1. Introduction

In the past ten years, metal-dielectric nanostructures have attracted a tremendous amount of attention due to its extraordinary electromagnetic properties [1]. Compared to other complex metal-dielectric nanostructures, one dimensional periodic metal-dielectric nanograting have been widely investigated recently, which have revealed many fundamental properties of novel nanostructures. Many novel optical properties and new functionalities based on metal-dielectric slit arrays have been demonstrated, such as color filters [2–4], planar lenses [5], negative index materials [6], and polarizer with wide bandwidth [7]. Some guided mode resonances filters made of a dielectric grating deposited on a thin waveguide layer have been reported [8]. Similarly, guided modes in a dielectric layer can be excited by using metallic grating. However, metal loss has been a limiting factor to the performance of these devices. One way to solve this problem is to mediate the coupling between metallic grating and dielectric waveguide [9–13]. Recently, some new bandpass filters have been designed based on the coupling between metallic grating and thin dielectric layer with high optical transmission and simple fabrication process [14]. To overcome the drawbacks of poor angular tolerance of the above filters, another bi-atom pattern grating-dielectric structure is designed that provides significant improvement of the angular tolerance without modifying the spectral lineshape [15]. But these filters are usually designed to work in the mid-infrared wavelength range. Currently, most studies about one dimensional nanograting have been mainly concentrated on single-mode resonance and only exhibit one resonance peak at certain wavelength [16, 17]. A filter that works for multimode and with multiple resonances is seldom reported in the telecom wavelength range [18], especially for the filter whose resonance wavelength and bandwidth can be easily tuned and modified.

We present a new metal-dielectric structure with two different metallic gratings deposited on each side of a free-standing dielectric layer in this paper. Compared to previous works, a distinct structure feature for the proposed double layer metallic gratings is the symmetry-reduced arrangement. We obtain two remarkable narrow band transmission dips with a peak in-between at normal incidence. The generation of these two narrow bands and non-degenerate resonance modes is attributed to the excitation of different current modes in the metallic grating, leading to different guided mode resonances in the dielectric layer, which is induced by the structural symmetry breaking of the nanograting. A frequency gap is opened at normal incidence(corresponding to the center of the Brillouin zone), which results in the existence of two dips at normal incidence, one corresponding to a symmetric mode, the other corresponding to an antisymmetric one; and thanks to the symmetry breaking, both of these mode can be excited. Furthermore, a frequency gap strongly depends on the thickness of the metallic grating. We also investigate the influence of lateral displacement between the two gratings above and underneath the dielectric layer and the grating period on these two transmission dips. The angular tolerance of two transmission dips can be increased by changing the thickness of metallic grating without modifying the spectral bandwidth.

2. Model construction

Figure 1 schematically illustrates a double layer nanograting based double-wavelength filter and its typical characteristics. We propose a metal-dielectric structure consisted of two symmetry-reduced double layer metallic gratings deposited on each side of a silicon nitride (SiN_x) thin film with a refractive index fixed at 2, respectively. As represented in Figs. 1(a) and 1(b), this symmetry-reduced arrangement can be obtained from a pair of symmetric double metallic gratings by alternately shifting the metal nanowires of the top layer metallic grating by half period (L = P/4). This configuration is designed to act as a double wavelength filter in the telecom wavelength range. Cross-sectional views of symmetry double layer metallic gratings (SDMG) and symmetry-reduced double layer metallic gratings (SRDMG) are shown in Fig. 1(b). This device can be fabricated by using a combination of electron beam lithography and a subsequent lift-off process. We select a thickness of t_d = 250 nm for the SiN_x film and a width w = 100 nm for the metal nanowire and keep them constant in the following work. Meanwhile, the period of the structure and the thickness of gold film are P = 1000 nm and t_m = 20 nm, respectively. The frequency dispersion of the permittivity of gold is taken into account [19]. The electromagnetic wave is transmitted through this structure with the magnetic field polarized along the metal nanowires (TM polarized light). We analyze the functional characteristics of this device by employing a finite-difference time-domain (FDTD) method (Lumerical FDTD Solutions, Inc.) [20]. More remarkable, only zero-order transmission is nonzero for our structure in the wavelength range being studied. In other word, all calculated transmission spectra in the following section are zero-order transmission.

 

Fig. 1 Structure schematic of multiple wavelengths guided more resonance filter and its typical optical phenomenon. (a) The SRDMG structure with two different metallic gratings deposited on each side of a free-standing dielectric layer. (b) Cross-section of the SDMG and SRDMG structures and their structure parameters. (c) Calculated transmission spectra of SRDMG with normal incidence (red line) and oblique incidence (red dashed line) for TM polarized light.

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To achieve high precision in the simulation, we use one period of the grating in the following simulation. Periodic boundary condition is used in the x direction and perfectly matched layer is used in the ± z direction under normal incidence. For oblique incidence, Bloch boundary condition in the x direction is used. The numerical calculations are performed with extremely well convergence condition. We assume that this structure is infinitely long in the y direction and all simulation results are normalized to the incident light power. The validity of our numerical method is confirmed by comparing the results with those obtained from the rigorous coupled-wave analysis method [21].

3. Results and discussion

Figure 1(c) shows its transmission spectra at incidence angle θ = 0° and θ = 6° for TM polarized light. It is interesting to see that there are two remarkable transmission dips (λ₁ = 1244 nm and λ₂ = 1276 nm) with a transmission peak in-between even at normal incidence. This SRDMG structure is obtained by alternately shifting the metal nanowires of top layer metallic grating from the SDMG structure [Fig. 1(b)], in which there is no appearance of the transmission dip (spectrum not shown here). Here, it is clearly seen that period of SDMG structure P₁ = 500 nm is a half of that of SRDMG structure P = 1000 nm. Moreover, the double resonance modes are non-degenerate resonance modes for the SRDMG structure because there is no further splitting of the double modes at oblique incidence. This transparency peak between the two dips is the nearly complete transmittance and its bandwidth is adjustable, which is promising to overcome the Drude damping limit for the EIT-like phenomenon in pure metallic resonant structures [22]. Moreover, for TE polarized light, there are also two transmission dips in the SRDMG structure at normal incidence (spectrum not shown here). Compared to that of TM polarized light, two transmission dips of TE polarized light have wide full width at half maximum (FWHM) and relatively low peak depth. So compared to the case of TM polarized light, TE polarized light is not a good choice for the design of dual-wavelength filter. Here, we only consider the case of TM polarized light.

To reveal the physical mechanism of double resonance dips in the SRDMG structure, a bare SiN_x planar waveguide with a thickness of 250 nm is implemented. As known, a guided mode cannot be excited for a bare planar waveguide since the normal incidence wave has zero momentum parallel to the waveguide layer [4]. Guided mode resonance is generated when a phase matching condition is satisfied, requiring that the propagation constant β for the excited guided modes equals the magnitude of the grating vector k_P = 2π/P. Figure 2(a) plots a calculated dispersion relation for TM guided modes in the waveguide with its refractive index n₁ set to 1. For this symmetric three-layered air/SiN_x/air waveguide, the dispersion relation is derived as [4]

 

Fig. 2 (a) Dispersion relation for a dielectric planar waveguide with the thickness t_d = 250 nm. (b) The dependence of the resonant wavelength on wire width w for the SDMG structure. (c) Calculated transmission (blue line) and phase (red line) for the SRDMG structure. The resulting group index is shown in (d) together with the transmission.

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Based on the above analysis on SDMG structure, we investigate the physical principle of the double transmission dips in SRDMG structure through a more detailed analysis. Figure 2(c) shows the calculated optical transmission and phase change for this configuration. To clearly illustrate the phase and group index change, the wavelength range of consideration is reduced to 1200 −1320 nm. Two transmission dips have narrow full width at half maximum of ∆λ ≈3 nm for the dip at λ₁ = 1244 nm and ∆λ ≈5 nm for the other at λ₂ = 1276 nm, leading to a high-Q transmission resonance (Q = λ/∆λ). Each dip is accompanied by a phase change of about π/2. The group index can be calculated as [9]:

To further investigate the mechanism of the generation of the double transmission dips, more analytical results are presented in Fig. 3. The normalized magnetic field distribution at two different wavelengths of λ₁ = 1244 nm and λ₂ = 1276 nm corresponding to the two dips are shown in Figs. 3(a) and 3(b), respectively. Figures 3(c) and 3(d) depict the electric field distribution (arrow map) at the positions of two dips. Arrows in Figs. 3(c) and 3(d) show direction and intensity of electric field at some location. Connecting beginning points of arrows in sequence make up some lines, which indicate electric field lines. The knowledge of near-field distribution is important to understand the physical mechanisms of the observed phenomena. It is observed that the standing wave is induced transversally in the thin SiN_x waveguide layer. One of the most promising signs of the standing wave is that the distance between two wave nodes is half of the structure period. A remarkable distinction between the electromagnetic fields for the two dips is that the standing wave shows a phase shift as a quarter of period. The field enhancements near the metal nanowires are different: the magnetic field distribution near the metallic nanowires of the down layer metallic grating has no enhancement for λ₁ = 1244 nm; however, that for λ₂ = 1276 nm is just the opposite, which is resulted from the different electron excitation of metal nanowires in Fig. 3(g) and 3(h). For the spatial distribution of electric field, electric field is localized near metal nanowires and mainly distributed at top and down layers metallic grating/waveguide layer boundaries. It shows that EM energy mainly propagates along the waveguide layer and the surfaces of top and down layer metallic grating. And a vortex electric filed is formed at the location of magnetic field enhancement in Figs. 3(c) and 3(d).

 

Fig. 3 Spatial distribution of magnetic field (color map) for the SRDMG structure at different wavelengths with the thickness of gold film t_m = 20 nm. (a) λ₁ = 1244 nm, (b) λ₂ = 1276 nm. Spatial distribution of electric field (arrow map) for (c) λ₁ = 1244 nm, (d) λ₂ = 1276 nm. Spatial distribution of energy flow for (e) λ₁ = 1244 nm, (f) λ₂ = 1276 nm. Spatial distribution of x-component of current density for (g) λ₁ = 1244 nm, (h) λ₂ = 1276 nm. Red arrows indicate directions of the current flow in Figs. 3(g) and 3(h).

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Figures 3(e) and 3(f) depict the Poynting vector (S) distribution at the positions of two dips, which shows how the light propagates in the SRDMG structure before it is absorbed and reflected. The Poynting vector of the transmission dip of λ₁ = 1244 nm [Fig. 3(e)] shows that a vortex of the electromagnetic field is formed and the incident electromagnetic energy propagates with a vortex flow in the waveguide layer along the surface of the metallic grating. The vortexes are located precisely at the places where the node of the standing wave appears and the maximum value of the energy flow is located at the places where the magnetic field is concentrated. For comparison, the Poynting vector at λ₂ = 1276 nm illustrates that the electromagnetic energy propagates mostly inside the waveguide layer which provides a weak vortex flow in the electromagnetic field. This reveals the physical mechanism of the specific phenomenon shown in Fig. 2(d), in which the group index at the wavelength of 1276 nm is less than that of 1244 nm. Furthermore, it is found that poynting vector on the metal nanowires in Fig. 3(f) is relatively dense and high intensity (the length of arrow indicating the intensity of poynting vector) than that of Fig. 3(e). This can illustrate that the dissipation losses of metal nanowires in Fig. 3(f) may be higher than that of Fig. 3(e). Although the formation of a vortex flow in the waveguide layer of Fig. 3(e) can increase the time of light propagating in the structure and the dissipation losses of metal nanowires. But the poynting vector on the metal nanowires in Fig. 3(e) is weak, which generates that a vortex flow in Fig. 3(e) plays an unimportance role in the dissipation loss of metal nanowires.

Moreover, our investigation shows that different current density distributions of metal nanowires at the positions of different dips are excited by incident light, and can lead to the generation of various guided mode resonance (symmetric mode and antisymmetric mode) mediated by the metallic grating, as shown in Figs. 3(g) and 3(h). To clearly illustrate the current density distribution of different metal nanowires in a period of the structure, the metal nanowires are denoted by numbers 1, 2, 3 and 4, respectively. In Fig. 3(g) with λ₁ = 1244 nm, current distributions in nanowires 1, 3, and 4 have opposite direction. This shows that the net current in nanowires 1, 3, and 4 always has zero x-component. In other words, there is no dipole-like resonance of these nanowires. Figure 3(g) shows that the dipole-like mode is only excited in nanowire 2, which has opposite x-direction current distribution. The cancellation of the dipole-like radiation of metal nanowire provides a low dissipation loss and ensures a high-Q transmission resonance. However, it is interesting to notice that current distribution of the metal nanowires in Fig. 3(h) is exactly opposite to that in Fig. 3(g): the net current of nanowire 2 is zero for the x-component, and the dipole-like mode is excited in nanowires 1, 3, and 4. Meanwhile, the current flow of nanowires 1 and 3 is excited in antiphase and forms a current loop (magnetic dipole radiation). Compared to the transmission dip at the wavelength of 1244 nm, both the electric and magnetic dipole radiation of the metal nanowires will increase the dissipation losses (high absorption peak), which lowers the Q of the transmission resonance [23]. These results are in agreement with those shown in Fig. 2(d) (Q-factor at λ₁ = 1244 nm is higher than that at λ₂ = 1276 nm). For the SDMG structure with P = 1000 nm shown above, the guided mode resonance (symmetric mode) is excited, which is relative to an antiphase current flow in x-direction in a pair of metal nanowires and an antiphase current flow is accordance with the current flow of nanowires 1 and 3 in Fig. 3(h). The dipole mode of all metal nanowires is excited for a SDMG structure with P = 1000 nm at the transmission dip, which leads to relatively wide full width at half maximum (data not shown).

In order to verify the above viewpoint, calculated reflection spectrum and absorption spectrum at normal incidence are shown in Fig. 4(a) and Fig. 4(b), respectively. It is shown clearly that absorption value at λ₂ = 1276 nm in our designed structure is higher than that of λ₁ = 1244 nm. High absorption value at λ₂ = 1276 nm indicates the larger dissipation losses of metal nanowires and the lower Q-factor. This further confirms that the excitation of electric and magnetic dipole radiation of the metal nanowires play an important role in the metal dissipation. Compared to the excitation of electric and magnetic dipole radiation of the metal nanowires, the role of a vortex flow in the structure at λ₁ = 1244 nm have relative weak in the absorption. The interaction between the incident light and the SRDMG structure induces different electron and current densities of the metal nanowires, which results in the formation of different guided mode resonances (symmetric mode and antisymmetric mode) in the SiN_x waveguide layer. One possible explanation is that the excitation of the guided mode resonance mediated by metallic grating is induced by the destructive interference between the dipole mode of the metal nanowire and the waveguide mode in the thin dielectric layer. This confirms that the dipole-like mode of the metal nanowires is canceled out due to the unique form of the coupling to the waveguide mode.

 

Fig. 4 Calculated (a) reflection spectrum and (b) absorption spectrum of SRDMG with normal incidence for TM polarized light. Structure parameter is identical to that of Fig. 1(c).

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As illustrated in Fig. 5, we also investigate the influence of other parameters on these double transmission dips for this SRDMG structure. Figure 5(a) shows the dependence of the double transmission dips on incident angle θ. We find that the gap between the two dips increases with increasing incidence angle θ, and the two transmission dips can keep narrow bandwidth simultaneously. It is worth noting that there is a good angular tolerance to the angle range for double transmission dips, which is very important for the development of practical filters. Moreover, angular tolerance can be further improved by adjusting the thickness of metallic grating (Fig. 7). The relationship between double transmission dips and the lateral displacement ∆ (∆ refers to lateral displacement between top and down metallic grating) is explored, as plotted in Fig. 5(b). It is interesting that lateral displacement ∆ has no influence on the position of two transmission dips, but the transmission dips vanish alternately as the lateral displacement increases. The insensitivity to lateral displacement of the transmission dips make the fabrication of the double metallic grating structure less demanding, as it reduces the requirement to the alignment of the double metallic grating.

 

Fig. 5 Transmission spectra for the SRDMG structure with fixed w = 100 nm, t_d = 250 nm and P = 1000 nm. (a) at different incidence angle θ, (b) different lateral displacement ∆.

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Figure 6(a) demonstrates the influence of the thickness of metallic grating t_m on the double transmission dips at normal incidence, in which the gap between the two dips decreases initially then increases as the thickness t_m changes from 20 nm to 240 nm, and the double transmission dips can be adjusted by simply changing the thickness of metallic grating. However, for the SDMG structure with P = 1000 nm, the thickness of the metallic grating hardly affect the position of dips, as shown in Fig. 6(b). It is more feasible and convenient to tune the position of transmission dip by modifying the thickness than by changing the period and width of the metal nanowires in the fabrication of some filters device. But for some application where many filters have to be fabricated on the same sample [24], it is easier to change the period or the width of the nanowires rather than the metal thickness to fabricate filters in only one lithography step. In addition, the dependence of the double transmission dips on the structure period is plotted in Fig. 6(c). The position of dips is approximately linear to the structure period, which confirms the formation of guided mode resonance mediated by the metallic grating. The last noticeable point is that the structure period has little effect on the separation between the two dips. It demonstrates that the position of the double transmission dips can be easily tuned in a larger spectral region without modifying their spectral separation with the change of structure period.

 

Fig. 6 (a) Transmission spectra for different structure at normal incidence with fixed w = 100 nm and t_d = 250 nm. The effect of the thickness of metallic grating on transmission spectra for (a) the SRDMG structure and (b) the SDMG structure with period P = 1000 nm. (c) The dependence of calculation transmission spectra on structure period with fixed w = 100 nm, t_d = 250 nm and t_m = 20 nm.

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As shown in Fig. 7, we further investigate the influence of different incidence angle θ on double transmission dips at thickness of metallic grating t_m = 162 nm and t_m = 280 nm. Compared to that of t_m = 20 nm in Fig. 5(a), the gap between two dips increases with increasing the thickness of metallic grating under normal incidence. Angular tolerance is improved by increasing the thickness of metallic grating. In Fig. 7(a) with t_m = 162 nm, the effect of incident angle on double transmission dips is weak in the range from −2° to 2°. In other words, incident angle hardly affect the position of two dips in this angle range. When the thickness of metallic grating increases t_m add to 280 nm, the capacity of angular tolerance for SRDMG structure is doubled, as illustrate in Fig. 7(b). Meanwhile, we find that FWHM (Full width at half maximum) of double transmission dips almost no change when adjusting the thickness of metallic grating. This is relatively simple method to improve angular tolerance by changing the thickness of metallic grating.

 

Fig. 7 Transmission spectra for the SRDMG structure with fixed w = 100 nm, t_d = 250 nm and P = 1000 nm at (a) thickness of metallic grating t_m = 162 nm, and (b) thickness of metallic grating t_m = 280 nm.

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To further investigate the mechanism of the increasing angular tolerance of transmission dips with the increase of the thickness of metallic grating, the normalized magnetic field distribution at two different wavelengths of λ₃ = 1500 nm and λ₄ = 1713 nm with the thickness of gold film t_m = 280 nm are shown in Figs. 8(a) and 8(b), respectively. The two transmission dips corresponds to that of Fig. 7(b) at normal incidence. It is observed that guided mode in the waveguide layer is weaken as the thickness of gold film increases. The magnetic field enhancement has a transfer from the waveguide layer to the slits of metallic grating. A remarkable distinction between magnetic field distribution for the two dips is that the location of magnetic field enhancement are different: at the wavelength λ₃ = 1500 nm, the magnetic field mainly distribute inside the metal slit of the top layer metallic grating and magnetic field of waveguide layer is weak; however, that for λ₄ = 1713 nm is just the opposite, the magnetic field mainly distribute inside the metal slit of the down layer metallic grating and waveguide layer. For λ₃ = 1500 nm, magnetic dipole in the metal slits of top layer metallic grating is excited. The excitation of magnetic dipole in the metallic grating increases the capacity of angular tolerance [25]. But for λ₄ = 1713 nm, the excitation of magnetic dipole of metal slits of metallic grating is relatively weak, and most of magnetic field is focus on the waveguide layer. This is why the capacity of angular tolerance for λ₃ = 1500 nm is better than that of λ₄ = 1713 nm.

 

Fig. 8 Spatial distribution of magnetic field for the SRDMG structure at different wavelengths with the thickness of gold film t_m = 280 nm at normal incidence: (a) λ₃ = 1500 nm, (b) λ₄ = 1713 nm.

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In Fig. 5(b), the transmission dip vanishes alternately as the lateral displacement ∆ increases. When lateral displacement ∆ equals 125 nm, short wavelength transmission dip vanishes and there is only one transmission dip at the wavelength λ = 1276 nm. However, longer wavelength transmission dip vanishes when lateral displacement ∆ increases to 375 nm. To explain the phenomenon, spatial distribution of x-component of current density for the case of ∆ = 125 nm and ∆ = 375 nm at the position of transmission dip is shown in Fig. 9. Compared to that of Fig. 3(h), the distribution of current density in Fig. 9(a) is different from Fig. 3(h) although the wavelength position of transmission dip is also at λ = 1276 nm for these two case. Different lateral displacement ∆ leads to different current density distribution for same wavelength position. In Fig. 9(a), the dipole mode of all metal nanowires is excited and the nanowires of top layer metallic grating have opposite x-direction current distribution. However, current density distribution of nanowires in the down layer metallic grating is same to that of Fig. 3(h). The excitation of dipole mode of all metal nanowires increase the dissipation losses, which result in the increasing of FWHM of transmission dip of 1276 nm, as shown in Fig. 5(b). There is only one dip of 1244 nm observed in the case of ∆ = 375 nm. In Fig. 9(b), we also find that nanowires of top layer metallic grating have opposite x-direction current distribution. Current density distribution of nanowires in the down layer metallic grating is same to that of Fig. 3(g). Furthermore, we find that when lateral displacement ∆ = 125 nm and ∆ = 375 nm, new structural symmetry (mirror symmetry) is formed. This make broken symmetry recover. This is why there is only one dip in the transmission spectrum when ∆ = 125 nm and ∆ = 375 nm.

 

Fig. 9 Spatial distribution of x-component of current density for (a) λ = 1276 nm and ∆ = 125 nm, (b) λ = 1244 nm and ∆ = 375 nm. There is only one dip in the above two structures. Red arrows indicate directions of the current flow in Figs. 9(a) and 9(b).

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Finally, as shown in Fig. 10, we investigate the influence of dielectric film thickness on double transmission dips. Figure 10(a) presents the wavelength position of two transmission dips can be tuned by varying the thickness of dielectric layer t_d. As thickness of dielectric layer increases, both transmission dips have red shifts. When the thickness of dielectric layer increase to about 460 nm, higher order guided modes is excited. Figure 10(b) demonstrates that both transmission dips can be adjusted by changing the refractive index of dielectric film. Therefore, both transmission dips have a larger red shift with the increase of refractive index of dielectric film. In addition, as depicted in Fig. 10(c), it is interesting that the gap between two dips has a good linear approximation in refractive index in a range from 1.5 to 2.8. It indicates that the gap between both dips can be also adjusted by the refractive index of dielectric film.

 

Fig. 10 Double transmission dips on dependence of structural parameters of dielectric film. (a) The thickness of dielectric film. (b) The Refractive index of dielectric film. (c) The linear approximations between the gap of two dips and refractive index of dielectric layer.

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4. Conclusions

In summary, we present a new metal-dielectric structure which can provide double narrow-band transmission dips and a transmission peak in-between based on symmetry-reduced double layer metallic gratings. We investigate the physical mechanism of this new two-resonance phenomenon, and demonstrate that symmetry-breaking in asymmetric double layer metallic grating structure excites different current modes in the metallic grating, and then generates different guided mode resonances (symmetric mode and antisymmetric mode) in the dielectric layer. Such mechanism is further confirmed by analyzing the high group index, a vortex phenomenon of the electromagnetic field and current density distribution. We also find that these two narrow band transmission dips and their frequency gap can be easily controlled by modifying the thickness of the metallic grating, providing a convenient solution to tune the resonance positions and designing bandwidths in the fabrication of some filters. Future work will be focused on the enhancement of angular tolerance of these two resonance dips by optimizing structure parameters and maintaining the spectral lineshape. This study is valuable for developing subwavelength-based multi-wavelength narrow spectral filter, an important photonic component that has extensive application in integrated optoelectronics system.