1. Introduction

Metamaterial, which was originally proposed by Pendry and D. R. Smith et al. in the very beginning of this century [1,2], has enjoyed a booming development in the past years. Distinguished from material that solely changing the optical constant by doping or other methods, metameterial can be seen as the combination of meta-atoms, with rationally designed, to manipulate the electromagnetic field. With the smart control of physical field of light, metamerial can achieve some inspiring phenomenon, like generating artificial negative permeability and permittivity [2]. With such outstanding ability in manipulating electromagnetic wave, metamaterial has been chosen as a promising solution for energy transformation control, as solar harvesting [3], thermophotovoltaic [4], radiative cooling [5,6] and so on. That being said, due to some intrinsic limitations, metamaterial based energy transformation devices have not been utilized in daily life and industrial manufacture.

In most recent years, it can be seen that various kinds of novel metamaterials have been proposed to overcome specific shortcomings for traditional metamaterial. Bo Zhao et al. have proposed a combination of hexagonal boron nitride and metallic grating [7]. With the addition of 2D anisotropic hexagonal boron nitride film, absorption of light can be greatly enhanced in specific wavelength, and electromagnetic energy can be focused in specific direction and location within hexagonal boron nitride. Such focusing effects can overcome the low energy density and low transformation efficiency that harass the traditional electromagnetic harvesting devices. Yakir Hadad et al. have built a novel antenna based on time-dependent index material [8]. That antenna has generated optical non-reciprocity, breaking the equilibrium between emission and absorption, and avoids the intrinsic loss due to the devices emission. Antoine Moreau et al. have fabricated a metasurface, in which film-coupled colloidal nanoantennas have been randomly distributed on the surface [9]. To fabricate that metasurface, no effort is needed to control the spatial arrangement of meta-atoms, thus provides a novel way to produce large scale metamaterial. Aaswath P. Raman et al. have built a macroscopic radiative cooler with multilayer structure [10]. That device can retain a temperature below the ambient temperature without any driving sources at all.

Among all the novel applications, nanoparticle-crystal has shown to be a promising candidate for large scale fabrication of metmaterial [11–13]. With closely packed nanoparticles arrange in a similar pattern with atomic crystal, nanoparticle-crystal has exhibited extraordinary optical response. For conventional nanoparticle-crystal, near-field light redistribution mainly originates from the collective oscillation between the particle array and the substrate [14,15]. That's to say, the functional metamaterial can only be utilized with the fixed substrate, which greatly limits its large scale application. Especially for thermophotovoltaic, to harvest waste heat a large area of surface is required. Also, the geometric features can be quite complex, requiring the radiative property should show incident and polarization angle insensitive. In this paper, a nanoparticle-crystal has been proposed, which serves as the prototype of novel absorbing meta-coating. The metamaterial can be produced by spraying specific mixture to various kinds of surfaces. To achieve it, the meta-coating must show substrate independence. In other words, optical properties of the substrate cannot affect the optical responses of the metasurface, which might seems impossible for traditional planar metamateial [16–18]. Also, the optical responses should show polarization and incident angle insensitivity to some extent, which makes it a more challenging task.

In this paper, we propose it can be achieved by near-field electromagnetic wave redistribution, or hot-spot generation within a double layer nanoparitcle-crystal. Near field effect comes from the coupling between evanescent wave and bodies whose spatial scale is approached to the electromagnetic wave [19]. The evanescent wave can enhance the photon transfer between bodies by several orders beyond far-field radiation transfer [20,21], showing a promising future of novel energy transformation devices like near-field thermophotovoltaic [22]. Specifically for light-matter interaction within the nanoparticle system, rational arrangement of nanoparticles can achieve a reshaping of the electromagnetic field distribution around the structure, and generate hot-spot between the plasmonic nanoparticles [23]. The hot-spot is certain part of a plasmonic nanostructure where the electromagnetic field has been greatly enhanced comparing the surrounding. With the strong coupling between electron and photon, electromagnetic energy has been greatly transformed into heat, generating extremely high temperature where hot-spot locates. Hot-spot originates from the strong plasmonic and photonic coupling in the near field, and can be utilized for superlenses [24], on-chip optical circuits [25,26] and so on. Previously, we have demonstrated the induction of the hot-spot in isolated nanoparticles trimer can be seen as the bond between nanoparticles in specific wavelength, analogous to the electronic bond in molecule [27]. The hot-spot cannot only redistribute the electromagnetic field distribution, but also greatly enhance the emission and absorption. In this paper, this concept has been extended to nanopaticle-crystal, in which near perfect absorption peaks associated with the hot-spot can be seen as the generation of the bond in the periodic crystal array, and makes a meta-coating possible.

The paper is arranged as follow: To the first, the radiative properties of the meta-coating has been shown. Spectral absorptivity has shown substrates independence, polarization and incident angle insensitivity. Then, the spectral near-field intensities have been shown, indicating the induction of plasmonic -photonic 'bond' inside the crystal. Finally, the physical picture of the plasmonic -photonic 'bond' has been demonstrated by the help of a three oscillators model.

2. Radiative properties of the nanoparticle-crystal

Two kinds of nanoparticle-crystal have been illustrated in Fig. 1(a), two layers of densely arrayed metallic nanoparticles are piled shoulder by shoulder on a planar layer. The piling mode is similar to the cubic or hexagonal crystal structure. Such types of nanoparticle-crystal can be fabricated via a solution-evaporation process. First, the particles are dispersed in a solution, in which the density has been precisely controlled. Then, a droplet of solution has been dried on a substrate, and will result in a closely packed nanoparticle-arrays [11–13]. The number of nanoparticle layers can be tuned via controlling the density of nanoparticle, and the volume of the droplet. The polarization angle of light is set as $\theta$, and the incident angle is set as $\phi$. The radius of the nanoparticle is r, the thickness of the supporting layer is $d$, and the period of the crystal $P=2r$. All the optical constant used in this study are obtained from Palik's book [28]. The finite-difference time-domain (FDTD) method has been illustrated in Fig. 1(b), a plane of meshes have been chosen as the incident source, another two planes of meshed have been chosen as reflection and transmission power monitors. With the calculation of the time average power in the monitor planes, one can obtain the spectral reflectance $\rho$ and transmittance $\tau$, thus the spectral absorptivity can be obtained as $\alpha =1-\rho -\tau$. The default mesh has been chosen as 7nm square cell, and later its numerical convergence will be verified.

 

Fig. 1 (a) A schematic for the nanoparticle-crystal with cubic and hexagonal pattern. (b) Illustration of FDTD method and calculation of radiative property. (c) Spectral normal absorptivity for the 4 kinds of nanoparticle-crystals. (d) Spectral absorptivity for cubic nanoparticle-crystal with different size of meshes. (e) Spectral absorptivity for hexagonal and cubic double layer nanoparticle-crystal.

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In the very beginning, the spectral absorptivity for various kinds of free-standing metallic nanoparticle-crystal with cubic pattern have been shown in Fig. 1(c). Later it will be shown that spectral normal absorptivity for that type of metamaterial is independent of substrate, free-standing cases are just employed for general consideration. Three kinds of metallic nanoparticles are used for investigation, as Ag, Au and Cu with $r=0.8\mu m$, $\theta =0$, $\phi =0$in Fig. 1(c). As can be seen, 2 nearly perfect absorption peaks can be seen in the infrared region for all three kinds of nanoparticle-crystal, one is near 1.75μm, the other is around 2.2μm. As been shown in Pailk's book [28], the optical constants of metal has exhibited wavelength dependence. Also, nanoparticle-crystal made of Ag, Au and Cu have all exhibited double absorption peaks. To separate the resonant physics from the constant variation and better understand the spectral selectivity caused by subwavelength light redistribution in a more general sense, an invariant constant has been used. An ideal metal with optical constant $n+i\kappa =1+10i$ is chosen for further discussion, which is also presented in Fig. 1(c).

To verify the numerical convergence, spectral abosorptivities of cubic nanoparticle-crystal obtained from various sizes of square cells have been shown in Fig. 1(d). With the size of mesh decrease from 30nm to 6nm, the absorptivities lines gradually approach to a fixed curve, indicating the numerical convergence and the mesh size independence has been achieved. The optical responses for hexagonal and cubic have been shown in Fig. 1(e), with double layer and $d=1.6\mu m$ ideal metal particles. The spectral absorptivities of the two kinds of crystal modes exhibit similar pattern, double major peaks with different resonant wavelengths. To provide a less complex demonstration, without specific notation, all the following demonstrations will base on the double layer cubic ideal metal nanoparticle-crystal aforementioned.

The spectral absorptivity with a supporting layer is presented in Fig. 2, 3 types of material, Au Fig. 2(a), SiO₂ Fig. 2(b), W Fig. 2(c) are selected to be supporting layer, as typical plasmonic, dielectric and normal metallic material. It can be easily seen that even the thickness of supporting layer ranges from 0.1 thin film to semi-infinite substrate, the spectral absorptivity will stick to a fixed line for all three types of material. On the contrary, the optical responses for monolayer nanoparticle-crystal vary greatly as shown in Fig. 2(d). It can be easily seen though double absorption bands exist to some extent, their peak value and the resonant wavelength vary with different types of supporting layer. This indicates conventional monolayer nanoparticle-crystal cannot be used as a coating material, as shown no supporting layer independence. In the calculation, it can be observed that for double layer nanoparticle-crystal, the transmission of the metasurface is nearly zero, while for single layer the transmissioIn the calculation, it can be observed that for double layer nanoparticle-crystal, the transmission of the metasurface is nearly zero, while for single layer the transmission cannot be neglected in some cases. As the light are all reflected or absorbed with the double layer, the optical property of the supporting layer can affect the response little. Whereas for single layer, as the transmission exist, the coupling between metasurface and supporting layer generate variant responses. For the very same free-standing nanoparticle-crystal, its spectral absorptivity as a function of polarization or incident angle are shown in Figs. 3(a) and 3(b). In the zone that we discuss, the spectral absorptivity of the free-standing nanoparticle-crystal does not change obviously, only slightly fluctuates when the incident angle is quite large around 1.6μm. As the optical response of the nanoparticle-crystal is insensitive to underlying material and incident spatial features, such nanoparticle-crystal can serve as the prototype of the meta-coating.

 

Fig. 2 Radiative properties for the nanoparticle-crystal with (a) Au, (b) SiO₂, (c) W as supporting layer/ substrate.(d) Spectral absorptivity of monolayer nanoparticle-crystal with various kinds of supporting layer.

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Fig. 3 Spectral normal abosrptivity for free-standing nanoparticle-crystal as a function of (a) polarization angle $\theta$, with $\phi =0\mathrm{deg}$, (b) incident angle $\phi$, with $\theta =0\mathrm{deg}$. Optical response transition for (c) mismatched top layer nanoparticles' diameter and (d) period.

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Furthermore, 2 types of crystal imperfections, as nanoparticle mismatch and period distortion, have been studied. The mismatched particle is set as a top layer one, with diameter d = 1μm. The mismatched cell is part of a larger periodic cell containing $n-1$ other unit cell in one direction, and the mismatch ratio can be defined as $1/n$ . As seen in Fig. 3(c), with mismatch ratio equals 1, double absorption peaks vanish. With the decrease of the mismatch ratio, the optical response approaches to the perfect case in general. Also for the period distortion, distorted period is set as 1.4μm, with $m-1$another normal cell in one direction, and distortion ratio is defined as $1/m$. With distortion ratio as 1, resonant peaks have shown blue shift. As the decreasing of distortion ratio, the optical responses generally approach to the perfect case.

3. Near-field spectral /spatial distribution

To quantify the local electromagnetic field enhancement due to the near field effect, 4 FDTD cells are chosen as the field monitors to present the spectral field intensity [27]. Field monitors are numbered with their locations shown by the 3-axis values, as x-y-z in a nanoparticle-crystal cell as presented in Fig. 4(d). The normalized near-field intensities are presented in Figs. 4(a)-4(c), which defined as$|E(i,\lambda )|/\left|E{(i)}_{\max }\right|$, wherein $i$ is the label of the monitor, $E{(i)}_{\max }$ is the maximum value a near field intensity line can reach in specific case.

 

Fig. 4 Normalized spectral near field intensity for free-standing nanoparticle-crystal with (a) $\theta =0\mathrm{deg}$, $\phi =0\mathrm{deg}$. (b) $\theta =0\mathrm{deg}$, $\phi =20\mathrm{deg}$. (c) $\theta =30\mathrm{deg}$, $\phi =0\mathrm{deg}$. (d) Schematic of the monitor location in the nanoparticle-crystal.

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For incident light with $\theta =0\mathrm{deg}$, $\phi =0\mathrm{deg}$, as shown in Fig. 4(a), at monitor 0-0-0, near-field intensity reaches to its maximum peak at $\lambda =1.62\mu m$, secondary peak at $\lambda =1.75\mu m$, and is slightly enhanced at $\lambda =2.19\mu m$. For monitor 0.4-0.4-0.57, near field intensity gets maximum at $\lambda =2.19\mu m$, and is slightly enhanced at $\lambda =1.62\mu m$ and $\lambda =1.75\mu m$. At monitor 0-0.8-0, electromagnetic field is greatly enhanced at $\lambda =1.75\mu m$, reaches to its secondary peak at $\lambda =2.19\mu m$, and slightly enhanced at $\lambda =1.62\mu m$. As for monitor 0.6-0-0, the normalized intensity at $\lambda =1.62\mu m$ and 1.75μm are even matched, and reaches its secondary maximum at $\lambda =2.19\mu m$. As for illuminated electromagnetic wave with $\theta =0\mathrm{deg}$, $\phi =20\mathrm{deg}$, as shown in Fig. 4(b), the near field intensity in monitor 0-0-0 is evenly enhanced at $\lambda =1.62\mu m$ and 1.75μm, slightly enhanced at $\lambda =2.19\mu m$. For monitor 0.4-0.4-0.57, the electromagnetic field shows its maximum intensity at $\lambda =2.19\mu m$. At $\lambda =1.62\mu m$ and 1.75μm the field is slightly enhanced. For monitor 0-0.8-0, light field is obviously enhanced at $\lambda =1.75\mu m$ and 2.19μm, and no enhancing effect can be seen at $\lambda =1.62\mu m$. For near field intensity at monitor 0.6-0-0, it has been evenly enhanced at $\lambda =1.62\mu m$ and 1.75μm, and is temperately enhanced at $\lambda =2.19\mu m$. For incident light with $\theta =30\mathrm{deg}$, $\phi =0\mathrm{deg}$, the electric field is enhanced at $\lambda =1.62\mu m$ and 1.75μm, temperately enhanced at $\lambda =2.19\mu m$ at monitor 0-0-0. At monitor 0.4-0.4-0.57, the intensity line is obviously enhanced at λ = 2.19μm, slightly enhanced at $\lambda =1.62\mu m$ and 1.75μm like previous cases. For monitor 0.6-0-0, the field intensity reach to its first and secondary peaks at $\lambda =1.62\mu m$ and 2.19μm, no peak can be found at $\lambda =1.75\mu m$. As for monitor 0-0.8-0, the field is enhanced at $\lambda =1.75\mu m$ and 2.19μm, no peak can be found at $\lambda =1.62\mu m$.

The spectral maximum field intensity can be seen in Table 1, at monitor 0-0.8-0, the electric field has been greatly enhanced, whose value is almost 20 times larger than the incident light. While in monitor 0.6-0-0, even the for maximum intensity in all the cases, it will not exceed the intensity of incident light. In this case field might be too weak that hot-spot cannot be generated. For monitor 0-0-0 and 0.4-0.4-0.57, orders of value for maximum intensity and incident light are the same, which means hot-spots have been moderately induced at those two locations.

Table 1. Value of the spectral |E_max| / E₀ for different monitors and incident geometric features.

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In order to investigate electromagnetic energy density distribution inside the structure, 5 crossing sections have been chosen as shown in Fig. 5. The energy density distributions of monochromatic electromagnetic field in specific crossing sections have been shown in Figs. 6-8. The energy density is defined as [29]:

 

Fig. 5 Schematics of the 5 crossing sections employed to observe electromagnetic energy density.

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Fig. 6 Electromagnetic energy density distribution within various crossing sections and wavelengths at 1.62μm

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Fig. 7 Electromagnetic energy density distribution within various crossing sections and wavelengths at 1.75μm.

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Fig. 8 Electromagnetic energy density distribution within various crossing sections and wavelengths at 2.19μm.

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As can be seen in Fig. 6 at 1.62μm, with $\theta =0\mathrm{deg}$, $\phi =0\mathrm{deg}$, two hot-spots can be seen in the conjunctions between bottom layer of nanopaticles in 0X section. With $\theta =0\mathrm{deg}$, $\phi =20\mathrm{deg}$, the change of incident angle has influenced the energy density distributions. The hot-spots within the junctions between bottom layer of nanopaticles vanish at 0X section. With $\theta =30\mathrm{deg}$, $\phi =0\mathrm{deg}$ at 0X section, the hot-spots located at z = 0 sustain, with a slight variation at 1.62μm. At 0Y section, field has been enhanced along the surface of particles, located in the cavity between top and bottom layer of nanoparticles with $\theta =0\mathrm{deg}$, $\phi =0\mathrm{deg}$. At the $\theta =0\mathrm{deg}$, $\phi =20\mathrm{deg}$, though the field distribution above the structure has changed, the inner enhancing pattern sustain. Whereas at $\theta =30\mathrm{deg}$, $\phi =0\mathrm{deg}$, enhancement locates at the junctions between bottom layer of nanopaticles. For sections 1X and 1Y, at the conjunctions between top and bottom layers of nanoparticels, the electromagnetic field has been greatly concentrated that only two symmetrically distributed bright hot-spots can be seen in the contour. The enhancing pattern has shown incident angle φ independence, while at $\theta =30\mathrm{deg}$ field is asymmetrically enhanced at the conjunctions.

Field distribution at 1.75μm has been shown in Fig. 7. At 0X section, no matter how the incident geometric features have changed, the enhancement between the bottom layer of nanoparticles changes slightly. At 0Y section with θ = 0 deg, the field has been enhanced along the surface of particles, located in the cavity between top and bottom layer of nanoparticles. At $\theta =30\mathrm{deg}$, $\phi =0\mathrm{deg}$, the energy density distributions can be seen as the hybridization of 0X and 0Y sections at $\theta =0\mathrm{deg}$, $\phi =0\mathrm{deg}$. That is, electromagnetic density has been concentrated along the surface within the cavity, while the hot-spots have also been generated. For 1X and 1Y section, the electromagnetic fields have been greatly concentrated at the conjunctions between top and bottom layers of nanoparticels, symmetrically distributed for $\theta =0\mathrm{deg}$ and asymmetrically for $\theta =30\mathrm{deg}$. As easily can be seen, in Fig. 8, the field distributions for 2.19μm have exhibited similar pattern with 1.75μm.

4. Physical picture for electromagnetic wave oscillating within the nanostructure

As noted in [27], the hot-spots in the nanocluster originate from the collective oscillating of electromagnetic wave. Wherein the particles can be seen as inductor, the junctions between them can be seen capacitor, and the nanocluster has made an equivalent inductor-capacitor loop. With the match of external excited field and intrinsic mode, great local field enhancement can be achieved, named as hot-spot. As the electromagnetic field is greatly enhanced in specific parts, it is quite similar with bond in atomic crystal as electron waves are concentrated around the bond. Despite field distributions varies case to case in Figs. 6-8, the collective oscillating inside the structure has made very little portion of light pass through the nanoparticle-crystal, making optical response nearly independent of substrate. To verify the collective electromagnetic oscillating mode occurred at 1.62μm, the dispersion relationship of surface plasmonpolariton has been employed.

The SPP originates from the collective oscillation of electrons and photons, when the intrinsic surface plasmon mode matches the wavevector scattered by the periodic structure. The pivotal factor of the structure is its period, while the inner geometric features affect the resonance little, so cavity and grating structure can get similar resonant equations [30,31].When the in-plane wavevector satisfies the dispersion relation as [31]:

Surface plasmon polariton can be excited in the interface of two dissimilar materials with permittivities ε₁ and ε₂. In the periodic grating, the in-plane wavevector can be matched for diffracted wave with grating Bloch condition:

As shown in Fig. 9(a), the field distribution also indicates surface plasmon ploariton has been excited. The electric vectors make up a current loop above the structure, with the enhancement along air-metal surface. The strong coupling between the incident light and intrinsic plasmon mode results in the collective oscillating and hot-spots inside the structure, as shown in Figs. 6-8. Also, the resonant wavelength of surface plasmon polariton is dependent with the incident wavefront with $k_{inc}=k_0\sin \phi$. Thus as incident angle shifts from 0 to 20deg, the mismatch of external field and intrinsic mode results in a vanished hot-spots as shown in Figs. 6-8. Moreover, despite resonant wavelength is independent of incident wavefront, surface plasmon polariton originates from the coupling between electric field and electric response material, and cannot exist for non-magnetic material with transverse electric wave showing obvious polarization dependence [29]. Thus as polarization angle changes from 0 to 30 deg, the hot-spots exist but distributes asymmetrically.

 

Fig. 9 Field distributions within the structure. The contours indicate the magnetic field distributions, the arrows represent for electric vectors. Visualizations of every crossing distribution can be seen in the supplemental material Visualization 1, Visualization 2, Visualization 3, Visualization 4, Visualization 5, and Visualization 6 corresponding to Fig. 9(a)-9(f).

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Back to Fig. 9, the 0Y sections have shown the general field distribution inside and outside the structure, and 1Z sections can be seen as the internal distribution within the structure. The visualizations of oscillating proposed in Figs. 9(a)-9(f) can be seen in the supplementary Visualization 1, Visualization 2, Visualization 3, Visualization 4, Visualization 5, and Visualization 6. It can be easily seen that at 1.62μm with surface plasmon polariton excited, the external mode has dominated the collective oscillating associated with a secondary internal oscillating mode. So surface plasmon polariton can be seen as a global collective oscillating. While at 1.75μm and 2.19μm, the internal oscillating has been fully induced comparing with 1.62μm, but no obvious external oscillating has been observed. It can be concluded that the double incident angle and polarization angle independent absorption peaks originate from the internal collective oscillating. Though global mode has been excited, it does not result in absorption. The double abosrptivity peaks originate from the internal oscillating inside the structure, as an analogy to intrinsic surface plasmon mode. This collective oscillating can also be seen as an intrinsic mode of that kinds of double layer nanoparticle-crystal, independent of external incident and polarization angle.

In order to further investigate the spectral oscillating absorption, a three oscillators model has been proposed in this paper, as shown in Fig. 10. When the light is illuminated to the structure, optical oscillations can be excited, quite similar to the oscillator bounded by spring. Similar with the mechanical oscillation, there is interaction between resonant modes, so spring is introduced to indicate the coupling effect between modes. The light dissipation in the structure has been described by the damping effect. In the model, every oscillator stands for a resonant mode, with resonant wavelength at 1.62μm, 1.75μm and 2.19μm. At 1.75μm and 2.19μm, as the resonance comes from the local resonance, oscillators on the left and right have been utilized to stand for them with harmonic driving sources. At 1.62μm, the oscillation originates from collective resonance with external field and internal structure, thus the oscillator in the central with no driving source has been utilized to stand for it.

 

Fig. 10 (a) Schematic of the three oscillators model. (b) Optical property obtained from FDTD method and analytical model. (c) Phase of the oscillator 2 as a function of energy.

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The displacement equation of that three oscillators can be written as:

That complex amplitude can take the form as $c_2=\left|c_2\right|e^{i\phi 2}$, has the modulus |c₂| and phase φ2. The dissipating rate of the system d can be written as $d=i\omega \gamma c_2{e}^{i\omega t}$, and |d| describes the dissipating amplitude of the system.

By setting $v_{12}=v_{23}=0.1$, $\gamma =1.1$, $a=0.14$, ${\omega }_1=0.57\text{eV}$, ${\omega }_2=0.77\text{eV}$, ${\omega }_3=0.70\text{eV}$, the red ball in the middle stands for global oscillating mode, and the blue and green balls stand for the internal oscillating modes. As can be seen in Fig. 10(b), double power dissipating peaks predicted by the oscillator mode well match the absorptivity line obtained from FDTD method. The spectral reflectivity of single layer particle array has also been shown, with a dip in 0.77eV, which stands for surface plasmon polariton. This can be explained that whether surface plasmon polariton can be excited does not depend on the internal structure in a period, but the length of a period itself [29]. Also, the double absorption peaks vanish within the single layer, indicates that the internal oscillating mode originates from the coupling between the top and bottom layer of nanoparticles. The phase of oscillator 2 has also shown in Fig. 10(c), at $\omega =0.57\text{eV}$ and 0.70eV which stand for the double absorptivity peaks, the phase is π and 0, means the real parts of the complex amplitude has reached its maximum.

5. Conclusion

In this paper, a double layer nanoparticle-crystal which serves as prototype of novel meta-coating has been proposed. Spectral normal absorptivity of this kinds of nanoparticle-crystal has shown incident and polarization angle independences, and optical properties of substrate also affect it little. The physics have been confirmed as the hot-spots induced by internal electromagnetic wave oscillating. A three oscillators mode has been proposed to understand the shift between global and internal modes, and verify the physical picture drafted in this paper.