1. Introduction

The development of high-resolution colour imaging and spectral imaging devices (or micro-optical system modules) has created a growing demand for compact and integrable high-performance thin-film optical filters/filter arrays. However, conventional dye-molecule-based colour filters widely used in CMOS colour image sensors and liquid crystal displays (LCDs) [1,2] are unable to meet this need due to their limitations in performance, scalability, and durability. In recent years, extensive research has been conducted on optical filters composed of micro/nano-structures [3–7]. These filters are typically based on the optical resonances within the structures, resulting in selective transmission or reflection of light in specific frequency ranges. Among them, dielectric nanostructure-based filters have garnered significant attention due to their compactness arising from a small mode volume of the resonator [8], as well as their compatibility with materials and fabrication processes used in planar technologies. In the early years following the emergence (or rapid development) of optical resonators, metagrating/nanostrip arrays in optically thick dielectric films have been explored for applications in colour filtering and sensing [6,9]. However, their performance has been found to exhibit wide bandwidths (>40 nm in wavelength) and significant sidebands [10]. Additionally, the fabrication of such intricate nanostructures in thick dielectric films is not compatible with prevailing CMOS processes and requires state-of-the-art nanofabrication techniques (e.g., electron-beam lithography or focused-ion-beam milling), which are not conducive to mass production. Fundamentally, the bandwidth of these optical filters has been limited by absorption loss in hybridized dielectric-metal (DM) nanostructures that result in low quality factors of plasmon resonances during the generation of filtering stopbands [11].

Therefore, the further development of optical filters has been focused on designing filtering structures with narrow-band transmission, low sidebands, and ease of fabrication. In this regard, some progress has been made in reducing the transmission bandwidth (e.g., down to <20 nm in the VIS-NIR regime) by incorporating additional dielectric metagratings/layers adjacent to the dielectric nanostructure layer to support resonances of low-loss Fano resonance modes [12–14] or GMR modes [3,15–18]. Moreover, absorption loss of waveguiding surface plasmon (SP) modes for resonances is minimized through the use of all-dielectric materials in the nanostructures; this also facilitates their compatibility with CMOS processes. However, challenges still remain regarding near-zero transmission in sidebands and/or background for such filters (particularly at short- and long-wavelength sides of the main stopband dip).

Meanwhile, the majority of the aforementioned all-dielectric metagrating structures exhibit a single operating band, which may not be optimal for various multispectral applications [18]. For instance, in near-infrared region spectroscopy applications where simultaneous monitoring of multiple spectral devices is required [19–21], filters or refractive index sensors with dual operating bands are highly sought after.

We proposed an all-dielectric metagrating composed of asymmetric binary nanostrip arrays, which enables narrow-dual stopband resonance line widths. The underlying physical mechanism can be attributed to two aspects: (i) The utilization of silicon (Si) in the formation of asymmetric binary nanostrip arrays induces Fano resonance modes, resulting in the trapping of incident light within the cavity while reflecting the remaining light due to interference. (ii) When transverse-magnetic (TM) incidence is coupled with the effective dielectric cavity, it gives rise to GMR modes where a portion of incident light is canceled within the cavity while the rest is reflected. For the Fano resonance modes, by manipulating the parameters of the vertically asymmetric nanostrip array parameters $\Delta h = |{{h_1} - {h_2}} |$, it is possible to tune the dipole-like resonator to resonate in an anti-symmetric manner, thereby canceling and reflecting antiphase wavelets radiated around the nanostrips $({R \ge {I_{in}}/2} )$ through destructive interference. For the GMR modes, by controlling the horizontal direction asymmetric spatial parameters $\Delta sg = |{s - g} |$, it is feasible to adjust the transmittance to approach zero. By introducing asymmetry in the vertical direction while maintaining symmetry in other aspects, we observe a gradual emergence of Fano resonance mode while keeping GMR mode unchanged. This intriguing observation suggests that both resonance modes can coexist simultaneously in an asymmetric structure, which represents a novel finding. With this innovative structure design, we achieve remarkable transmittance values of 0.1 and 0.07, with full-width half-maximum (FWHM) of 2 and 4 nm, respectively. Moreover, our proposed structure exhibits consistent transmission performance across a wide range of polarization angles. We thoroughly investigate how different structural parameters influence optical properties and evaluate its potential as a sensor device. The proposed design we present offers several significant advantages. It simplifies the structure, achieves a smoother surface, expands the bandwidth, and enhances sensing performance. These advancements will greatly facilitate the widespread adoption of metamaterials in practical applications [22,23]. Moreover, the proposed structure holds great promise for applications in dual-band optoelectronic devices and bio-chemical sensing devices. This is due to its ability to facilitate strong light-matter interactions.

2. Structure and characteristics

As shown in Fig. 1 (a), the nanostructure presented here consists of asymmetric dielectric (Si) nanostrip arrays in the substrate (n = 1.46). It displays a typical transmittance spectrum of asymmetric binary nanostructures when transverse-magnetically (TM) polarized light, which is polarized perpendicular to the grating lines, is incident normally. This has been calculated using the finite-difference time-domain (FDTD) simulation method. The simulation environment is bounded along the y-axis by perfectly matched layer (PML) boundary conditions, while periodic boundary conditions are considered in the x-direction. The light source consists of a plane wave with TM-polarized incident light propagating in the x-direction. Figure 1 (b) illustrates a single unit cell of the asymmetric binary nanostrip arrays. As depicted in Fig. 1(c), under normal incidence, the nanostructures exhibit various transmittance, reflectance, and absorptance behaviours, which are determined by their structural characteristics. The material properties of the Si are obtained from the Palik’s handbook [24]. Asymmetric parameters, i.e., ${h_1} \ne {h_2}$, g≠s for Fano resonance and GMR, respectively. The initial step in the structural design and preparation process involves designing an appropriate asymmetric metamaterial unit structure, which may entail selecting suitable basic components and adjusting their size and arrangement. Although the preparation of periodic metagrating structures has posed challenges in the past, advancements in technology have resulted in a diverse range of preparation methods including electron-beam lithography, nano-printing techniques, shadow masks and thin film deposition techniques, which offer new avenues and innovative approaches for mass production. [25,26]. Among these methods, nano-printing technology stands out as particularly noteworthy [27]. It utilizes electron beam lithography to etch the required pattern onto a silicon wafer, creating a raised structure on a nano-printed template. The material is then coated onto this template with precise control over its transfer onto the silica substrate to ensure accurate replication of the pattern. Following transfer, heat treatment or chemical treatment is employed to enhance adhesion and preserve pattern integrity while excess material is removed for achieving a smooth surface.

 

Fig. 1. (a) Schematic view of the proposed dual-and narrow asymmetric dielectric metamaterials. (b) cross-sectional view of the unit cell. (c) Schematic illustration of a metagrating is presented to model it as an effective medium exhibiting multiple reflections and transmissions.

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3. Characteristics and mechanisms

Figure 2 (a) shows the spectral transmittance and reflectance for the system's normal incidence. The asymmetric binary nanostrips are in a subwavelength array (p = 500 nm) with an equal strip thickness (t) of 50 nm, gap (g, edge-to-edge) of 80 nm, and separation (s, unit-to-unit) of 320 nm. At the height (h₁ and h₂) of 200 nm and 320 nm, two sharp transmittance dips (T_Fano, T_GMR) appear at the wavelength of 755 nm ($\lambda _1^{\textrm{Fano}}$) and 837 nm ($\lambda _2^{\textrm{GMR}}$) with FWHM of 2 nm and 4 nm, respectively. The transmittance dip at $\lambda _1^{Fano}$ is attributed to the Fano resonance modes caused by symmetry-breaking (i.e., ${h_1} \ne {h_2}$) in an individual binary nanostrip array at the vertical direction. The transmittance dip at $\lambda _2^{\textrm{GMR}}$ is caused by symmetry-breaking (i.e., g≠s) in the interspacing at the horizontal direction, resulting in GMR modes. The corresponding reflectance (R) of asymmetric binary nanostrip array structures can be calculated, and spectral absorptance (A) can be obtained by A = 1-R-T, as shown in Fig. 2 (b). The transmission at $\lambda _1^{\textrm{Fano}}$=755 nm and $\lambda _2^{\textrm{GMR}}$=837 nm is only 0.1 and 0.07 respectively. Since the material does not contain any metal, there is no radiation loss from metal, which results in a much lower absorption rate compared to ordinary ones with metal structures, as shown in Fig. 2 (b). Later on, it will be demonstrated that the T_Fano and T_GMR are due to the intercoupling of Fano resonance and GMR, respectively.

 

Fig. 2. (a) Transmittance, (b) Reflectance and absorptance spectrum of the proposed asymmetric binary array (${h_{1,\,2}}$=200, 320 nm) structure showing dual-and narrow band transmittance at ($\lambda _1^{\textrm{Fano}}$, $\lambda _2^{\textrm{GMR}}$) = (755, 837) nm. The spectra of transmittance and reflectance for (c) symmetric binary nanostrips (${h_{1,2}}$=200 nm or 320 nm) structures and (d) symmetric single nanostrip (h = 200 or 320 nm) structures are also plotted for reference. p = 500 nm, g = 80 nm, and s = 320 nm for all structures.

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The effective index plays a crucial role in both Fano resonance and GMR as shown in Fig. 1(c). In the case of Fano resonance, it influences the coupling strength and frequency characteristics between discrete and continuous states. Regarding GMR, it governs the formation, propagation, frequency, and coupling strength of the lead mode. These effects necessitate further investigation through experimental and theoretical studies in specific systems and structures. The effective medium layer functions as a waveguide, as depicted in Fig. 1(c). Thus, the effective index ${n_{eff}}$ in TM mode is [28]

The transmission coefficient of ${T_{\textrm{Fano}}}$ is defined by the classical Fano formula [29,30].

Here, Ω is the dimensionless frequency and ${T_0}$ and ${T_{bg}}$ represent the smooth background contributions to the amplitude and offset of the resonant peak from the off-resonant modes, respectively. The asymmetric parameter q in formula Eq. (3) is crucial for inducing Fano resonance, which leads to the generation of a new sharp peak in spectra. It is noteworthy that adjusting the asymmetric parameter of h_{1, 2}= 200, 320 nm will result in the appearance of this Fano resonance-induced peak.

Comparing the transmittance/reflectance spectra in Fig. 2 (c), it is inferred that the T_GMR of the horizontal asymmetric binary nanostrip arrays (i.e., ${h_1} = {h_2},\; g\textrm{s}$) at around 782 nm (${h_1} = {h_2} = 200\; nm$) or 886 nm (${h_1} = {h_2} = 320\; nm$) originates from the guided mode resonance in the same period; At resonance, part from the applied wave is coupled into the guided mode. The guided mode slowly leaks out from the waveguide effective medium and concealed in the far field by destructive interference. As the nanostrip arrays changes from symmetric to asymmetric (${h_1} = 200\; nm,\; \; {h_2} = 320\; nm$) in the vertical direction, while the original GMR mode is not affected, a transmission dip appears. Both transmittance dips demonstrate narrow spectral widths and near-zero transmittance. In addition, for reference, numerical calculations were performed for a single nanostrip (i.e., g=s) as shown in Fig. 2 (d). It is found that, if we have a single nanostrip in the same period, there are no existing transmittance/reflectance dips/peaks, implying weakened or no interference of the incidence. But if the parameters (i.e., p, h, and s) are set properly, there will still be a single narrow transmission trough within the short wavelength range. It should be noted that the near-zero binary narrow-band transmittance with low radiative losses is achieved by all dielectric binary asymmetric nanostructures in all directions. The loss of the substrate should be taken into account in actual simulations to achieve a more accurate representation of material behavior. Electromagnetic field simulation tools, such as the FDTD simulation method or other numerical methods, can be employed to analyze and simulate these effects in detail, facilitating a better understanding of the structure's performance in practical applications.

In the following, we focus on elucidating the resonance modes and their roles in the filtering and sensing properties, with the assistance of distributions of the fields (|E|, Hy) and illustration of the basic principle for light trapping in the resonance states, as shown in Fig. 3. The field values are expressed in ratios with respect to corresponding field magnitudes of the incidence light in air (|E₀| and |H₀|). To visualize the resonance and their inter-coupling, we show distributions of the transverse electric field |E| and magnetic field Hy in binary asymmetric nanostrip arrays, and symmetric single nanostrip (h = 200 or 320 nm) structures are also analyzed for reference. Here we will have a detailed analysis of resonance modes in the periodic structure at $\lambda _1^{\textrm{Fano}}$=755 nm, $\lambda _{12}^{\textrm{GMR}}$=837 nm, $\lambda _1^{\textrm{GMR}}$=782 nm, and $\lambda _2^{\textrm{GMR}}$=886 nm, shown in Fig. 3(a1)-(a2), (b1)-(b2), (c1)-(c2) and (d1)-(d2) respectively. It can be seen that, at $\lambda _1^{\textrm{Fano}}$=755 nm, the electric fields (|E|) are mainly bound to the top and bottom in the small nanostrip and some part concentrated between the unit cell (i.e., s), resonance fields are asymmetrically distributed, demonstrating antiphase resonance in the asymmetric binary structures, as shown in Fig. 3(a1)-(a2). This effect can also be called Fano resonance [10,11,31]. It will be shown that the dipole-like resonance modes oscillate anti-symmetrically when the asymmetry parameter of the structure satisfies a critical condition for the intercoupling. This results in anti-phase leaky radiation emanating from the asymmetric segment; and their destructive interference in the near field leads to part of the incident light being canceled by the optical trapping effect, while the remaining part is reflected back by the interference, it eventually behaves as near zero in the transmitted far field.

 

Fig. 3. Distributions of the transverse electric field magnitude (|E|) (a1 − d1), magnetic field (Hy)(a2 − d2) at the resonance positions of $\lambda _1^{\textrm{Fano}}$=755 nm (a1 − a2), $\lambda _{12}^{\textrm{GMR}}$=837 nm (b1 − b2), $\lambda _1^{\textrm{GMR}}$=782 nm (c1 − c2) and $\lambda _2^{\textrm{GMR}}$=886 nm (d1 − d2), as labeled in Fig. 2 (a)-(c). (e) Illustration of the basic principle for trapping of light. Light is incident from the top side (air) in the subplots.

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The principle is schematically illustrated in Fig. 3(e). We have explained the effect of such coupled asymmetric resonators with a theoretical model in a previous report and also suitable for application to this structure [32]. When the physical parameters of the resonator satisfy a critical condition for at $\lambda _1^{\textrm{Fano}}$, the resonator oscillates antisymmetrically and give rise to antiphase wavelets of leaky radiation such that they cancel in the transmittance far field. This results in radiative losses from the interaction process. The critical matching condition is described by [32].

4. Effects of structural dimensions and configurations on the transmittance for filtering

In this section, we first investigate the effect of structural dimension on the transmittance to further validate the proposed mechanism and provide critical information for designing the filter structures. In the survey, the structural dimensions were varied with respect to those of the structures studied above, i.e., h₂= 320 nm, t = 50 nm, g = 80 nm, s = 320 nm, p = 500 nm. Figure 4(a) indicates that the effects of the structural asymmetry in the binary nanostrip array at vertical dimension are investigated by varying the height of the one nanostrip array (h₁) concerning a fixed size of the additional nanostrip array (h₂). It is shown that the matching condition, corresponding to the transmittance of the coupled Fano resonance mode, is close to zero twice at the variant height of both h₁= 200 and 440 nm, in nearly-equal difference ($|{{h_1} - {h_2}} |$) to the fixed height of h₂= 320 nm. When the difference decreases, the transmittance resonance dip reduces to that of symmetry structure (h₁= h₂= 200 nm). When the height difference increases to above $|{{h_1} - {h_2}} |> $120 nm, the coupled Fano resonance dips a slight red shift. For $\lambda _{12}^{\textrm{GMR}}$, as $|{{h_1} - {h_2}} |$ increases, the resonance strength is approximately constant, the resonance position is slightly redshifted, and the FWHM is considerably wider.

 

Fig. 4. (a) Dependences of the resonance wavelengths ($\lambda _1^{\textrm{Fano}}$, $\lambda _{12}^{\textrm{GMR}}$) and corresponding transmittance values of the asymmetric structures on high of one dielectric segment (${h_1}$), as the other one is fixed (${h_2}$=320 nm). (b) Transmittance spectral map for various thicknesses (t) of the dielectric nanostrip arrays. (c) As the designated parameter varies (g), the others are kept invariant [${h_{1,\,2}}$= (200, 320) nm, s = 320 nm, t = 50 nm].

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In the following, we discuss the effects of structural dimensions other than the asymmetry, which are essential in determining the resonance modes. For instance, the resonant modes are fundamentally based on the waveguiding modes in the all-dielectric nanostructures. Since thicknesses (t) of both nanostrip are critical parameters for the waveguiding mode [37,38], they consequently influence frequencies (${\omega _1},\,{\omega _2}$) of the resonance modes. As for interspacing between the dielectric nanostrip segments (g, s) obviously influences the inter-coupling (${k_{12}}$) of the resonance modes at the neighboring asymmetric dielectric components. Figure 4(b) demonstrates the effects of the thickness of asymmetric binary nanostrip arrays on resonance characteristics in the transmittance spectra. It is striking to find that, for the pair of as given thickness of matched asymmetric dielectric segments (${h_1}$=200 nm, ${h_2}$ = 320 nm), the transmittance dip ($\lambda _1^{\textrm{Fano}}$ and $\lambda _{12}^{\textrm{GMR}}$) always exists, and the resonance position redshifts with the variation of asymmetric dielectric nanostrip thicknesses (t), but the FWHM becomes wider. This is easily understood; as the thickness of the asymmetric dielectric nanostrip is larger, the effective index (${\lambda _{res}} \approx {N_{eff}}\cdot p$) also increases. When the asymmetric dielectric nanostrip thickness is smaller than the optical skin depth (e.g., t < 30 nm), the matching condition is broken, resulting in a reduction in the resonance strength. Figure 4(c) shows that the interspacing (g) has a strong impact on the resonance characteristics. For a given structure with matched highest of the dielectric segments (e.g., ${h_1}$=320 nm and ${h_2}$=200 nm for s = 320 nm), change of the interspacing (e.g., to be g > 80 or g < 80 nm) breaks the matching condition, causes a reduction in the strength of the resonance mode, which eventually leads to the disappearance of the resonance dips or the widening of the FWHM. But even as the interspacing is changed to be off balance (e.g., g > 80 or g < 80 nm) [32]. In addition, their resonance positions are redshifted due to p = 2t + g + s.

In the following, we investigate the influence of the polarization and incidence angle on the properties of the resonant modes, which will be of interest for potential applications. Essentially, one motivation in designing array of asymmetric structure is our desire for polarization insensitive properties of the structures. Figure 5(a) shows that the transmittance spectra, the transmittance resonance dip positions, are hardly changed when the polarization angle of the normal incidence light is varied. In most practical applications, the polarization angle requirement will not exceed 20°. Therefore, our one-dimensional filter performs adequately over a wide range (0∼60°) of polarization angles. The emergence of additional resonant dips is observed as the polarization angle increases. The majority of two-dimensional structures incorporate the polarization insensitive characteristic [39]. However, achieving this feature in one-dimensional structures poses a significant challenge. It is also shown in Fig. 5(b) that, when the incidence angle of light is varied to 2°, both resonance dips always exist and rarely shift in position. However, since the Fano resonance ($\lambda _1^{\textrm{Fano}}$) is extremely sensitive to the angle of the incidence light, the resonance intensity decreases rapidly with the increase of the incidence angle (i.e., 3°, 5°…) [40]. For GMR ($\lambda _{12}^{\textrm{GMR}}$), the resonance strength and resonance position are unchanged and these properties are expected. The sensitivity of Fano resonance to incidence angles is attributed to the interference effects involving discrete and continuum states, while GMR, relying on well-confined guided modes, is less affected by changes in incidence angles, making it comparatively insensitive in this regard [41].

 

Fig. 5. Effects of the polarization and incidence angles on the transmittance spectrum. The transmittance spectral maps are calculated with the structure parameters of ${h_{1,\,2}}$=(200, 320) nm, (g, s) = (80, 320) nm, t = 50 nm. The polarization angle is with respect to x-axis in (a), and the incidence plane is the xz-plane in (b). Light is incident from the top side (air) in the subplots.

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V. Application in dual-band refractive index sensing

In the above discussion, the proposed structure can achieve bi-narrow and efficient resonant dip in the near-infrared region, which can be applied to dual-band refractive sensors. To assess the capability of the dual-band refractive index sensor, the surface of the nanostructure was filled with gas which has a different refractive index (n). Both resonance wavelengths of the asymmetric dielectric nanostrip arrays are dependent on the surrounding background medium, which is promising for gas-sensing applications [42]. Based on this [43,44], we designed an asymmetric dielectric nanostrip array gas sensor composed of asymmetric dielectric nanostrip segments, a low refractive index dielectric substrate (${n_s}$=1.46), and an integrated microfluidic channel, as shown in Fig. 6(a). Figure 6(b) shows the calculated transmittance spectral; we can see that the resonance wavelength exhibits an apparent redshift with the variation of the ambient refractive index. A resolvable spectral tuning of the transmittance can be found as a consequence of a rather small change in the reflective index of the gases. Relying on this capability, the asymmetric dielectric nanostrip arrays can be used as a biological sensor to detect changes in the refractive index of the environment. The resonance properties can be tuned by adjusting the periodicity of the array. As shown in Fig. 6(b), increasing the refractive index of gas from 1.1 to 1.4, can cause a redshift of the resonant wavelength, ${\lambda ^{\textrm{Fano}}}$, 760.79 to 783.46 nm, with the FWHM being smaller than 2 nm and the step interval, Δλ, being about 5.8 nm. The resonance wavelength, ${\lambda ^{\textrm{GMR}}}$, redshifts from 842.9 to 867.05 nm, with the FWHM being smaller than 4 nm and the step interval, Δλ, being about 7.1 nm. Table 1 list published information on refractive index sensing performance and the present results [41–45,39]. Although our structure may not possess significant qualities factors of 378 and 209 nm per se, it exhibits unparalleled advantages and potential originality within specific application domains. We anticipate utilizing this design across a broader range of optical applications in order to showcase its extensive application potential. In the sensing applications, the major challenge of achieving high sensing performance is still relevant today due to the lack of stability of the designed structures and complex fabrication process [22,44]. In addition, most of the operating wavelength of the refractive index sensor is distributed in the long-wave infrared spectral region, and the FWHM is a little wide, which considerably limits the practical application [43,44]. Despite not excelling in certain performance indicators, our structure demonstrates unique value through its ease of preparation and superior surface quality capabilities suitable for specific scenarios. These features partially compensate for the lack of sensitivity while providing a valuable solution within targeted application areas. Additionally, operating in the near-infrared spectral range, where numerous low-cost optical components and sources are widely available, the proposed stable dual-narrow-band optical filter or refractive index sensor benefits from its simple geometry.

 

Fig. 6. (a) Schematic of the metamaterial gas sensor. (b) Transmission spectra versus the refractive index of gas 1–1.4. Light is incident from the top side (air) in the subplots.

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Table 1. RI sensing performances for Asymmetric dielectric metamaterials

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VI. Conclusion

In summary, we propose and numerically investigate a narrow-dual band optical filter structure consisting of binary asymmetric dielectric nanostrip arrays. The structure exhibits distinctive characteristics of narrow-dual stopband filtering within the visible-to-near-infrared spectrum range. These near-zero transmission dips in the narrow-dual stopbands correspond to Fano resonance and GMR, accompanied by discernible near-field distributions. The metagratings have demonstrated relatively high Q-factors and field enhancements through numerical simulations. The influence of geometric parameters on the two resonance modes is discussed. Based on these characteristics, Fano resonance modes with high sensitivity to bulk refractive index and larger near-field spatial dimensions/field enhancements are achieved in the short wavelength range, enabling the filtration of large-sized biomolecules. However, the transmission stopband dip at longer wavelengths, resulting from GMR coupling, exhibits high surface sensitivity and moderate bulk refractive index sensitivity, making it particularly suitable for filtering small biological molecules. Therefore, the proposed nanostructure utilizes complementary near-field distributions between different resonant modes to effectively filter a wide range of biomolecules with varying sizes, offering great potential for developing versatile filtering and sensing platforms for various applications. Moreover, such structures provide accurate spectra without noise perturbations, which is especially advantageous for spectroscopic gas-sensing.