid-infrared tunable plasmonic polarization filter,” Nanotechnology 23(44), 444007 (2012). [CrossRef] [PubMed]

8. S. R. Vangala, I. Avrutsky, P. Keiffer, N. Nader, D. Walker Jr., J. W. Cleary, and J. R. Hendrickson, “Asymmetric photonic resonances in GaN slab waveguide for mid infrared selective filters,” Opt. Express 22(20), 24742–24751 (2014). [CrossRef] [PubMed]

9. J.-N. Liu, M. V. Schulmerich, R. Bhargava, and B. T. Cunningham, “Sculpting narrowband Fano resonances inherent in the large-area mid-infrared photonic crystal microresonators for spectroscopic imaging,” Opt. Express 22(15), 18142–18158 (2014). [CrossRef] [PubMed]

10. X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012). [CrossRef] [PubMed]

11. K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012). [CrossRef] [PubMed]

12. M.-W. Tsai, T.-H. Chuang, C.-Y. Meng, Y.-T. Chang, and S.-C. Lee, “High performance midinfrared narrow-band plasmonic thermal emitter,” Appl. Phys. Lett. 89(17), 173116 (2006). [CrossRef]

13. J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011). [CrossRef]

14. C.-Y. Chen, M.-W. Tsai, Y.-W. Jiang, Y.-H. Ye, Y.-T. Chang, and S.-C. Lee, “Coupling of surface plasmons between two silver films in a plasmonic thermal emitter,” Appl. Phys. Lett. 91(24), 243111 (2007). [CrossRef]

15. A. Sharon, S. Glasberg, D. Rosenblatt, and A. A. Friesem, “Metal-based resonant grating waveguide structures,” J. Opt. Soc. Am. A 14(3), 588–595 (1997). [CrossRef]

16. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial Electromagnetic Wave Absorbers,” Adv. Mater. 24(23), OP98–OP120 (2012). [PubMed]

17. R. Feng, J. Qiu, Y. Cao, L. Liu, W. Ding, and L. Chen, “Omnidirectional and polarization insensitive nearly perfect absorber in one dimensional meta-structure,” Appl. Phys. Lett. 105(18), 181102 (2014). [CrossRef]

18. L. Meng, D. Zhao, Z. Ruan, Q. Li, Y. Yang, and M. Qiu, “Optimized grating as an ultra-narrow band absorber or plasmonic sensor,” Opt. Lett. 39(5), 1137–1140 (2014). [CrossRef] [PubMed]

19. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared Spatial And Frequency Selective Metamaterial with Near-Unity Absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010). [CrossRef] [PubMed]

20. H. Zhou, F. Ding, Y. Jin, and S. He, “Terahertz Metamaterial modulators based on absorption,” Prog. Electromagnetics Res. 119, 449–460 (2011). [CrossRef]

21. J. Grant, I. J. H. McCrindle, and D. R. S. Cumming, “Multi-spectral materials: hybridisation of optical plasmonic filters, a mid infrared metamaterial absorber and a terahertz metamaterial absorber,” Opt. Express 24(4), 3451–3463 (2016). [CrossRef] [PubMed]

22. P. Liu and T. Lan, “Wide-angle, polarization-insensitive, and broadband metamaterial absorber based on multilayered metal-dielectric structures,” Appl. Opt. 56(14), 4201–4205 (2017). [CrossRef] [PubMed]

23. W. Fu, Y. Han, J. Li, H. Wang, H. Li, K. Han, X. Shen, and T. Cui, “Polarization insensitive wide-angle triple-band metamaterial bandpass filter,” J. Phys. D Appl. Phys. 49(28), 285110 (2016). [CrossRef]

24. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

25. R. Hu, Y. Liang, S. Qian, and W. Peng, “Dual-band bandpass filter based on compound metallic grating waveguide structure,” Opt. Commun. 336, 110–115 (2015). [CrossRef]

26. Y. Zhong, Z. Goldenfeld, K. Li, W. Streyer, L. Yu, L. Nordin, N. Murphy, and D. Wasserman, “Mid-wave infrared narrow bandwidth guided mode resonance notch filter,” Opt. Lett. 42(2), 223–226 (2017). [CrossRef] [PubMed]

27. E. Li, X. Chong, F. Ren, and A. X. Wang, “Broadband on-chip near-infrared spectroscopy based on a plasmonic grating filter array,” Opt. Lett. 41(9), 1913–1916 (2016). [CrossRef] [PubMed]

28. Z. Wang, R. Zhang, and J. Guo, “Quadrupole mode plasmon resonance enabled subwavelength metal-dielectric grating optical reflection filters,” Opt. Express 26(1), 496–504 (2018). [CrossRef] [PubMed]

29. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

30. D. B. Mazulquim, K. J. Lee, J. W. Yoon, L. V. Muniz, B.-H. V. Borges, L. G. Neto, and R. Magnusson, “Efficient band-pass color filters enabled by resonant modes and plasmons near the Rayleigh anomaly,” Opt. Express 22(25), 30843–30851 (2014). [CrossRef] [PubMed]

31. M. Stolarek, D. Yavorskiy, R. Kotyński, C. J. Zapata Rodríguez, J. Łusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013). [CrossRef] [PubMed]

$n$	$f_{1}$	$f_{2}$	$f_{1} f_{2}$
1	0.116	1	0.116
2	0.5	0.38	0.19
3	0.52	0.46	0.2392
4	0.52	0.52	0.2704
5	0.53	0.55	0.2915
6	0.53	0.59	0.3127
7	0.54	0.61	0.3294
8	0.54	0.63	0.3402
9	0.54	0.65	0.351

Suppressing the unwanted resonance mode in a metal-insulator-metal structure using fine-structured gratings

Abstract

1. Introduction

2. Design and results

3. Physical mechanism

4. Discussion

5. Conclusion

Funding

References

Cited By

Figures (7)

Tables (1)

Equations (8)

Optics Express