1. Introduction

Optical filters are functional elements which selectively transmit light depending on the condition of wavelength, polarization, and momentum. Among these, a spectral filter has been widely used in various fields of industry and research including color displaying [1], optical sensing [2], and bio-sensing devices [3]. In the past, traditional candidate materials such as dyes or micromachined glasses have been used to realize a spectral filter [4], with limited applications. To overcome the limitation of conventional filters, diverse studies have been proposed using stacked structures, including metal-dielectric alternating layers [5,6] and one-dimensional photonic crystals [7,8]. In addition, structural surfaces such as gratings [9] and nano hole arrays [10] developed, and emerging materials such as organics [11,12] and colloidal quantum dots (CQD) [13,14] serve as effective spectral filters. Unfortunately, there still remain many challenges to realize the spectral filters with the performance comparable to commercialized ones due to the limited choice of materials, fabrication technology and the spectral performance necessary to further scale down the optical device. Thus, it is essential to develop a next-generation spectral filter which is capable of controlling designer spectral transmission and compatible with CMOS fabrication for the applications of ultrathin and miniaturized pixel-based devices

Meanwhile, recent development of metasurface attracts significant attention due to its ability to control light in designer purposes [15–20]. Metasurface typically consists of a subwavelength array of meta-atoms which are composed of metal or dielectric nanostructures. Metasurfaces allow realization of ultrathin optical elements including metalens [21,22], waveplates [23–25], and other filters with effective control of wavefronts [26–29]. In particular, metasurface-based spectral filters have grown in popularity for their ability to control light transmission at the target wavelength by simply changing meta-atom geometrical design. The constituent metal or dielectric materials typically support plasmonics [30–33] or Mie resonance [34–36], respectively to tune the phase or amplitude of incident light. Such resonance occurring in the individual nanostructures can be classified as localized resonance and generally exhibits Lorentzian spectral line shape. [37–41] Unfortunately, because of such intrinsic features in the Lorentzian spectral curve, most of the recently demonstrated metasurface-based filters illustrate significant spectral crosstalk, which results in spectral crosstalk and decrease in efficiency in spectral detectivity.

To overcome this decrease in efficiency, we design a conceptually new type of metasurface spectral filter by relying on the effect of non-local resonances in the array of nanostructures. Harnessing the non-local effect in guided mode resonance (GMR) [42–45] or Fano resonance [46–49] leads to the realization of metasurfaces which are capable of controlling wavefront, transmission, and polarization with precise spectral selectivity, due to the nature of high-quality factors of such resonances. In this work, we leverage these benefits to demonstrate a non-local metasurface-based spectral filter which features a flat-top bandpass and relatively negligible spectral crosstalk. In particular, the proposed spectral filter is designed targeting to the spectral range of near-infrared, which can be used for various IoT sensors such as a time of flight sensing or face recognition devices. The filter’s performance can be comparable to commercialized bandpass filters with averaged transmission of more than 90% across the target spectral band.

2. Theory

Figure 1(a) shows the schematics of the metasurface-based spectral filter, which is designed as the double-layered optical filter (DLOF). It is composed of the double-layered array of poly-silicon (poly-Si) nanobeams, each of which spaced by the silicon dioxide (SiO₂). Light is normally incident on the surface of the DLOF, with the polarization perpendicular to the axis of the beams. Each layer operates as a partial reflector with abrupt increase and decrease of spectral transmission at the upper and lower metasurface, respectively. By judiciously combining each layer, which functions as high- and low-pass filter, the DLOF effectively transmits the target range of spectrum which closely follows the spectral feature of an ideal bandpass filter. Detailed design parameters of the DLOF are described in the explanations below.

 

Fig. 1. a) The overall structure of the DLOF. b) The transmittance of Lorentzian and bandpass filters. c) The transmittance of the DLOF and bandpass filter. d) E-field at 850 nm wavelength. Reflection occurs in the top layer. e) E-field at 950 nm wavelength. Light penetrates two layers. f) E-field at 1050 nm wavelength. Reflection occurs in the bottom layer. g) Performance of various filters based on the In-band transmission (I.T.), Out-of-band transmission (O.T.), and Quality of filter (Q.F.). The evaluations are based on the spectral range of the three times of FWHM of each filter. Quality of filter is defined as the O.T. divided by I.T.

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To qualitatively evaluate the performance of the DLOF, we compare its spectral shape with that of the Lorentzian and ideal bandpass filters as exhibited in Fig. 1(b) and 1(c). Figure 1(b) illustrates the spectra of Lorentzian filters observed in typical localized resonances with three different full-width half-maximum (FWHM) of 42 nm, 86 nm, and 165 nm. Center wavelength (${x_0}$) is fixed to 950 nm. The center wavelength of resonance is located at 960 nm. Compared to the ideal bandpass filter with spectral width of 120 nm, which is indicated as a black dotted line, the Lorentzian curve with FWHM of 165 nm shows the significant deviations by expanding transmission spectrum out of the target rectangular range and results in serious spectral crosstalk. On the contrary, the Lorentzian curve with minimum FWHM of 42 nm shows the sharp decrease in transmission from the center wavelength of resonance, which results in decrease of efficiency due to the lowered filling ratio of a rectangular bandpass region. Figure 1(c) shows the transmission spectrum of the designed DLOF, which results in a sharp spectrum rise near the 900 nm wavelength and sharp decrease near the 120 nm wavelength, by the combinational effect of cascaded metasurfaces. Compared to the Lorentzian examples, the spectrum closely follows the rectangular bandpass with high filling ratio and minimal spectral truncation.

To understand the operating principle and role of each layer, we visualize electric field profiles at the three representative wavelengths as illustrated in Fig. 1(d)–(f). At the 850 nm wavelength, the top metasurface starts to resonate and strongly reflects incident light. As a result, regardless of the condition of the bottom layer, filter transmittance approaches zero (Fig. 1(d)). At the 950 nm wavelength, both top and bottom metasurfaces operate as transmission filters and enable strong transmission as light passes both layers (Fig. 1(e)). Finally, at the 1050 nm wavelength, the bottom metasurface starts to resonate and strongly reflects light, resulting in low transmission. Note that in the electric field images of Fig. 1(e) and 1(f), light is reflected partially through the higher diffraction channel due to different period values between the top and bottom metasurfaces, by which overall periods of the DLOF system become supra-wavelength.

Figure 1(g) shows the summarized performance of the DLOF and aforementioned Lorentzian spectral filters. Each filter is evaluated based on the in-band and out-of-band transmission, which are defined respectively as the degree of spectral matching and mismatching with the ideal bandpass filter. These values are numerically calculated by following expressions.

As observed in the graph, close correlation exists between the Lorentzian filter in-band transmission and out-of-band transmission. For example, increased in-band transmission results in increased out-of-band transmission with respective maximum values of 87% and 61%, for the case of 165 nm FWHM. On the contrary, the DLOF filter exhibits opposite trends of operation with the large value of in-band transmission (93%) and the small value of out-of-band transmission (10%), which is desirable for optimal operation. An inset in the figure maps the evaluated values. While the Lorentzian filters show correlated increases in both rates, the DLOF is located at the fourth quarter area close to the ideal bandpass filter. Q.F. is defined as the O.T. divided by I.T, and the ideal filter typically has Q.F. close to 0%. The designed DLOF has a Q.F. value of 10%, which is closest to the ideal bandpass filter.

3. Result

To understand the underlying physics of the DLOF, three representative types of subwavelength nanobeam array are designed and analyzed. Since light is incident on the nanobeam along the transverse axis, different resonance phenomena occur depending on the gap size of the structure. When light is incident on a subwavelength nano grating structure with a gap size smaller than the wavelength, guided mode resonance (GMR) occurs across the structure. On the other hand, when the gap size becomes relatively large, localized Mie resonance is supported in the structure. Unlike GMR, Mie resonance does not sharply change transmittance and reflection spectra under resonance conditions.

The first type of array is constructed by carving small trenches on the poly-Si film with the period of 310 nm as seen in Fig. 2(a). Figure 2(b) shows the transmission spectra with continuous height change of the poly-Si film, which reveals four enhanced transmission bands due to Fabry-Perot resonances with increased resonance order as the film thickness increases. Sharp spectral line interfering with Fabry-Perot resonance band is observed, caused by GMR generated by the interaction of light with trenches. Narrow trenches with a 10 nm gap size = induce weak coupling with relatively high-quality factor, compared with than the other remaining types. Figure 2(c) and 2(d) capture the spectrum at 300 nm height and the corresponding magnetic field image at the 950 nm wavelength. A sharp spectral dip occurs from the broad transmission line by GMR featuring Fano type resonance, represented by an enhanced magnetic field in the resonant film. As the second type of nanobeam array, the gap size increases to 160 nm (Fig. 2(e)), and the localized Mie resonance dominates as exhibited in the image of transmission spectra (Fig. 2(f)). Such localized resonance generates a transmission spectrum with low quality factor as exhibited in Fig. 2(g) and 2(h) at the height of 300 nm. Finally, the design of a nanobeam array with optimized width of 280 nm and 30 nm gap size = is presented in Fig. 2(i). Localized Mie resonance is supported and interferes with non-local GMR to function optimally for a spectral filter (Fig. 2(j)). At the height of 300 nm, the transmission spectrum is divided into bands of strong transmission and suppressed transmission at the spectral boundary of Fano resonance, which can operate as a high-pass filter (Fig. 2(k)). Figure 2(l) shows the magnetic field of Fano resonance by the interaction of localized Mie and non-local GMR at 880 nm wavelength. The interaction with the Mie resonance due to a gap size increase results in a magnetic field pattern similar to the GMR resonance, yet with weaker intensity. The general trend of operation for a different structure is numerically characterized by the Fano resonance with the following numerical expression of total scattering cross-section:

 

Fig. 2. a) Schematic diagrams of poly-Si array with small trenches and 310 nm period. b) Transmission spectra with continuous height change. Sharp spectral line is observed due to guided mode resonance. c) Spectrum at the height of 300 nm. d) Magnetic field at the 950 nm wavelength. e) Schematic diagrams of poly-Si array with 150 nm width and 160 nm gap size. f) Transmission spectra with localized Mie resonance. g) Spectrum of low quality factor at the structural height of 300 nm. h) Magnetic field at the 900 nm wavelength. i) Schematic diagrams of optimized structure with 280 nm width and 30 nm gap size. j) Transmission spectra of optimized grating geometry with continuous height change. k) Spectrum of optimized structure at the height of 300 nm. l) Magnetic field with interaction of guided mode resonance and Mie resonance at the 880 nm wavelength.

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We performed FDTD simulation to optimize the structural parameters and found a trend between them and the Fano formula. The period of the structure dominantly affects the resonant frequency$\; {w_0}$, causing a blue shift when it increases and a red shift when it decreases. As the gap decreases, the effect of GMR becomes dominant within the nanostructure, and thus $\mathrm{\Gamma}$ decreases and a sharp transmission dip occurs. On the other hand, when the gap increases, the effect of the Mie resonance dominates causing an increase in $\mathrm{\Gamma}$ and broad spectral line. The height of the structure affects the Fano parameter q, and the shape of the Fano spectrum is related to the height of the structure. Based on the analysis of Fano resonance in a single layered metasurface, a flat-top spectral filter is designed by cascading the optimized metasurfaces which operate as either low-pass or high-pass filters. As shown in Fig. 3(a), each layer of the filter is composed of Poly-Si nanorods, with a refractive index of 3.66 (${N_{Si}} = 3.66$) at the center wavelength of 950 nm, arranged on the quartz wafer. The corresponding imaginary part of poly-Si refractive index is 0.001. And the optical spacer between the layers is a planarized, lossless SiO₂ (${N_{Si{O_2}}}$=1.45). The refractive index of poly-Si is obtained by experimentally measured values using ellipsometry, which is subsequently fitted to FDTD simulation based on the Kramers-Kronig relations. The double layered array of poly-Si nanobeams suggested by this work for a new type of spectral filter can be fabricated by the following steps. First, poly-Si film is deposited on SiO₂ substrate by low pressure CVD (LPCVD). Second, the grating pattern is realized by photolithography with a negative photoresist. Third, etching poly-Si by reactive ion etching (RIE) method with the removal of a residual PR. Next, thin SiO₂ layer is deposited on the Si grating followed by a planarization process. Finally, additional poly-Si is deposited and similar photolithography with RIE step is applied to pattern the second layer. Based on the suggested fabrication, only the bottom nanobeam array is embedded in SiO₂. The geometric parameters of the designed DLOF are ${\mathrm{\Lambda}_1}$=310 nm, ${h_1}$=300 nm, ${\; }{w_1}$=280 nm, ${g_1}$=30 nm of top layer, ${\mathrm{\Lambda}_2}$=375 nm, ${h_2}$=250 nm, ${w_2}$=325 nm, ${g_2}$=50 nm of bottom layer, and d = 140 nm as indicated in the schematic. Due to the effect of the periodic structure and the low absorption of poly-Si in the near-IR region, the transmittance of the DLOF is approximately expressed as ${T_{top}} \times {T_{bot}}$. Figure 3(b) shows the transmittance of the DLOF with the indication of 890 nm (${\lambda _1}$) and 1020 nm (${\lambda _2}$) as cut-off frequencies. To achieve high transmittance, each layer needs to have a transmittance close to unity. For the case of $\lambda < {\lambda _1}$, since the transmittance of the top layer is close to zero, the total transmittance is suppressed regardless of the bottom layer. For the case of ${\lambda _1} < \lambda < {\lambda _2}$, the transmittance of both the top layer and bottom layer approaches unity, and this leads to overall flat-top transmittance close to unity. Finally, when ${\lambda _2} < \lambda $, bottom layer transmittance is near zero, which dominantly affects the total transmittance. Figures 3(c) and 3(e) are the images of transmission spectra for each metasurface layer with a continuous change of height. As the height increases, the amplitude of resonant scattering changes, and eventually an inverted Fano spectral line can be obtained at the specific height condition as illustrated in Figs. 3(d) and 3(f). For the top metasurface, the transmittance increases rapidly at 890 nm and for the bottom metasurface, the transmittance decreases rapidly at 1020 nm, which leads to the operation as a band-pass filter with the flat-top transmittance of 130 nm bandwidth.

 

Fig. 3. a) Cross-sectional view of the DLOF. b) Flat top spectral transmission at the spectral band from 890 nm (${\lambda _1}$) to 1020 nm (${\lambda _2}$) in the DLOF. c) Transmittance for the continuous change of top layer height. d) Top layer transmittance at 300 nm height which operates as a high-pass filter. e) Transmittance for the continuous change of bottom layer height. f) Bottom layer transmittance at 250 nm height which operates as a low-pass filter.

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To analyze the effect of spacing between two layers, transmission spectra for various thicknesses of spacer are calculated as shown in Fig. 4(a). The thickness of the spacer is adjusted to be thick enough to avoid near-field coupling between two metasurfaces. Since the optical spacer enables Fabry-Perot resonance, the constructive and destructive interferences are repeated at a cycle of ${\; }\frac{\Lambda}{{2{N_{Si{O_2}}}}}$. As shown in Fig. 4(b), we analyzed transmittance at the spacer thickness when constructive interference and destructive interference occurred. Figure 4(c) is the electric field when the thickness of 140 nm leads to destructive interference and suppresses transmission out of the target spectral band. On the contrary, the thickness of 300 nm leads to transmission-side constructive interference at the wavelengths of 800 nm and 1100 nm, which results in two-sided transmission peaks near the target spectral band in Fig. 4(d). It is noteworthy that there is a relatively broad range of choice in spacing thickness for the suppressed transmission than the transmission peaks for the reliability of potential fabrication and operation.

 

Fig. 4. a) Total transmittance for the continuous change of spacer thickness. b) Transmittance of the spacer thickness at 140 nm and 300 nm which induces destructive (red line) and constructive (dotted line) interference, respectively. c) E-field profile of the DLOF at the spacer thickness of 140 nm. Incident light with 800 nm and 1100 nm wavelength. d) E-field profile of DLOF at the spacer thickness of 300 nm which causes a transmission-side constructive interference at the wavelengths of 800 nm and 1100 nm.

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Since the proposed DLOF is analyzed at element level including meta-atoms, single layer, and double layers, adjusting the transmission bandwidth is simple, by changing the condition of Fano resonance in each constituent metasurface. Figure 5 shows that four representative designer spectra which can be adjusted by varying the periods of metasurfaces, which control the spectral position of Fano resonance. As seen in Fig. 5(a), the top metasurface, which functions as a high-pass filter, controls the left-side cut off frequency, i.e. high frequency of the transmission band. When the top layer’s period increases from 300 nm to 330 nm with 10 nm intervals, the wavelength of cut-off frequency gradually increases from 850 nm to 930 nm, and FWHM decreases from 144 nm to 79 nm. To control the right side or equivalently low frequency of the transmission band, the bottom layer’s period needs to vary from 350 nm to 380 nm as illustrated in Fig. 5(b). In Fig. 5(c), by independently controlling the top and bottom periods, the spectral width of FWHM decreases by 25%. In this way, both the high and low cutoff frequencies can be designed dynamically. Figure 5(d) illustrates the electric field images at the two or three representative wavelengths, indicated as black dotted lines in the transmission graphs. Depending on metasurface design conditions, the DLOF effectively transmits incident light at the target spectral range, or reflects incident light as indicated by the formation of standing waves at the reflection side.

 

Fig. 5. Adjustment of filter bandwidth through the DLOF. a) Transmission bandwidth related to top layer period. b) Transmission bandwidth related to bottom layer period. c) Transmission bandwidth related to both layer periods. d) Electric field image of the DLOF at representative wavelengths.

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Next, we demonstrate DLOF efficiency and exclusive filtering over near-infrared spectrum ranging from 880 nm to 1150 nm. We optimized the nanostructure geometry to closely model three ideal pass band with center wavelength separated by 90 nm and 90 nm bandwidth, denoted as black dotted lines in Fig. 6. Tuning the parameters similarly to the examples in Fig. 5 engineers center wavelengths with cut-off frequencies, and the corresponding spectrum closely matches ideal rectangular bands. Summarized parameters of the design are contained in Table 1. Compared to the examples of three representative Lorentzian filters in Fig. 6(d), DLOFs show near flat-top transmission and minimized spectral crosstalk with neighboring spectra as shown in Fig. 6(e). In Fig. 6(f), we numerically compare the performance of the average Lorentzian filter in three wavelength bands with the performance of normalized DLOFs named S1, S2, and S3. I.T. exceeds 80% for both DLOFs and Lorentzian filters as reference. Each DLOF has an average O.T. of 30%, of which 15% is spectral cross-talk with the other two adjacent filters. The DLOF exhibits superior performance compared to the Lorentzian filters with O.T. of 53% and cross-talk of 38%.

 

Fig. 6. Simulated transmittance spectra of three DLOFs. FDTD simulations of transmittance spectra for 1) 880 nm - 970 nm, 2) 970 nm - 1060 nm, and 3) 1060 - 1150 nm. d) Numerically modelled Lorentzian filters in the spectral range of 880 - 1150 nm e) Overlapped transmittance spectra for three spectral bands. f) Performance of three representative spectral filters. The evaluation is based on wavelengths from 850 nm to 1200 nm. The factor, cross-talk, is the area of overlap between adjacent filters.

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Table 1. Geometric parameters of a double-layer optical filter

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Finally, to evaluate the availability of DLOFs under both polarizations of TE and TM, a pad-type DLOF is designed and optimized as seen in Fig. 7(a). Since the underlying physics and the role of each design parameter does not change significantly, a polarization-independent DLOF can be designed with similar steps of analysis. The designed pad-type DLOF features ${\mathrm{\Lambda}_1}$=320 nm, ${h_1}$=330 nm, ${\; }{w_1}$=280 nm, and ${g_1}$=50 nm for the top layer, and ${\mathrm{\Lambda}_2}$=400 nm, ${h_2}$=270 nm, ${w_2}$=330 nm, and ${g_2}$=70 nm for the bottom layer. Figure 7(b) shows the transmission spectrum of a 200 nm spacer thickness with a flat-top feature in the spectral range of 875 nm to 1025 nm. Figure 7(c) shows total transmittance for the continuous change of spacer thickness. Interestingly, the designed DLOF shows relatively relaxed side peaks for various spacer thickness compared to the one-dimensional structures. Figure 7(d) shows various spectra by controlling the spectral positions of the Fano resonance. By changing the period of the bottom layer from 380 nm to 410 nm with 10 nm intervals, the wavelength of cut-off frequency gradually increases from 980 nm to 1030 nm, and FWHM increases from 107 nm to 153 nm. As shown in Fig. 7(e), with similar design steps, DLOFs show near flat-top transmission and reduced cross-talk with adjacent spectra. Figure 7(g) and (h) show the transmission spectrum of DLOF for various incident angles of light. Since the DLOF physically operates based on a GMR, additional transmission dips and peaks emerge as an incident angle increases more than 5 degree. Despite the limited response to an incidence angle, DLOF can be utilized in various near infrared IoT devices operating under normally incident light such as Finger On Display sensing.

 

Fig. 7. Angle-dependent analysis of a DLOF and polarization-independent structure. a) Overall structure of polarization-independent DLOF. Blue pads indicate a bottom metasurface and dotted pads indicates a top metasurface. b) Transmission spectrum of a DLOF related to incident angle of light. c) Total transmittance for the continuous change of spacer thickness. d) Transmission bandwidth related to bottom layer period. e) Overlapped transmittance spectra for two spectral bands f) Transmission spectra versus incident angles for a one dimensional DLOF. g) Transmission spectra versus incident angles for a two dimensional DLOF.

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4. Conclusion

To summarize, we demonstrate a metasurface-based optical filter which effectively mimics the spectral features of an ideal band-pass filter. By leveraging the sharp spectral features of non-local resonances, spectral crosstalk is minimized. After analyzing each constituent metasurface, which functions as a high-pass or low-pass filter, efficient bandpass filtering is demonstrated by cascading the two optimized metasurfaces to form a DLOF. High transmission near 90% is shown in the overall near-infrared spectrum with exclusive suppression of light less than 10% to prevent spectral crosstalk. In addition, we demonstrate effective manipulation of transmission bandwidth by geometric changes of the metasurface design. Broadband and flat-top transmission in the DLOF is a unique feature which differs from the typical nanophotonic filters with Lorentzian shape. Color filtering may be realized by using a lossless material in the visible spectrum such as TiO₂. We believe our design paves practical pathways toward realizing nanophotonic optical filters, compatible with monolithic CMOS integration and suitable for the various applications of optical sensors.