Optical filters are an important element in optical displays,^[1] sensors,^[2] digital photography,^[3] and so on. Various filters have been proposed in recent decades, including dye or pigment filters,^[4] dielectric filters,^[5,6] and metallic filters.^[7] Compared with conventional dye or pigment filters,^[4] dielectric and metallic filters based on micro/nano-structures exhibit better ultraviolet, power, and temperature reliability. Additionally, the filtering properties of dielectric and metallic filters can be easily manipulated by geometrical dimensions, such as the shape and size of the nanostructures. However, miniaturization of dielectric filters is hampered by the diffraction limit of light. What is worse, because of small contrasts of refractive indices, reflection on an interface of different dielectric materials is very low (e.g., reflectivity ∼ 16% on a Si–SiO₂ interface), making the bandwidths (full width at half-maximum, FWHM) of dielectric filters with several layers greater than 100 nm.^[5,6]

Surface plasmon polaritons (SPPs) supported by metallic nanostructures are electromagnetic waves confined on metal surfaces at the visiable and infrared frequencies.^[8] Due to subwavelength field confinements and large field enhancements, SPPs are promising to significantly miniaturize photonic devices.^[8] Recently, various metallic nanostructures based on SPPs have been proposed to realize metallic filters, including periodic subwavelength metallic hole arrays,^[9–11] metallic metasurfaces,^[12–14] and metal–insulator–metal (MIM) nanoresonators.^[15–17] For example, by periodically designing subwavelength hole arrays on a metal film with optical thickness, a metallic filter could be achieved based on the extraordinary optical transmission (EOT).^[18] However, due to the subwavelength diameters of the hole arrays on the optical thick metal film (thickness > 150 nm), the absolute transmittance was rather low (T < 50%).^[9,11] Moreover, the transmission spectra were broad (Δλ_FWHM > 100 nm) because of the inherent ohmic losses in metals. Metallic metasurfaces could be used to achieve reflective plasmonic filters based on resonant absorptions of gap SPP modes in MIM nanoresonators (gap thickness < 50 nm).^[12,13] Although the maximum reflection peak was as high as T = 90%,^[14] their reflection spectra were still rather broad (Δλ_FWHM > 100 nm) because of the large resonant absorptions of the MIM nanogaps.^[12,13] Recently, by designing a metasurface with arrays of elliptical and circular nanoholes on an 80-nm-thick gold film, which was covered by a 300-nm-thick SiO₂ layer, the transmittance and bandwidth were reported to be T = 44% and Δλ_FWHM ≈ 79 nm, respectively.^[14] By using planar MIM structures (the thickness of the insulator > 100 nm), a narrowband (Δλ_FWHM ≈ 40 nm) metallic filter was realized based on the Fabry–Perot effect because of the high reflectance (> 60%) of the metals, and the maximum transmittance was T ≈ 60%.^[17] The thicknesses of these filters based on multilayer MIM structures were larger than 150 nm.^[15–17] In the above metallic filters,^[9–17] the bandwidths could not be further decreased due to the inherent ohmic losses of the metals. Therefore, it is a great challenge to realize thin metallic filters with both narrow bandwidths and high transmittances, which are important for high resolution optical imaging, dense wavelength-division-multiplexed optical information processing, and high-sensitive sensing in the micro/nano optics.

In this paper, an extra-narrowband metallic filter is numerically and experimentally demonstrated with an ultrathin (thickness H = 60 nm) single-layer metallic grating. When a p-polarized incident beam illuminates the one-dimensional (1D) metallic grating, huge field enhancements occur in the nano-slits, and interference of radiative fields from the periodic nano-slits gives rise to the Wood’s anomaly in the thin periodic metallic grating. Unlike localized field enhancements of SPPs on metal–dielectric interfaces, the Wood’s anomaly results in large field enhancements in the substrate, which efficiently reduces the ohmic losses in metals. The strong field in the substrate can pass through the nano-slits, resulting in an extra-narrowband and high-transmission filter because of the reduced ohmic losses in metals. Numerical simulation results show that a transmission peak is up to T = 80%, and a transmission bandwidth at λ = 1200 nm is as small as Δλ_FWHM ≈ 1.6 nm, which is much smaller than that in the previous reports (Δλ_FWHM ≥ 40 nm).^[9–17] The corresponding quality factor is as high as Q = λ/Δλ_FWHM = 750, which is 40 times greater than that in the previous reports.^[9–17] Experimentally, metallic gratings are fabricated on an ultrathin single-layer gold film, and the experimental results consist with the simulation data. Due to polycrystalline gold films and fabrication defects, the narrowest bandwidth in the experiment becomes Δλ_FWHM ≈ 10 nm, which is still smaller than 25% of that in the previous reports (Δλ_FWHM ≥ 40 nm).^[9–17]

The ultrathin metallic grating structure is schematically shown in Fig. 1(a). This structure comprises periodic nano-slits with a width of w and a period of P in a metallic film (thickness of H), which is placed on a K9 glass substrate. An incident beam with a p-polarization state (vacuum wavelength of λ) can excite strong SPPs in the metallic slits under back illumination from the substrate. The interference of the backward radiations from the periodic metallic nano-slits results in the Wood’s anomaly in the glass substrate.^[19] The resonant wavelength of the Wood’s anomaly depends on resonant order m, refractive index of the substrate n_d, and the grating period P,^[20]

Fig. 1.

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Fig. 1. (a) Schematic of a metallic grating with geometric parameters. (b) Simulation transmission spectra under a p-polarized and an s-polarized incidence. Field distributions (|E|/E0|) at the first-order resonant wavelength (λ = 900 nm) under incident light of (c) p-polarizaion and (d) s-polarization. (e) Resonant wavelength as a function of P. (f) Peak transmittance and (g) bandwidth of the metallic filter as functions of the resonant wavelengths.

For the verification of the analysis, a commercial software COMSOL Multiphysics is firstly adopted for simulating the transmission spectra of the nano-struectures.^[21] The metal film is selected as a gold film with a thickness of H = 60 nm. The thickness is smaller than 40% of that in the previous dielectric and metallic filters (thickness ≥ 150 nm).^[9–17] The geometric parameters of the grating are P = 600 nm and w = 60 nm. The permittivity of gold is derived from the experiment results in Ref. [22]. The substrate is K9 glass with a refractive index of n = 1.5. For the gold film with H = 60 nm, the reflection is as high as 96.3%, and the transmittance is only 0.5% at λ = 9000 nm. Figure 1(b) plots the transmission spectra of the metallic grating under the normal illumination with p-polarization (electric vector parallel to x axis) and s-polarization (electric vector vertical to x axis) from the substrate. Under an incident light with p-polarization, it can be observed that the transmittance reaches to a peak of T ≈ 80% at λ = 900 nm, and the bandwidth is Δλ_FWHM ≈ 3.0 nm. The resonant wavelength (λ = 900 nm) matches well with the first-order resonant condition (m = 1) of the Wood’s anomaly based on Eq. (1). The normalized electric field amplitude distribution (|E|/E₀|) at the Wood’s anomaly resonance (λ = 900 nm) is shown in Fig. 1(c). Here, |E₀| is the amplitude of the electric field of the incident light. The simulation shows that a large field enhancement (|E|/E₀|≈ 12) occurs in the metallic nano-slits. The strong field in the metallic nano-slit leads to the forward and backward radiations. Since the refractive index (n = 1.5) of the glass substrate is greater than that of the air (n = 1.0), the simulation reveals that the backward radiation (energy flow) into the glass substrate is 2.4 times the forward radiation into the air. The interference of the backward radiations from the periodic nano-slits results in the Wood’s anomaly resonance, which leads to the interference pattern with large field enhancements (|E|/E₀|∼ 8) in the glass substrate, as shown in Fig. 1(c). It can be seen that the interference pattern with a period of 300 nm is perpendicular to the gold film, further confirming the Wood’s anomaly resonance. Since the field is mainly distributed in the glass substrate, the ohmic losses in the thin metallic grating are greatly reduced. The enhanced field in the substrate can pass through the nano-slit in the ultrathin gold film, resulting in a high transmittance (T ≈ 80%) and a narrow bandwidth (Δλ_FWHM ≈ 3.0 nm), as depicted by the black line in Fig. 1(b). The maximum transmittance (T ≈ 80%) is about 160 times of that (T = 0.5%) of the 60 nm-think gold film.

However, under an s-polarized incident beam, the transmission peaks vanish, and the transmittance is about 1% at λ = 900 nm, as shown by the red solid line in Fig. 1(b). The reason is that the s-polarized incident beam can not cause field enhancements in the metallic nano-slits. Further simulations show that the field (|E|²) in the single metallic nano-slit under an s-polarized incident light is much weaker (< 24 times) than that under a p-polarized incident light. Due to the weak fields in the metallic nano-slits under an s-polarized incident light, the Wood’s anomaly resonance does not happen. In this case, the metallic grating exhibits high reflectance (e.g., R = 95.4% at λ = 900 nm), just like a complete gold film (R = 96.3%). The interference of the incident light and the reflected light results in the interference pattern (|E|/E₀|) (parallel to the gold film with period of 300 nm) in the substrate, as shown in Fig. 1(d), which is quite different from that [Fig. 1(c)] caused by the Wood’s anomaly.

Additionally, to verify the linear relationship between the resonant wavelength and the period P of the metallic grating in Eq. (1), we plot the first-order resonant wavelength (m = 1) as a function of P when H = 60 nm and w = 60 nm, as shown by the black dots in Fig. 1(e). The red line is a linear fitting curve. It can be seen that the resonant wavelength linearly increases with the period P of the metallic grating. For the red line, the slope is calculated to be 1.5, which is consistent with the refractive index of the glass substrate n_d = 1.5. This good consistence strongly verifies the Wood’s anomaly resonance. In Fig. 1(f), the peak transmittances of the grating are plotted as a function of resonant wavelengths. The peak transmittances are greater than 60%. At a resonant wavelength of λ = 675 nm, the transmittance reaches up to 83.3%. The bandwidth of the metallic filter as a function of resonant wavelengths is plotted in Fig. 1(g). It can be observed that the bandwidth of the metallic filter decreases with the wavelengths due to the lower loss of gold in longer wavelengths. The bandwidth is less than 10 nm, and the narrowest bandwidth is as small as Δλ_FWHM = 1.6 nm at λ = 1200 nm.

Unlike conventional metallic filters with localized field enhancement of SPPs on the metal–dielectric interface,^[9–14] the enhanced field generated by the Wood’s anomaly in our scheme is mainly distributed in the substrate, which can efficiently reduce the ohmic losses in the metallic film. As a result, the bandwidth is effectively decreased, and the narrowest bandwidth (Δλ_FWHM ≈ 1.6 nm at λ = 1200 nm) is smaller than 4% of that in the previous reports (Δλ_FWHM ≥ 40 nm).^[9–17] The bandwidth (Δλ_FWHM ≈ 1.6 nm at λ = 1200 nm) is also much narrower than that (Δλ_FWHM ≈ 10 nm) of commercial dielectric filters (e.g., FB1200-10 in Thorlabs). Moreover, the transmittance (> 60%) is greater than that (< 50%) of commercial dielectric filters (e.g., FB1200-10 in Thorlabs). The corresponding quality factor is as high as Q = λ/Δλ_FWHM = 750, which is 40 times greater than that in the previous reports.^[9–17] By using a silver grating, the bandwidth of our metallic filter can be further narrowed at long wavelengths because of lower ohmic losses in silver.

According to the polarization dependence of the one-dimensional (1D) metallic grating above, it is possible to develop a switchable metallic filter, which has great potential applications in the active digital display and high-density data storage.^[23] Herein, an ultrathin two-dimensional (2D) orthogonal metallic grating with different periods is designed as shown in Fig. 2(a). The gold film thickness is also H = 60 nm in the simulation. The periods along x-axis and y-axis are P₁ = 500 nm and P₂ = 600 nm, respectively. On the other hand, the widths along x-axis and y-axis are w₁ = 80 nm and w₂ = 60 nm, respectively. Figure 2(b) plots simulation transmission spectra under a normal illumination with p-polarization (electric vector parallel to x axis) and s-polarization (electric vector vertical to x axis). It is found that two peak transmittances reach to ∼ 80% with bandwidths of Δλ_FWHM ≈ 3.0 nm under p-polarized and s-polarized incident beams. Different resonant wavelengths (λ₁ = 750 nm and λ₂ = 900 nm) match well with the first-order resonant condition (m = 1) of the Wood’s anomaly in the metallic grating with different periods of P₁ = 500 nm and P₂ = 600 nm. As for the 1D gratings, the transmission spectra with the corresponding geometric parameters are simulated in Fig. 2(c) under a p-polarized incident beam. Compared with Fig. 2(c), the 2D orthogonal grating still maintains the same high-transmission and narrowband responses of the 1D metallic gratings. Hence, the filtering property can be switchable by rotating the 2D metallic grating or incident polarization.

Fig. 2.

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	Fig. 2. (a) Schematic of the 2D orthogonal metallic grating with the geometric parameters. (b) Transmission spectra of the 2D orthogonal metallic grating under the p-polarized and s-polarized incidence. (c) Transmission spectra of the 1D metallic grating with the corresponding geometric parameters under the p-polarized incidence.

In order to verify our theory and simulation, we use focused ion beams (FIB) to fabricated 1D metallic gratings in a gold film with a thickness of 60 nm, which is deposited on a 20 mm × 20 mm K9 glass substrate. A scanning electron microscopy (SEM) image and its zoomed-in view are displayed in Figs. 3(a) and 3(b), respectively. The grating comprises 40 nano-slits with a length of 18 ×m. The width of the nano-slit is approximatedly w = 100 nm. Transmission spectra are measured with a homemade microscope system.^[24] A Fianium super-continuum light source illuminates the sample normally from the back side. A Glan–Taylor prism is used to obtain a p-polarized incident light, and a lens (focal length f = 10 cm) focuses the polarized light on the sample. A Mitutoyo microscope objective (100 × and N. A. = 0.5) collects the transmitted light from the sample, and the collected light is coupled to a spectrograph through a fiber.

Fig. 3.

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	Fig. 3. (a) SEM image of one gold grating with the period of P = 400 nm. (b) Zoomed-in view of the sample. Experimental transmission spectra of the samples with (c) P = 400 nm, (d) P = 450 nm, and (e) P = 500 nm.

A measured transmission spectrum of a gold grating with P = 400 nm is shown in Fig. 3(c). The maximum transmittance is T ≈ 48.4% at the transmission peak of λ = 611.5 nm, and the bandwidth is Δλ_FWHM ≈ 16 nm. Figure 3(d) depicts a transmission spectrum of a gold grating with P = 450 nm. The maximum transmittance is T ≈ 31.7% at the transmission peak of λ = 689.8 nm, and the bandwidth is Δλ_FWHM ≈ 11 nm. When the period of the gold grating becomes P = 500 nm in the experiment, a transmission peak can be observed at λ = 759.3 nm in Fig. 3(e). The maximum transmittance is T ≈ 27.8%, and the bandwidth is Δλ_FWHM ≈ 10 nm, which is much smaller than the previous results (Δλ_FWHM ≥ 40 nm).^[9–17]

The experimental transmission spectra exhibit lower transmittances and broader bandwidths than the simulation results. The broader bandwidths originate from the large losses caused by the polycrystalline gold film^[25] and the fabrication roughness^[26] in the experiments. These large losses also result in lower transmittances in the experiment. Additionally, the slit width w and thickness H of the nanoslits in the experiment deviate from those (when H = 60 nm and w = 80 nm) in the simulation. This deviation also leads to lower transmittances in the experiment, which can be observed in the simulation results of Fig. 4. Figure 4 shows that the largest transmittance of the metallic grating with the period P = 500 nm is obtained when H = 60 nm and w = 80 nm.

Fig. 4.

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	Fig. 4. Transmittance of the gold grating as functions of (a) the thickness H when P = 500 nm, w = 80 nm and (b) the slit width w when P = 500 nm, H = 60 nm.

To decrease the bandwidths of the metallic filter, a monocrystalline metallic (gold or silver) film, which has lower ohmic losses, can be prepared based on an chemically synthesis^[27,28] or molecular beam epitaxy (MBE).^[29] More importantly, the bandwidth of our metallic filter can be further narrowed by using monocrystalline silver films. By using an FIB technology based on helium^[30] or an advanced method based on a lift-off process using high-resolution electron beam lithography (EBL) with a negative-tone hydrogen silsesquioxane (HSQ) resist,^[31–33] the slit width can be reliably fabricated to satisfy the designed structural parameters. As a result, the transmittance of the metallic filter could be increased.

A 2D orthogonal grating is also fabricated in a 60 nm-thick gold film on a 20 mm × 20 mm K9 glass substrate. A SEM image of the 2D orthogonal gold grating with P₁ = 400 nm and P₂ = 430 nm and its zoomed-in view are displayed in Figs. 5(a) and 5(b), respectively. The numbers of nano-slits in each dimension are both 40, and the size of the 2D grating is 18 μm × 18 μm. The width of the nano-slits is approximately w = 100 nm. An experimental transmission spectrum of the sample is depicted in Fig. 5(c) under a p-polarized incident light. A transmission peak appears at λ = 618.7 nm with a maximum transmittance of T ≈ 39% and a bandwidth of Δλ_FWHM ≈ 38 nm. Figure 5(d) depicts an experimental transmission spectrum of the sample under an s-polarized incident light. A resonant wavelength is observed at 659.9 nm with a maximum transmittance of T ≈ 39% and a bandwidth of Δλ_FWHM ≈ 30 nm. When the angle between x-axis and the polarization of the incident beam becomes 45°, it can be observed that there are two transmission peaks at 618.7 nm and 658.3 nm in Fig. 5(e). The maximum transmittance and the bandwidth of the peak at the shorter wavelength (λ = 618.7 nm) are T ≈ 26% and Δλ_FWHM ≈ 42 nm, respectively. At the same time, the maximum transmittance and the bandwidth at the longer wavelength (λ = 658.3 nm) are T ≈ 25% and Δλ_FWHM ≈ 32 nm, respectively. The differences between experimental results and simulation data stem from the fabrication imperfections and limit as discussed above. As a result, the transmission spectra can be adjusted by rotating the incident polarization effectively.

Fig. 5.

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	Fig. 5. (a) SEM image of the 2D orthogonal grating with the periods of P1 = 400 nm and P2 = 430 nm. (b) Zoomed-in SEM image of the 2D orthogonal grating. Experimental transmission spectra of the samples under (c) p-polarization, (d) s-polarization, and (e) 45° polarization incident beam illumination.

In summary, by employing both strong field enhancements in metallic nano-slits and the Wood’s anomaly in an ultrathin (H = 60 nm) single-layer gold grating, a metallic filter with an extra-narrow bandwidth was demonstrated. Our filter was 40% thinner than the previous dielectric and metallic filters (thickness ≥ 150 nm).^[9–17] Unlike localized field enhancement of SPPs on metal–dielectric interfaces, the Wood’s anomaly in the ultrathin single-layer gold grating led to large field enhancements in the substrate, which efficiently reduced ohmic losses in the metals. The narrowest transmission bandwidth (transmittance > 60% ) at λ = 1200 nm was as small as Δλ_FWHM ≈ 1.6 nm, which was smaller than 4% of that (Δλ_FWHM ≥ 40 nm) in the previous reports.^[9–17] The corresponding quality factor was as high as λ/Δλ_FWHM = 750, which was 40 times greater than that in the previous reports.^[9–17] The performances (bandwidth, transmittance, and thickness) of the metallic filter were even better than commercial dielectric filters (e.g., FB1200-10 in Thorlabs). Based on the polarization-dependent property of the metallic grating, the transmission spectra could be adjusted by rotating the incident polarization or the the metallic grating. In the experiment, metallic gratings were fabricated on a single-layer gold film. A narrowband metallic filter with a bandwidth of Δλ_FWHM = 10 nm, which was smaller than 25% of that (Δλ_FWHM ≥ 40 nm) in the previous reports,^[9–17] was demonstrated. This extra-narrowband metallic filter with polarization-dependent properties would offer great potential for the practical applications in optical display technology, optical information processing, hyperspectral imaging, and high-density optical storage.