1. Introduction

Currently, sensitive, low-cost and miniature sensing systems are highly demanded with increasing requirements like indoor air monitoring or outdoor portable environment monitoring. NDIR (non-dispersive infrared analyzer) sensing, based on the finger-print absorption of gases or liquids in mid-infrared, is better potential technique to satisfy these demands than high-cost and complex spectroscope adopted in laboratory [1]. Conventional NDIR sensor mainly contains optical filter to tailor the broadband spectrum into narrowband, whose working waveband coincided with the unique absorption of the specimen to improve the specificity. However, filter remarkably increases the complexity of the whole system and wastes most parts of the energy. Although the quantum cascade laser with the ability to probe the individual absorption line has been developed to increase the efficiency [2], the high-cost fabrication limits their wide usage for low-cost application in the near future. On the other hand, NDIR based on MIM emitters with lower-cost, smaller volume, lower power consumption and filter-free, have been proposed and proved to be feasible recently [3,4].

The MIM (Metal Insulator Metal) structure is also known as the metamaterial perfect absorber, because they can exhibit nearly perfect absorption at specific frequencies ranging from visible to microwave, and from narrowband to broadband applications [5–10]. In the optical range, LSPRs (Localized Surface Plasmon Resonances) inside the metallic particles are responsible for the selective absorption. However, relatively large imaginary part of the metals indicate large losses, resulting in quality factors of LSPRs usually less than 10 [11], which is unable to meet the challenges in high sensitivity applications. Although alternative plasmonic materials, such as doped conventional semiconductors, have been proposed to replace metals to realize high Q resonances in theoretical, noble metals still outperform doped semiconductors in the experiment, even with their larger ohmic losses for their higher plasma frequencies in the metals. Heavy doping levels can improve plasma frequencies effectively, while the losses rise up quickly simultaneously. Balance between the ohmic losses and plasma frequencies makes metals and alternative plasmonic materials incapable of being the substitution for each other, which has been indicated in [12].

In this paper, C-MIM (Coating-MIM) structure is proposed, in which delocalized SLRs (Surface Lattice Resonances) with ultra-narrow bandwidth are stimulated at mid-infrared. In the last decades, SLRs have rarely been researched in the MIM structure, especially in mid-infrared [13,14], but drawn increasing attention in the MS structure (Metallic particle arrays on Substrate) [15–23]. Differently, transmissions in MIM Structure are forbidden by the bottom metallic film whose thickness is greater than skin depth. Hybrid coupling between LSPRs and the lattice RAs (Rayleigh Anomalies) gives rise to SLRs, besides, coatings with hundreds of nanometers are employed to modulate the coupled efficiency in the C-MIM structure.

SLRs are considered to have prospects in replacing LSPRs for the ultra-narrowband applications or shaping this lorentzian line shapes to a Fano-like line shapes [18,24–26]. Besides, enhanced near-field by SLR is attractive for surface-enhanced Raman scattering (SERS) [19] or refractive index sensing [14, 20, 21]. Typically, to obtain this collective resonance in the MS structure, homogenous media condition is required to make sure that there is no suppression of diffraction by abrupt changes in the refractive index [27]. Refractive index matching layer is the most common method [17,18,28,29], besides embedded structure [30] and thin film [31,32] have also been introduced. Unfortunately, homogenous media condition dramatically restricts its practical applications. Besides, only orthogonal coupling, in which propagation direction of diffraction orders is orthogonal to the external electric field, is enhanced. Recently, parallel coupling has been demonstrated to show stronger vertical field delocalization and greater tolerance to index asymmetry in the environment surrounding the array, which can be more suitable than orthogonal coupling in applications for sensing or emission enhancement [33,34]. In the C-MIM structure, homogenous media condition surrounding the particle array for SLRs seems to be unnecessary, because particle array is fabricated on the insulator whose thickness is much smaller than the incidence wavelength and transmissions are forbidden by the bottom layer. Besides, the superior parallel coupling is stimulated without homogenous media condition satisfied and modulated by coatings conveniently. Unlike matching layer which modulates the orthogonal coupling, coating only modulates parallel coupling remarkably, including enhancing, suppressing and shifting confirmed both in numerical simulations and experiments.

The proposed C-MIM multi-layer structures not only have low cost and thin volume (approximately 1 µm) inheriting from traditional MIM structures, but support the superior parallel coupling for emissive or absorptive enhancement, which may propel the well-suited MIM structure in ultra-narrowband applications.

2. Analysis and simulation

The ideal C-MIM four-layer structures researched in this paper are schematically shown in Fig. 1. Bottom layer is the Au-film with thickness greater than skin depth and insulator is deposited on it. Golden disks with square arrangement are covered by dielectric coating with hundreds of nanometers. Besides, TE-polarized (Transverse Electric) oblique light has also been defined in Fig. 1(a) and TM(Transverse Magnetic)-polarized can be deduced as the TE-polarized rotated by 90° along the k-axis. Abbreviation of structure parameters defined throughout this paper is explained in Fig. 1(b).

 

Fig. 1 Schematic views of C-MIM structure in rectangular arrangement. To clearly explain the multi-layer structure, wrapped disks are revealed by removing part of the dielectric coating on the edge. Definition of TE-polarized plane-wave has also been indicated in (a), counter TM-polarized can be deduced as the TE-polarized rotated by 90° along the k-axis. Structure parameters used throughout the research are indicated in (b) and explained as follows: R (radius of disk), Px (lattice constant along x-axis), Py (lattice constant along y-axis), h_c (thickness of coating), h_d (thickness of disks), h_i (thickness of insulator), h_m (thickness of Au-mirror).

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2.1. Theory

Diffractive couplings among metallic particles are considered as the origin of these collective resonances, hence SLRs can be well predicted near, but not exactly at the RAs (Rayleigh Anomalies) [25]. RAs correspond to the transitional process of diffraction orders from evanescent to radiative ones in the array, which can be well explained in the far-field hemispheric diffraction screen (Fig. 2(a)). As wavelength decreases, the nonzero radiative diffraction orders will move to the edge of the screen and disappear in the end, leading to evanescent ones (Fig. 2(b)).

 

Fig. 2 (a) demonstrates the oblique incident light (k) that strikes onto the 2D lattice at θ. Corresponding specular and scattering lights are indicated by red-solid lines and red-dash lines, respectively. Hemispheric diffraction screen with great enough radius is placed upon the lattice to collect total reflected light. (b) demonstrates the top view of this diffraction screen, in which the dash-circles are contour lines, indicating the angle between normal and diffraction orders. Reflected lights are presented by red dots, while the visible dots on the screen indicate the radiative orders and the invisible dots on the screen indicate the evanescent orders (such as i = −1, j = 0).

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As polarized light(k) incidents upon the 2D microparticle array (seated on the xy-plane) with lattice constants of P_x and P_y, the in-plane wave vector ${\mathbf{k}}_{\mathbf{i},\mathbf{j}}^{\parallel }$ is dependent on incident angle and lattice constants (Fig. 2(a)). ${\mathbf{k}}_{\mathbf{i},\mathbf{j}}^{\parallel }$ is determined by Bragg’s equation

In the square lattice, momentum-matching condition between the free space and the in-plane is satisfied by reciprocal lattice vectors introduced by the periodic structure. However, the matching processes happen both on the top of disks and the coating, which means that λ^RA can be classified into λ^RA_c (in the free space; above the coating) and λ^RA_d (in the hybird environment; above the disks). It should be noted that the incident lights can interact with the disk array by going through a layer of photonic crystal layer (coating) rather than interact with the disk array directly. Incident light from the free space should satisfy the condition of the 2D lattice under specific wavelength, and then couple with photonic crystal layer modes. Finally, the transmitted lights interact with the disk array. For λ^RA_d, refractive indexes of the the environment (n) in Eqs. (3) and (4) have to be replaced by equivalent indexes when coatings are applied. When collective SLRs are motivated by the coupling between LSPRs and the RAs above the disks, coatings may dramatically affect the SLRs near RAs. In this situation, as coating with higher index is applied, value under the radical sign in Eq. (2) is approaching to positive number under fixed wavelength, which makes $k_{i,j}^{\top }$ approach to a real number and indicate a radiative diffraction order. Oppositely, as coating with lower index is applied, $k_{i,j}^{\top }$ is approaching to an imaginary number and indicates an evanescent diffraction order. More than that, obvious shifting of SLR can be predicted in Eqs. (3) and (4).

2.2. FDTD simulations

Firstly, 3D finite different time domain (FDTD) [36, 37] has been carried out to obtain the reflected spectra and the near-field distribution. Corresponding simulated model was established according to Fig. 1. Silicon substrate was ignored in the model because there were no lights transmitted from Au-film. Bloch boundary conditions were used to describe the infinite rectangular arrangements and realize the oblique incident simulations (θ = 10°). It should be noted that k_║, in-plane component of k are always along with x-axis in this paper, and our research primarily focuses on SLR(0,±1). Material parameters of gold were described as fitted curves per Palike’s handbook [38]. Coatings were defined as nondispersive materials with n_c = 1 or n_c = 1.4. The four-layer structure was immersed in the free space whose refractive index was n_fs = 1.2. Meanwhile, refractive index of insulator in the C-MIM structure was fixed on n_i = n_fs. Condition n_fs = n_air = 1 abandoned was owing to the Kramers-Kronig relations, which claimed that index of nondispersive materials must be greater than one. In other words, conditions n_c < n_fs cannot be achieved, which restricts the scope in this paper. Besides, k = 0.001 was adopted in all the dielectrics to prevent the simulations from being diverging and accelerating the convergence.

Refer to direction of diffraction in this configuration, overlapped RA(0,1) and RA(0,−1)) are always propagating along x-axis with opposite direction, while split RA(1,0) and RA(−1,0) propagate along y-axis with opposite direction. LSPRs, located inside the disks, have the directions along with driving electric field, namely the in-plane electric field of incident light. SLR(0,±1) are stimulated by parallel coupling under TE-polarized light, but stimulated by orthogonal coupling under TM-polarized light. SLR(1,0) and SLR(−1,0)) are stimulated by parallel coupling under TM-polarized light, but stimulated by orthogonal coupling under TE-polarized light.

First of all, total reflectance (R) and zero-order reflectance (R00) were obtained under TE- or TM-polarized oblique lights (Fig. 3). Corresponding RAs in the free space are illuminated by vertical dash-lines. It’s well known that total reflectance is higher than zero-order reflectance when the nonzero diffraction order appears, which can be confirmed at RA(1,0) in Fig. 3. Besides, only SLRs stimulated by parallel coupling are observed. Valid coatings are defined in this paper, whose indexes are much greater or less than the environment (free space). Both n_c = 1.4 and n_c = 1 are valid coatings in the simulations, and n_c = 1.4 (n_c = 1) under TE-polarized light enhances (suppresses) the parallel coupling remarkably in contrast to C-MIM without coating. Notably, LSPR and SLRs express red-shifting as high index coating is applied in Fig. 3(a). Shifting of SLRs may attribute to the fact that localized LSPRs couple with the RAs above the disks instead of the RAs above the coating, where λ^RA_d must be adopted to predict the SLRs. Besides, fixed diffraction orders above the coatings (λ^RA_c) are always presented and can be verified at where the zero-order reflectance lower than the total reflectance. Positions of SLRs in the C-MIM structure under different incident angles and different polarizations are simulated as an extension of Fig. 3(a), in which RAs (λ^RA_c) are also calculated according to Eqs. (3) and (4). Simulated SLRs and calculated RAs are plotted as circles and lines, respectively. As indicated in the inset, simulated SLRs in C-MIM structures are always located at the longer wavelength of RAs under different incident angles or different polarizations, which is consistent with the red-shifting behavior mentioned above. Besides, the simulated SLRs have remarkably good agreements with the calculated RAs, both the split SLR(±1,0) and the overlapped SLR(0,±1).

 

Fig. 3 Total reflectance (R) and zero-order reflectance (R00) of C-MIM immersed in the free space with n_fs = 1.2 under TE- or TM-polarized oblique light (θ = 10°). The refractive indexes of coatings are n_c = 1.4 (a), n_c = 1.2 (b) and n_c = 1 (c), respectively. Positions of SLRs by simulations under 5°, 10°, 15° and 20° are indicated by circles in the inset of (a), in which lines indicate the calculated RAs according to Eqs. (3) and (4). Geometrical parameters of the model are defined as follows: R = 1 µm, P_x = P_y = P = 4.5 µm, h_c = 400 nm, h_d = 100 nm, h_i = 180 nm, h_m = 100 nm. Calculated λ^RA are based on n = n_s = 1.2 and plotted by dash lines (${\lambda }_{0,\pm 1}^{RA}=5.32\text{μm}$, ${\lambda }_{1,0}^{RA}=6.34\text{μm}$, ${\lambda }_{-1,0}^{RA}=4.46\text{μm}$). SLRs near RAs are pointed out by green arrows.

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Normalized field distributions of C-MIM with valid coatings n_c = 1.4 were obtained under TE-polarized oblique lights, namely RA(0,±1) parallel to the LSPR. Simulated wavelengths were selected at the dips of SLR(0,±1) and LSPR. As shown in Figs. 4(a)–4(d), SLR(0,±1) and LSPR are both the electric dipole resonances excited on the disks along the y-axis for TE-polarized. However, the distributions of |H_x| in yz-plane are significantly different. In Fig. 4(e), |H_x| mainly concentrates among the disks and above the disks at λ^SLR, which indicates a propagative resonance. |H_x| transfers into the insulator at λ^LSPR in Fig. 4(f), which indicates a localized resonance. As explained by [34], |E_z| indicates the situation that diffraction order grazes the surface of the lattice when parallel coupling appears. In Fig. 4(g), |E_z| mainly concentrates at the upper edge of disks and attenuates quickly into the coating, which can be clearly recognized by the electric-field ears inside the coating. These ears are reshaped at the upper edge of coating and propagate into the free space. As indicated in the far-field spectra, LSPRs couple with the RAs above the disks, which means that coatings play the role of intermediary to transmit lights. To warrant that propagating orders in the transmission media couple with photonic crystal layer modes, coatings with greater thickness or greater refractive index have to be employed. Lobes in the free space correspond to a standing wave formed by two resonances with the same frequency but traveling in opposite direction. As concerned wavelength shifts to λ^LSPR, electric-field transforms to the lower edge of the disks and concentrates inside the insulator. The intensity of |E_z| in Fig. 4(h) indicates the induced antisymmetric electric dipole at the surface of the mirror layer. The mimicking dipole resonances can be also verified in the magnetic-field distribution (Fig. 4(f)).

 

Fig. 4 Normalized field distributions of C-MIM with valid coatings n_c = 1.4 under TE-polarized oblique light at λ^SLR and λ^LSPR, in which both planes (xy and yz) intersect the unit cell at the center of disk. Geometrical parameters are identical with the parameters used in the previous simulations. (a,b) and (c,d) indicate the |E_y| distributions in xy- and yz-plane, respectively, while (e,f) indicate the |H_x| distributions in yz-plane. (g,h) indicate the |E_z| distributions in yz-plane.

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3. Experiment

To better verify the modulated effects by coatings, C-MIM structures were fabricated on silicon wafers by MEMS (Micro-electro Mechanical Systems) process and measured by FTIR (Fourier Transform Infrared Spectrometer).

3.1. Fabrication

The C-MIM four-layer structures were fabricated on the 4-in. (1 in. = 2.54 cm) single-side polished silicon wafers. The first step was the deposition of golden mirror layer with thickness h_m = 100 nm by magnetron sputtering in a vacuum system at a base pressure of 2.1 mTorr, besides 10 nm titanium was used as the adhesion layer. Then SiO₂ layer with thickness h_i = 180 nm was deposited by PECVD (Plasma Enhanced Chemical Vapor Deposition) system, Oxford plasmalabsystem 100. The disk array was fabricated as follows: First, a layer of Au-film with thickness h_d = 100 nm was deposited through exactly the same conditions, refer to the golden mirror. Photoresist was spined on the Au-film directly without HMDS (Hexamethyl Disilazane), besides the spinning parameters had been verified to obtain the thickness of 1 µm. After spinning, the wafer was baked on a hot plate for 90 seconds at 110 °C, then periodic disks were transferred to the photoresist by contacting exposure. Ultraviolet curing was adopted as follows, which prevents the disks from being out of shape. After that, IBeam was applied to transfer the disk array to the Au-film. However, IBeam may damage the SiO₂ insulator below the disks because it’s a physical bombing method. To remove the photoresist completely, wafers were immersed into the resist stripper solutions provided by VERSUM for 15 minutes in 75 °C, then were placed in the RF plasma ashing system to remove the residual particles of the photoresist. Coatings were deposited in the end by PECVD method with various thickness of SiO₂ or SiN_x.

Table 1 describes the structure parameters of samples detailed and Figs. 5(a)–5(b) demonstrate the oblique view and the sectional view of a single disk by SEM in the accomplished C-MIM. It is worth mentioned that the coatings have good step coverage, affirmed from the sectional view.

Table 1. Structure parameters of different samples.

View Table

 

Fig. 5 SEM images of the C-MIM structure with h_c = 200 nm in oblique view(a) and sectional view(b), in which the multilayered structure with good step coverage can be affirmed.

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3.2. Optical constants of dielectrics

In this paper, SiO₂ and SiN_x deposited by PECVD with various thickness are chosen as the coatings. Optical properties of thin films in mid-infrared have been researched by Kischkat et al [39] through sputter deposition. In their conclusions, n (Refractive index) and k (Extinction coefficient) of SiO₂ are much more stable than SiN_x as synthesis conditions are altered, such as the flow rate or pressure. To better understand the modulated effects on SLRs by coatings, SiO₂ and SiN_x were prepared on single-side polished wafers, whose synthesis conditions were referred to the coatings. Corresponding fitting results of n and k, fitted by mid-infrared spectroscopic ellipsometry (IR-VASE MARK II) are shown in Fig. 6, both SiO₂ and SiN_x. Besides, results by Kischkat are also plotted by dot lines in those figures for comparison, which indicates the unstable n and k of SiN_x.

Extinction coefficients, describing the losses of EM energy, increase remarkably both in SiO₂ and SiN_x, when the wavelength exceeds 7.5 µm, as the results shown in Fig. 6. Losses in mid-infrared are commonly caused by molecular vibrations or phonon vibrations. Besides, losses lead to a remarkable degeneration of the resonances’ quality factors.

 

Fig. 6 Refractive indexes (n, refer to the black labels) and extinction coefficients (k, refer to the blue labels) of SiO₂-film(a) and SiN_x-film(b). Dot-lines and solid-lines indicate the results by Kischkat et al and results in this paper, respectively. The positions of n = n_air = 1 are pointed out by horizontal and vertical lines.

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3.3. Spectra measurement

Reflectance spectra were measured through FTIR by Bruker Vertex 70V, equipped with a reflectance accessory, Pike 10Spec (Refer to Fig. 7). The collimated plane wave was featured by this accessory, and struck on the samples at 10°. Besides, a mid-infrared polarizer was adopted to feature the linear polarized beam. Corresponding definitions of TE- and TM-polarized oblique plane wave can be found in Fig. 1.

 

Fig. 7 Diagram of the light path in the accessory, Pike 10Spec. To obtain the TE and TM reflected spectra, a mid-infrared polarizer was applied. Corresponding spectra were calculated via the background single-channel spectra (Golden mirror) and the specimen single-channel spectra (C-MIM structure). Because of the limitation of the measurement equipment, reflectance spectra must be obtained at 10° incident light.

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Typically, the original size of the collimated beam, featured by the accessory, is approximately 12 mm. Aperture, under the sample, redefines the incident beam to 3 mm by absorbing external lights of the hole. Obviously, only ideal black-body can realize the perfect absorption, which means that the aperture cannot obtain a 100% absorptivity. That may lead to a relatively higher reflectance results, which means that the measuring system cannot obtain the absolute reflectance, but with relatively good reflectance results. Besides, only the zero-order reflectance can be observed, because the accessory is a specular reflectance.

3.4. Results and discussions

First of all, zero order reflectance spectra of samples-A with 300 nm SiO₂-coating were measured and simulated under TE- and TM-polarized oblique light at 10° (Fig. 8). SiO₂-coating can be considered as valid coatings at this waveband, because n_c is much greater than the free space (n_c = 1.43 > n = 1 at ${\lambda }_{0,\pm 1}^{RA}$). SLR(0,±1) at 4.56 µm and LSPR at 5.7 µm can be well recognized and have good positional agreements between simulated and measured results. However, LSPR, especially SLRs in the experiments, is more weakened than the results in simulations. To better quantitate the discrepancy between simulations and experiments, FWHM (full width at half maximum) is used to measure how narrow the resonance is. As indicated in Fig. 8, FWHM of SLR(0,±1) and LSPR under TE-polarized oblique light are 38 nm and 372 nm, respectively in the simulations. However, these values drop to 116 nm and 389 nm, respectively in the experiments. Discrepancy of LSPR between simulated and measured spectra might be attributed to the imperfection of the patterns, such as elliptical disks or the inconsistent radii and lattice constants. Besides, coupled efficiency among dipoles inside disks may be degenerated by these inconsistent radii or the inconsistent lattice constants, which leads to lower quality factor of SLRs in the experiment. To better assess the fabrication imperfections, diameters and lattice constants along x-axis and y-axis are measured in one sample by 16 SEM-images. Images are obtained throughout the 3mm*3mm area uniformly, and 64 disks are captured (4 disks per image). Approximately normal distributions are observed and the mean values have biases from the designed value (See Data File 1). Besides, parameters along x-axis (Diameter range from 1.75 µm to 1.83 µm; Lattice constant range from 4.45 µm to 4.51 µm) have better consistency than y-axis (Diameter range from 1.74 µm to 1.86 µm; Lattice constant range from 4.4 µm to 4.56 µm), which indicates the overall deviation of fabrication, for example, the gradient parameters due to sample bowing. Typically, FWHM of LSPR in the noble metal can be optimized down to 250 nm in the Mid-infrared, by adopting suitable insulator with applicable thickness and losses, or distance among disks. Even so, the FWHM of LSPR is still inferior to the degraded SLR in the experiments. Above all, taking into account the imperfect fabrication as well as the measurement error, there are still good agreements between the simulated and experimental results. As indicated in spectra, only parallel coupling are observed, for example the SLR(0, ±1) near RA(0, ±1) under TE polarization. Corresponding orthogonal coupling of SLR(0, ±1) under TM polarization are totally vanished. Results can also be observed in the SLR(1,0) near RA(1,0), while only parallel coupling arouse this obvious dip. (Confused SLR(−1,0) with higher order are not discussed here.)

 

Fig. 8 Reflectance spectra of sample-A with 300 nm SiO₂-coatings under TE- or TM-polarized oblique light (θ = 10°), in which solid lines are for measured results and dash lines are for simulated results. Simulated models are rebuilt according to the authentic parameters of sample-A obtained by SEM. Calculated positions of λ^RA_c are illuminated by vertical dash lines (${\lambda }_{0,\pm 1}^{RA}=4.43\text{μm}$, ${\lambda }_{1,0}^{RA}=5.28\text{μm}$, ${\lambda }_{-1,0}^{RA}=3.72\text{μm}$).

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In general, parallel coupling have been confirmed in C-MIM structures both in simulations and experiments. To better understand the modulation effects by coatings, C-MIM structures with various thickness of SiO₂- and SiN_x-coating on sample-A, sample-B and sample-C were fabricated and measured. Besides, scattering calibrations were employed on the original spectra to adjust the base lines and made the comparison more convenient. Corresponding reflected spectra were all obtained under TE-polarized light.

As indicated in Fig. 9(a), SLR at the right of RA(0,±1) approaches to longer wavelength gradually and is enhanced remarkably, when SiO₂-coating gets thicker. These asymmetric Fano-like resonances include dips in the shorter-wavelength and peaks in the longer-wavelength. Calculated ${\lambda }_{0,\pm 1}^{RA}$ in the free space is supposed to overlap with the dip of SLR, when coating is unemployed on the MIM structure.

 

Fig. 9 SLRs in sample-A (a), sample-B (b) and sample-C (c) with various thickness of SiO₂ or SiN_x coatings under TE-polarized oblique light. Besides, inset in (b) indicates ${\lambda }_{0,\pm 1}^{SLR}$ shifting with h_c by simulation, in which red and blue arrows indicate ${\lambda }_{0,\pm 1}^{RA}$, calculated by n_fs and n_c, respectively. Besides, calculated positions of RA(0,±1) in the free space are illuminated by vertical dash lines in these three figures (${\lambda }_{0,\pm 1}^{RA}=4.43\text{μm}$ for sample-A, ${\lambda }_{0,\pm 1}^{RA}=6.89\text{μm}$ for sample-B and ${\lambda }_{0,\pm 1}^{RA}=2.42\text{μm}$ for sample-C).

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In Fig. 9(b), SLRs in sample-B stimulated in the longer wavelength are also measured and illuminated, in which SLRs near RA(0,±1) can barely be seen even when SiO₂-coating is employed or gets thicker, which is much different to sample-A. The failure of coatings on SLRs in longer wavelength may attribute to the decline of $n_{Ci{O}_2}$. As indicated in Fig. 6, $n_{Ci{O}_2}$ decreases from 1.43 at 4.43 µm to 1.17 at 6.89 µm. SiO₂-coatings may be considered as invalid coating near 6.89 µm, which explains the modulation failure in sample-B. The threshold value of valid coating increasing may attribute to the imperfection of the patterns mentioned above, in which stronger modulation must be adopted to enhance the coupling in the imperfect sample. Inset in Fig. 9(b) indicates ${\lambda }_{0,\pm 1}^{RA}$ shifting with h_c when valid coating is applied in C-MIM by simulation. An obvious convergent tendency of the SLR can be verified. The convergence can be explained by the electric-field ears in the coating and free space. As h_c increases, ears above the disk array completely concentrates inside the coatings. In other words, SLRs can be considered as to be immersed in the coating media, hence n used for calculating λ^RA_c is convergent to n_c. In the inset, red arrow indicates ${\lambda }_{0,\pm 1}^{RA}$ calculated by n_fs, while blue arrow indicates ${\lambda }_{0,\pm 1}^{RA}$ calculated by n_c. According to the above analysis, the modulation range of this method is mainly depending on the thickness and the refractive index of the coating. While the refractive index of coating determines the limitation of modulation, the thickness determines the level of modulation.

In Fig. 9(c), valid coatings made of SiO₂ and SiN_x are applied in sample-C, where index of SiO₂ and SiN_x are equal to 1.36 and 1.79 respectively at ${\lambda }_{0,\pm 1}^{RA}$ as indicated in Fig. 6. The asymmetric SLRs stimulated by parallel coupling can be well recognized and enhanced while coatings get thicker, which are consistent with aforementioned results. Besides, more efficient modulations on SLRs are achieved when low-index coatings (SiO₂) are replaced by high-index coatings (SiN_x). As illuminated in Fig. 9(c), dip of SLR locating at ${\lambda }_{0,\pm 1}^{RA}$ shifts from 5.42 µm to 5.62 µm when 400 nm SiO₂-coating is employed. However, SiN_x-coating makes this shifting up to 5.91 µm with the same thickness, which indicates the fact that coatings with higher indexes bring to stronger modulations on the parallel coupling. Besides, the strength of SLR with 400 nm SiN_x-coating is also stronger. It should be noted that SLRs in sample-A and sample-C with the same thickness of SiO₂-coating have different strength, which contributes to the dispersion of n_c in these samples (${\lambda }_{0,\pm 1}^{RA}=4.43$ in sample-A, ${\lambda }_{0,\pm 1}^{RA}=5.42$ λ^RA in sample-C).

Above all, thicker valid coatings on C-MIM enhance the parallel coupling and dramatically improve the strength of SLR without any matching layers, and coatings with higher-index make the modulations more efficient. Both the strength and the position of SLRs can be adjusted by the thickness of coatings, more than which the relatively stable area of h_c makes this adjustment much robust to the manufactural tolerance.

4. Conclusion

In this paper, MIM structure with dielectric coating on it has been researched both in the simulations and the experiments. Parallel coupling between LSPRs and RAs have been obtained in the C-MIM structures in the mid-infrared. Coatings with refractive index much greater or lower than the environment show efficient modulations on the parallel coupling including strength and position. Besides, modulations get more efficient when n_c is much greater (enhanced) or lower (suppressed) than n_fs. Different from matching layers for MS structure, coatings are much suitable in the practical applications because their hundreds of nanometers thickness and various kinds of choices, such as SiO₂, SiN_x, Si, Al₂O₃, MgF₂ or even multilayered. More than that, parallel coupling in C-MIM structure are much suitable than orthogonal coupling in MS structure for far field narrowband emitters or absorbers. Dielectric coatings provide a low-cost and multidimensional modulations on parallel coupling, which propels this ultra-narrowband resonance in the practical applications. For example, in the NDIR sensing, ultra-narrowband emitters without filters based on C-MIM not only decrease the complexity of the whole system, but also significantly increase the selectivity of the device. Not only that, the conclusions of coatings can also be used in broadband devices based on MIM. For example, coatings with lower refractive index suppress the undesired cutoff in working band and play as passivation layer to protect the resonant cells.