1. Introduction

There has been an increasing need for compact and integrable high-performance thin-film optical filters/filter arrays in development of devices (or micro-optical system modules) for high-resolution color imaging and spectral imaging [1–4]. This cannot be fulfilled with conventional dye-molecule-based color filters that have been widely used in CMOS color image sensors and liquid crystal displays (LCDs) [5,6], because of their limitations in performance, scalability and durability. In the past years, various optical filters consisting of micro/nano-structures have been investigated [7–18]. They are usually based on optical resonances in the structures, which results in selective optical transmission/reflection in the frequency domain. Among them, plasmonic filters [10–18] based on metallic nanostructures draw particular attention due to their compactness arising from small mode volume of plasmons [19] and compatibility in materials and fabrication with planar processing technologies. In the early years since the emergence (or booming) of plasmonics [20], nano-hole/slit arrays in optically thick metal films have been considered for color filtering [15–18]. But their performances are shown to exhibit broad bandwidths (>100 nm in wavelength) and considerable sidebands. Besides, fabrication of such fine nanostructures in thick metal films is not compatible with prevalent CMOS process, and has to be resorted to state-of-the-art nanofabrication techniques (e.g., electron-beam lithography or focused-ion-beam milling) that are not favorable to mass production. Fundamentally, bandwidth of the plasmonic filters has been limited by absorption loss in the metallic nanostructures that results in low quality factors of plasmon resonances in generation of the filtering passband.

Thus, further development of plasmonic filters has been in endeavor to design filtering structures with narrow-band transmission, low sidebands and ease of fabrication. Therein, some progresses were made in reducing the transmission bandwidth (e.g., down to <30 nm in the VIS–NIR regime) by introducing additional dielectric layers adjacent to the metallic nanostructure layer to support resonances of low-loss hybrid surface plasmon (SP) waveguiding modes [21–26], or called guided-mode resonance (GMR) modes. Additionally, absorption loss of the waveguiding SP modes for resonances are reduced by using optically thin metal layers (<50 nm in thickness) in the nanostructures; and this also facilitate their fabrication to be compatible with the CMOS process. Nevertheless, problems of high transmission in sidebands and/or background still exist for such filters (particularly in the short- and long-wavelength sides of the main passband peak).

Meanwhile, plasmonic filters consisting of multilayers of metal-dielectric nanostructures, e.g., metal-insulator-metal (MIM) stacks in each unit cells, were also studied [27–34]. Nonetheless, their performances as filters are still limited, showing broad bandwidths (>100 nm, in the VIS–NIR regime) and/or high sidebands in general, except that, in Ref. [30], a 5-layer metal-insulator-metal-insulator-metal (MIMIM) structure demonstrates narrow passbands (down to a few tens of nanometers) and low sidebands under very critical structural and polarization conditions. It is also worth to mention that, in Ref. [31], suppression of sidebands of a MIM-stack-array filter is achieved by introducing a hetero-MIM structure with asymmetric metal materials (Ag and Al) for the top and bottom metal layers.

In this paper, we propose a plasmonic filter structure of asymmetric bi-layer metallic nanoslit arrays with different slit-widths, as shown in Fig. 1(a). With this structure, we not only suppressed sidebands in the filtering transmission spectrum, but also reduced bandwidth of the main transmission peak, down to a few tens of nanometers (e.g., <30 in the VIS–NIR regime). The filter structure is different from that of multilayered metal-dielectric stack arrays [27–31], in that the interspacing dielectric layer is not cut through together with the nanoslits, and the structured metal layers can be laterally shifted (misaligning the nanoslits) in a tolerant extent without degrading the filtering performances, besides the asymmetry introduced by different widths of the nanoslits. As such, they differ in operation mechanisms to achieve the improved performances. Additionally, two-dimensional version of the structure also performs as well as a filter, and can be used for high-transmittance filtering of arbitrarily polarized or unpolarized light.

 

Fig. 1. (a) Schematic illustration of the filter structure consisting of asymmetric bi-layer metallic nanoslit arrays sandwiching a dielectric interspacing layer. (b) Transmission, reflection and absorption spectra of such a typical structure with t_m1=t_m2=50 nm, t_d= 140 nm, s₁= 100 nm, s₂=40nm, and p=600 nm. The metal is silver, and refractive indices of the dielectric substrate and interspacing layer are assumed to be 1.46.

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2. Structure, characteristics and mechanisms

Figure 1(a) schematically illustrates the filter structure, in which the asymmetric constitutive metallic nanoslit arrays have equal periods (p) but different widths of the nanoslits (s₁, s₂) in the top and bottom layers. The structured metal layers are optically thin (t_m1, t_m2) and closely spaced by a thin dielectric layer (t_d). In the study by numerical simulations, the method of finite-different time-domain (FDTD) is used. We assume the metal is silver (Ag) with its permittivities fitted from experimental data in Palik’s handbook [35], and the medium for the transparent substrate and the interspacing dielectric layer is silica, assumed to have a fixed refractive index of n_d=1.46 at all wavelengths. In the simulations, light is normally incident on the structures from the top side air (index n₀=1) in transverse-magnetic (TM) polarizations (E//x).

Transmission spectrum of such a filter structure with parameters t_m1=t_m2=50 nm, t_d= 140 nm, s₁= 100 nm, s₂=40 nm, and p=600 nm is shown in Fig. 1(b). It’s clearly demonstrated that a distinct narrow transmission peak appears at the vacuum wavelength of λ=865 nm, which is considered as the passband of the proposed filter. Its narrow bandwidth (FWHM=26 nm) and low-transmittance sidebands are to be clarified mainly due to two types of plasmonic resonance modes, i.e., intercoupled local plasmon resonance (LPR) modes in the nanoslits of the top and bottom metal structure layers (at λ = 865 nm) and various in-plane waveguiding surface plasmon resonance (SPR) modes with their fields respectively bound to the top (at λ = 610 and 658 nm) and bottom (λ = 897 and 906 nm) metal layers of the structure. Besides, mismatches of the higher-order in-plane SPR modes induced at the top and bottom metal structure layers, due to the structural asymmetry, suppress sidebands of the transmission peaks at the shorter wavelength side (e.g., below λ = 600 nm); and, at the longer wavelength side (e.g., above λ = 1000 nm), non-resonant transmission of light through the subwavelength structure is also suppressed as increased total thickness of the two metal layers are present. In the following, we focus on elucidating the resonance modes and their roles on formation of the filtering passband, with the assistance of distributions of the fields (H_y, |E|) and power flow densities (S) in the resonance states, as shown in Fig. 2. The field values are expressed in ratios with respect to corresponding field magnitudes of the incidence light in air (|H₀|, |E₀| and |S₀|).

 

Fig. 2. Distributions of the transverse magnetic field (H_y) (a1–e1), electric field magnitude (|E|) (a2–e2) and power flow S (a3–e3) at the resonance positions of λ = 610 nm (a1–a3), 658 nm (b1–b3), 865 nm (c1–c3), 897 nm (d1–d3) and 906 nm (e1–e3), as labeled in Fig. 1(b). Light is incident from the top side (air) in the subplots.

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In the analysis, we can refer to the optical transmission of single-layer optically thick metallic nanoslit arrays in some aspects, for which LPR in the nanoslits assists the transmission and in-plane SPRs at the top and bottom metal-dielectric interfaces suppress the transmission [36,37]. Specifically, the nanoslits effectively work as dipolar optical nanoantennas [38,39], harvesting the incidence light to undergo LPRs and reradiating it into the far field as transmitted light. Here in the bi-layer structure, the top-layer nanoslits and bottom-layer nanoslits are closely spaced, which results in near-field coupling of the dipolar LPRs in them. Thus, it happens successively that the top-layer nanoslits harvest the incidence light by converting it into the LPR mode in them, then the energy is transferred to the bottom-layer nanoslits by near-field coupling of the LPR modes in them, and finally the energy in LPR mode in the bottom-layer nanoslits is radiatively converted into the transmitted light. Plasmon-enhanced transmission as such is supposed to have a broad spectral band due to low quality factors (Q) of LPR modes in the metallic nanoslits. But in fact, the final transmission band can be narrower, subjected to influences of other resonance modes in neighboring spectral ranges, e.g., suppressive tailoring effects of in-plane SPR modes at the shorter- and longer-wavelength sides of the passband peak (to be discussed later). Thereby, the transmission band at λ = 870 nm in Fig. 1(b) is formed. Nonetheless, it is also special in this case that, due to asymmetry of the nanoslits (both in their widths and ambient media), positions of the LPR modes in the top- and bottom-layer nanoslits will be slightly mismatched. Thus, cooperative interaction of the asymmetric LPR modes by near-field coupling can result in a coupled resonance mode with a higher quality factor [40]. Consequently, the main passband due to resonant transmission is modified to have a narrower bandwidth. Physical pictures of the resonant transmission at the passband peak can be viewed in Figs. 2(c1)–(c3); particularly observed are the strongly confined LPR field of optical antennas in the nanoslits shown in Fig. 2(c2), and the power flow transmitting through the bi-layer metallic nanoslit arrays shown in Fig. 2(c3).

For the in-plane SPR modes, since the structure consists of two interspaced optically thin metal layers, they can be based on various SP waveguiding modes in the composite structure. Here we will not have a detailed analysis on the waveguiding modes, but instead to verify them from their resonance modes in the periodic structure, relying on simulated field distributions of the resonance modes at λ = 610, 658, 897 and 906 nm, shown in Figs. 2(a1)–2(a3), (b1)–(b3), (d1)–(d3) and (e1)–(e3) respectively. It can be seen that, at λ = 610 and 658 nm, the fields are mainly bound to the top metal structure layer with antisymmetric-sign distribution of the transverse magnetic field (H_y) in opposite-side vicinities of the metal layer. Thus, they are ascribed to resonances of the antisymmetric bound surface plasmon (ab–SP) waveguiding mode (or so-called short-range surface plasmons, SRSP), excited by the incidence light for asymmetric index of the media on opposite sides of the metal layer [41,42]. At λ=897 and 906 nm, the fields are mainly bound to the bottom metal structure layer with symmetric-sign distribution of the H_y-field in opposite-side vicinities of the metal layer. They are ascribed to symmetric bound surface plasmon (sb–SP) waveguiding mode (or so-called long-range surface plasmons, LRSP) [41]. It seems that the sb–SP modes at the bottom metal layer are more influenced by the other (top) metal layer, which results in stronger fields at the bottom (at λ=897 nm) or top (i.e., interspacing-region) (at λ=906 nm) side of the bottom metal layer.

Waveguiding resonance modes in a periodic structure are fundamentally Bloch waves at bandgap edges. If the periodic perturbation (e.g., by the metallic nanoslits) on the waveguiding mode is strong, the bandgap will be larger, which results in two split waveguiding resonance modes locating at the upper and lower bandgap edges. As such, the resonance modes at λ = 610 and 658 nm are thought to originate from split resonance of the ab–SP waveguiding mode. It is evidently shown that, at λ = 610 nm (higher frequency), the transverse field (H_y) concentrates more in the nanoslits of lower-effective-index regions; while, at λ = 658 nm (lower frequency), the antisymmetrically distributed H_y-field concentrates more at the metal segments of higher-effective-index regions. All the characteristics are consistent with those of resonant Bloch waves at the bandgap edges [43]. For resonances at around λ=897 and 906 nm, they are shown belonging to different sb–SP waveguiding modes with close effective mode indices, as the media on both sides of the bottom metal layer are symmetrically the same. Note that, positions of the in-lane SPR modes of the first-order can be estimated by $\lambda = {N_{eff}} \cdot p$, where N_eff is effective index of the SP waveguiding mode, and is usually slightly larger than index of the mode-confined dielectric medium adjacent to the metal layer. A reasonable estimation of the resonance positions matches what are obtained from the simulation results.

Usually, in-plane SPR modes have negative roles on transmission [36,37], e.g., for the SPR modes at λ = 658 and 897 nm here, because in-coupling of incidence light into the resonant SP modes and out-coupling of the SPs into the reflected light mode are reverse and reciprocal processes, subjected to the same phase matching conditions. Thus, it’s usually shown that, as the resonance mode results in a transmission minimum, a spectral reflection maximum is present at the resonance position. Negative roles of the in-plane SPR modes at neighboring frequency positions thus appear to tailor the transmission band induced by the intercoupled LPR modes in the nanoslits for the filtering passband. While, at λ = 610 and 906 nm, the resonance fields are more confined in the nanoslits and the interspacing region, referring to Figs. 2(a1)–2(a3) and Figs. 2(e1)–2(e3), which results in enhanced absorption [44,45] and transmission leakage. Thus, as shown in Fig. 1(b), besides appearance of low transmission peaks, strong absorption peaks are present at (or approximately at) the resonance positions (at λ=610 and 901 nm), accompanied with deep narrow reflection dips. Note that, as the resonance modes at λ=897 and 906 nm are closely spaced and both boost near-field confinement of light, the maximum confinement and absorption of light hereby appears at the midst wavelength of λ=901 nm that subjected to both resonances, instead of at either one. In summary, tailoring of the main transmission band and suppression of the sidebands are achieved by resonant reflections at λ=658 and 897 nm and resonant absorptions at λ = 610 and 901 nm respectively.

3. Effects of structure dimensions and configurations on the transmission for filtering

In this section, we firstly have a study on effects of structure dimensions on the transmission to further verify the proposed mechanisms and provide critical information for designing of the filter structure. In the investigations, the structure dimensions are varied with respect to those of the structure studied above, i.e., t_m1=t_m2=50 nm, t_d = 140 nm, s₁=100 nm, s₂=40 nm, p=600 nm.

 Figure 3(a) indicates effects of thickness of the interspacing dielectric layer, which is supposed to directly influence the near-field intercoupling between the LPRs in the top- and bottom-layer nanoslits and effective indices of the SP waveguiding modes in the metal-dielectric structures for in-plane SP resonances. It is shown that a variation of the thickness in the subwavelength range [t_d<λ/(2n_d)], e.g., down to t_d = 60 nm or below and up to t_d = 220 nm, does not largely change the critical features (e.g., peak position and bandwidth) of the passband for filtering, except for a small variation of the passband peak transmittance. Though there are some changes of the in-plane SPR spectral features, they do not apparently degrade the filtering performance because of their low transmittance. But, as the thickness is increased to a dimension in the order of wavelength (∼λ/n_d), e.g., t_d = 400 nm, additional transmission peaks distinctly come to appear in the spectra (e.g., at λ=733 and 1204 nm). This is thought due to Fabry-Perot resonances formed between the top- and bottom-layer metallic nanoslit arrays that behave like mirrors. Thus, the interspacing dielectric layer should be thin enough and optimized in the subwavelength range for optimal performance for filtering.

 

Fig. 3. Transmission spectra of the filter structure for (a) different thicknesses (t_d) of the interspacing dielectric layer (t_m1=t_m2=50 nm, s₁=100 nm, s₂=40 nm, p=600 nm) and (b) different widths of the slit (s₂) in the bottom metal layer (t_m1=t_m2=50 nm, t_d = 140 nm, s₁=100 nm, p=600 nm).

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As shown in Fig. 3(b), effect of the structural asymmetry in the bi-layer structure is investigated by varying the width of the nanoslits in the bottom metal layer (s₂) with respect to a fixed width of the nanoslits in the top metal layer (s₁=100 nm). It is shown that, as s₂=s₁=100 nm (no structural asymmetry), the main passband peak is rather wide and have relatively lower transmittance. On the other hand, if the nanoslit width s₂ is too small (e.g., s₂=20 nm, for enlarged asymmetry), the passband peak becomes narrower, but its transmittance largely drops down. It is also shown that, as other structure dimensions (particularly the period) are invariant, positions of the low-order in-plane SPR modes are unshifted. The phenomena tell that intercoupling of the LPR modes in the top- and bottom-layer nanoslits, instead of the in-plane SPR modes, boosts resonant transmission in the passband; besides, the asymmetry of different nanoslit widths is critical for the intercoupled LPR modes to cooperatively result in a passband with narrower bandwidth and higher transmittance [40]. Thus, it should be optimized for optimal performance.

In Fig. 4(a), effect of lateral relative shift (Δx) between the top- and bottom-layer metallic nanoslit arrays are studied. This parameter is important in that it is also supposed to directly influence near-field intercoupling of the LPRs in the asymmetric metallic nanoslits, and consequently affect the resonant transmission in the passband. Additionally, its influence on the filtering performance determines required accuracy on alignment of the nanoslits in the top and bottom metal layers in fabrication of the structure. It is shown in Fig. 4(a) that, when the lateral shift is small, e.g., Δx<100 nm, there is no degradation of the filtering performance; instead, the passband gets narrower for a larger shift, at the cost of a slight reduction of the peak transmittance. It suggests that a small lateral shift does not seriously influence the intercoupling of the local plasmon resonances in the asymmetric metallic nanoslits. But when the lateral shift becomes much larger, up to an order of half-period, e.g., Δx=200 and 300 nm, the transmission spectra near the passband position are seriously degraded, due to weakened intercoupling of the LPR modes in the top- and bottom-layer nanoslits, such that it cannot be used as a bandpass filter. Besides, when approaching Δx = p/2 = 300 nm, intercoupling of LPRs takes place not in paired nanoslits, but in series of nanoslits alternately locating at the top- and bottom metal layers, via an in-plane surface plasmon waveguiding mode in the composite metal structure [46].

 

Fig. 4. (a) Influence of lateral relative shift (Δx) between the top- and bottom-layer metallic nanoslit arrays on the filtering effects (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm, p=600 nm). (b) Transmission spectra of the filter structure for different periods (p) (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm).

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Figure 4(b) shows dependence of the passband peak on period of the metallic structure. The passband peak redshifts with increase of the period. It’s mentioned above that the passband transmission is due to assistance of intercoupled LPR modes, but the LPR modes intrinsically have broadbands. Thus, the passband position is largely determined by tailoring effects of the neighboring in-plane SPR modes. As the in-plane SPR position is straightforwardly determined by the structure period, the passband peak position is also dependent on the period. But, tuning the passband peak position as such, simply by varying the period, is supposed to be limited in the LPR band range for acceptable filtering performance. Therefore, if a filter array is to be designed tunable in a broader spectral range, it’s better that the filter array is divided into a few spectral sub-bands; in each sub-band, the structure dimensions other than the period are optimized and invariant, while the passband peak position is tuned solely by varying the period.

Angular dependence of a filter is often concerned in applications. Figure 5(a) demonstrates filtering transmission spectra of the structure (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm, p=600 nm) at various incidence angles (θ=0°, 10°, 20° and 30°) for incidence of TM-polarized light. It is shown that, with increase of the incidence angle, the filtering passband peak position barely shifts, except for a degradation of the peak transmittance value. And it’s shown that, if the incidence angle is limited to be in a small variation range (e.g., less than 10°), the degradation is rather weak.

 

Fig. 5. (a) Angular dependence of the filtering transmission spectra for incidence of TM-polarized light (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm, p=600 nm). (b) Transmission and reflection spectra of the filter structure (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm) with different periods (p=600 and 700 nm) for normal incidence of TE-polarized light, in comparison with those of a counterpart Fabry-Perot cavity consisting of continuous metal layers without slits.

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As shown in Fig. 5(b), effects of polarization of the incidence light is also investigated. As the filter structure is one-dimensionally periodic, it is supposed to functionally operate only for incidence of TM-polarized light. For incidence of TE-polarized light, there is no excitation of SPs in near field of the metallic structure to assist/enhance transmission of the light through the subwavelength nanoslits. Thus, the structured metal layers effectively function as partially transmitting mirrors and the bi-layer structure operates as a Fabry-Perot (F-P) cavity resonator. In Fig. 5(b), transmission and reflection spectra of the filter structures with different periods (p=600 and 700 nm) are demonstrated for TE-polarized light, in comparison with those of a counterpart F-P cavity consisting of continuous metal layers without slits. In the figure, the transmission peaks at around λ=560∼590 nm are ascribed to fundamental-order resonances of the F-P cavities. And it’s shown that the transmission peaks (or reflection dips) for the bi-layer structures with or without slits and of different periods locate closely; presence of the slit and subwavelength periods of the slits do not have large impacts on the transmission/reflection characteristics. The spectral variations are only due to different effective optical parameters (e.g., effective reflection coefficient) of the metal layers in presence of the slits.

Lastly, we extend our study to a two-dimensional (2D) version of the periodic filter structure. Configuration of the structure is schematically shown in the inset of Fig. 6, the 2D metallic nanoslit array in each layer has equal periods in orthogonal directions (p_x=p_y=p). Here we assume the structure dimensions of t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm, p=600 nm, same as those for the 1D structure in Fig. 1(b), and its transmission spectra are calculated for incidence of light in different polarization directions (φ=0°, 30° and 45°) with respect to the x-axis, as shown in Fig. 6. For the polarization angle φ=0°, the spectrum demonstrates a passband peak at λ=881 nm with a bandwidth of FWHM=40 nm. When the polarization angle φ=30° and 45°, there is no shift of the passband peak position, but the peak transmittance drops for about 18%. Additionally, as SP-assisted transmission of light through the slits are feasible in both polarization directions, the effect of F-P resonant transmission as that for TE-polarized light in 1D structure shown in Fig. 5(b) is not that serious. Overall, performance of the 2D filter structure is only slightly degraded, but still comparable to that of the 1D one. The degradation is thought mainly due to additional scattering losses introduced from the nanoslit structures in the other orthogonal directions, i.e., influence of nanoslits periodic in y-direction on resonant transmission of light through nanoslits periodic in x-direction, and vice versa. Despite all these, advantage of the 2D filter structure is clear that it can be used for arbitrarily polarized or unpolarized light for improved passband transmittance.

 

Fig. 6. Transmission spectra of the filter structure with asymmetric bi-layer 2D metallic nanoslit arrays (t_m1=t_m2=50 nm, t_d=140 nm, s₁=100 nm, s₂=40 nm, p=600 nm) for incidence of light in different polarization directions. The inset is a schematic illustration of the 2D structure.

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4. Conclusion

In conclusion, we propose and numerically studied a plasmonic filter structure of asymmetric bi-layer metallic nanoslit arrays. The structure shows narrow-passband, low-sideband filtering characteristics in the visible-to-near-infrared spectrum range. In designing of filter arrays based on this structure, period of the structure can be varied to tune the passband peak positions in different cells of a filter array. Variation of lateral dimensions (i.e., in the x-y plane) of the filter structure in different cells, instead of vertical structural dimensions, is more feasible and easier in fabrication based on planar processing technologies; this advantage is also supported by using optically thin metal layers in the structure. The cooperative role of intercoupled asymmetric plasmon resonances also provides a way in designing higher-Q plasmon resonance modes in metallic micro/nano-structures for improved performance of plasmonic devices. It’s lastly mentioned that the filter structure can also be adapted to work in the other spectral range (e.g, in the UV–VIS or mid- to far-IR range) following its operational principles, though the results above are demonstrated in the VIS–NIR range.