1. Introduction

Plasmonic nanostructures have been developed to modify the light propagation behaviors such as their reflection [1], transmission [2], and absorption characteristics [3] for various applications and novel physics [4]. At the beginning stages of the meta-material design evolution, considerable interests were mainly focused on the realization of three-dimensional bulk meta-materials and metallic structures [5]. Nevertheless, study interest recently shifts toward two-dimensional and layered meta-surfaces [6–8] since they can exhibit higher potential for fabrication and provide wider applications in optical sensing [9–11], light energy harvesting and photo-thermal applications [12,13]. These studies were mainly focused on the metallic elements and their resonant plasmonic nano-structures. Nevertheless, the inherently high loss of metallic materials limits their further applications.

In order to avoid the drawback and to increase the feasibility of fabrication, comprehensive studies were conducted on the all-dielectric meta-materials or meta-surfaces by utilizing Mie resonances and their far-field coupling effects [14–17]. Based on the optical resonators consisting of high-index dielectric (HID), strong electric and magnetic dipole modes can be excited [18,19]. These resonant modes can be utilized to efficiently modify the electromagnetic wave propagation [20–23]. Spectral hybridization and narrowband light transmission behaviors have been developed in all-dielectric meta-materials or meta-surfaces [15]. Although novel approaches for light manipulation have been shown based on these resonant dielectrics [20–25], there is still with the need of a feasible way for efficient light transmission/reflection propagation controlling. In addition, it is also difficult to overcome the fabrication issue since the precisely controlled gap distance with nanometer level is the key point for achieving narrowband transmission in dielectric metamaterials [15,24].

The focus of this work is to implement the concept of HID meta-surface for light propagation manipulation by utilizing an ultra-thin dielectric film, which is partially perforated with an air cavity array. Strong electric, magnetic resonances and hybridized coupling between the HID slits and the film cavity are the main contributions for the multi-band sharp transmission manipulation. The sharp and narrowband transmission platform can hold potential applications in filtering, optical signal process and non-plasmonic metamaterial behaviors including the enhanced electromagnetic fields without undesirable losses [26].

2. Method and materials

In contrast to the need of complex and precise structural features for the multimer systems and the intrinsic broadband spectral response in single resonator systems [14,27–29], we propose and demonstrate a novel dielectric meta-surface platform for sharp transmission manipulation. As depicted in Fig. 1(a), the partially hollowed dielectric meta-surface (p-HDMS) consists of a hexagonally packed air cavity array with a height of h, which is intercalated in the HID film (thickness, t). The period P of the cavity array and the width w of the cavity are 800 nm and 600 nm, respectively. The HID resonant structure used here is made of silicon (Si) with permittivity of 12.25 and the background medium is 2.25, i.e., SiO₂. Three-dimensional finite-difference time-domain method [30–32] has been employed to calculate the spectral response and the field distributions. Periodic boundary conditions are used in the x- and y-directions to reproduce the periodic array (Fig. 1(a)). This proposed structure can be feasibly obtained by using the standard lithography and other patterning techniques since it only needs a simple hollowing process in the flat HID film [2,33].

 

Fig. 1 (a) Schematic of the partially hollowed dielectric meta-surface (p-HDMS) consisting of a hexagonally packed air cavity array (height, h) in the HID film (thickness, t). (b) Transmission and reflection of the p-HDMS. Four transmission dips are noted as λ₁-λ₄. (c) Transmission spectra of a continuous HID film with t = 250 nm (black line) and the HID film with an air cavity array (h = 250 nm, red line).

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3. Results and discussion

Figure 1(b) shows the transmission and reflection spectra of the p-HDMS with a hollowed air cavity array (P = 800 nm, w = 600 nm, t = 250 nm, h = 100 nm). Four sharp transmission dips (λ₁-λ₄) are observed in the near-infrared frequencies. For the first transmission stop-band at λ₁, spectral intensity is changed from 0.99143 at 1.150 μm to 0.00374 at 1.154 μm. The maximal spectral slope exceeds 51%/nm, indicating an ultra-sharp transmission filtering response. That is, within a 4 nm spectral shift, a complete transformation between the near-perfect light transmission (“bright” window) and the transmission inhibition (“dark” window) can be achieved. At 1.268 μm, transmittance (T) is 0.00001, suggesting a complete suppression of transmission. For the third dip at λ₃, T is increased from 0.00312 to 0.96800 with the spectral wavelength shifted from 1.729 μm to 1.735 μm. For the dip at λ₄ = 1.768 μm, spectral intensity is 0.00225. For the reflection spectrum, four peaks are observed at the corresponding resonant wavelengths for the transmission inhibition bands. These features confirm a double-direction filtering for the reflective and transmissive propagation manipulation. In addition, it should be noted that only one layer of dielectric with an approximate thickness of λ/6 is employed for the multi-band sharp transmission manipulation, suggesting an ultra-thin dielectric meta-surface with strong electric and magnetic resonances [14–16].

Figure 1(c) presents the transmission responses for the continuous flat HID film without the air cavity array and the completely hollowed HID film structure. A broadband spectrum response for the flat HID film with t of 250 nm is observed due to the cavity resonances [2]. The spectral positions of the enhanced reflection and inhibited transmission can be obtained based on the optical interference theory followed by kλ = 2nt + λ/2, where k is the order of the resonance and the λ/2 is the additional optical path difference for this device. For instance, the observed transmission dip (T = 0.37934) at λ = 1.167 μm is the exact result of the case with k = 2, suggesting the excitation of the 2th cavity resonance by the film. The transmission peak centered at 1.750 μm is the main result of the destructive interference of the reflection with k = 1, which therefore leads to a high transmission. In contrast to these broadband transmission windows by the flat HID film, a complete transmission stop-band is observed λ = 1.247 μm (T = 0.00012) for the HID film hollowed by an air cavity with h equal to the film's thickness t owing to the excitation of the dipolar resonance by the HID slits built by the adjacent air cavity dimmers [14,16,20].

Normalized electric field intensity distributions for the transmission dips at λ₁-λ₄ in the xoz plane are shown in Figs. 2(a)-2(d), respectively. Corresponding magnetic field distributions for the transmission dips at λ₁-λ₄ are shown in Figs. 2(e)-2(h), respectively. At λ₁, strong electric field is confined in the HID film and the magnetic field is mainly distributed at the surfaces of the film, suggesting the excitation of the film cavity mode. For the dip at λ₂, the electric field is mainly confined at the rear sides of the slits coated on the film, suggesting the dipolar resonance excited by the slit resonators built by the adjacent air cavities. This is confirmed by the magnetic field distribution with the main field located on the areas close to the slits. At λ₃, the main electric and magnetic fields are confined in the film area with only one main point of the pattern, indicating the excitation of the 1th resonant mode by the film cavity. These features eventually lead to a transmission stop-band. At λ₄, the main electric and magnetic fields are observed at the proximity areas of the slit resonators. The distribution patterns suggest the lattice resonance by the diffractive coupling in the periodic array [7,34] and the hybridized coupling to the 1th mode of the film cavity. Thereby, the excitation of the dipolar resonances of the slit particles and their coupling with the film modes by the HID cavity is the main contribution for the observed multispectral sharp transmission manipulation.

 

Fig. 2 (a)-(d) Normalized electric field intensity distributions for the transmission dips at λ₁-λ₄ in the xoz plane, respectively. (e)-(h) Normalized magnetic field distributions for the transmission dips at λ₁-λ₄ in the xoz plane, respectively.

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Figure 3(a) shows the contour mapping of transmission evolution with increasing the polarization angle from 0° (electric field paralleling to x-axis) to 90° (electric field paralleling to y-axis) with a step of 10°. Distinct spectral responses for the dips are observed. In addition, a new transmission dip (λ_dip) emerges under a large polarization angle. Figure 3(b) shows the plotted curves for the transmittance of the dips as a function of polarization angle. For the dips at λ₁ and λ₄, the spectral intensity is nearly invariable. This is because the dips (λ₁ and λ₄) are the main results of the cavity resonance of the film and the lattice resonance of the array, which are with polarization-independent response. For the other dips, the intensity curves show clear evolution with tuning the polarization states. To well understand the evolution, the corresponding theoretical Malus law (I = I_o(cosϕ)^2, where I is the transmission intensity and I_o is the illumination intensity and ϕ is the polarization angle) [20,35] based transmission intensity curves for the dips (λ₂ and λ_dip) are shown in Fig. 3(b). The transmission curves are reproduced well by the classical Malus Law, suggesting a multispectral filtering with polarization adjusting response.

 

Fig. 3 (a) Contour mapping of the p-HDMS with a cavity array under a tuning polarization state. (b) Plotted transmission curves for the dips at λ₁-λ₄ and the new emerged dip (λ_dip) as a function of polarization angle. The corresponding theoretical Malus law curves of the dips (λ₂ and λ_dip) are also plotted for comparison study.

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With decreasing the cavity width from 650 nm to 550 nm, a four stop-band transmission behavior with the corresponding spectral red-shift is observed in Fig. 4(a). The spectral shift is the main result of the larger refractive index since a smaller cavity width can lead to a larger HID slit resonator. Moreover, much narrower transmission bands are obtained for the system with a larger cavity array. For instance, the bandwidth of 4 nm is observed for the first transmission dip for the system with a w of 650 nm, which leads to a ultra-high quality factor of 285 and indicates orders of magnitude than that of the conventional plasmonic resonant structures [9,11]. Moreover, the maximal and average spectral slopes exceed 80%/nm and 44%/nm for the third dip at λ = 1.709 μm. These features confirm the ultra-sharp transmission manipulation by this simple p-HDMS structure. With increasing the hollowing height of the cavity, spectral stop-bands with a broadened evolution and the number of the stop-bands drops down to two for the deeply hollowed system with h of 200 nm are observed in Fig. 4(b). These features provide alternative way for tuning optical properties.

 

Fig. 4 Scalability of the transmission manipulation for the p-HDMS with a cavity array (P = 800 nm, h = 100 nm) by tuning the cavity width (a) and by tuning the hollowing height of the air cavity (b) within a 250-nm-thick HID film. (c) Transmission response of the p-HDMS under a tuning refractive index n of the HID film. (d) Transmission comparison of the p-HDMS comprised of lossy and lossless HID film.

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Figure 4(c) shows the spectral responses of the system with different refractive index n of the dielectric film. With n of 1.45, there is no obvious transmission band in the spectrum. High light transmission is observed in the whole spectral range for the structure with a low n due to the absence of the Mie resonance for efficient optical field coupling and confinement. Increasing n to 2.0, dual-band transmission dips are observed. For the case with a larger n (2.5 and 3.0), tri-band transmission spectra are observed. In addition, a red-shift in the spectrum is observed. These findings not only confirm the necessary of high-index dielectric for efficient optical field interaction and light propagation manipulation but also pave a way to achieve two or three sharp transmission windows by utilizing different dielectric resonators. Figure 4(d) shows the transmission comparison of the p-HDMS comprised of lossy and lossless HID films. It is observed that the transmission spectrum is well reproduced by the system with actual dielectrics. Overall, multi-band sharp transmission is observed to be supported by the Si dielectric structure since there is rather weak absorption loss in the infrared region [36]. Moreover, only an air cavity array is needed to be simply introduced in the HID film for the proposed p-HDMS. Thereby, these optical properties and simple structural features can hold the proposed p-HDMS with applications in filtering, propagation manipulation and so on.

4. Conclusion

We have proposed and demonstrated a simple and universal strategy for multispectral light propagation manipulation by utilizing a partially hollowed dielectric meta-surface. In contrast to the broadband transmission response with a weak modulation depth in a thin HID film, multispectral transmission band-stop response with near-perfect spectral modulation depth is achieved for the p-HDMS. The spectral slop is up to 80%/nm, indicating sharp and narrowband transmission behaviors. Moreover, classical Malus law is confirmed in this optical filtering platform. Such configurations can serve as excellent alternatives for plasmonic meta-surfaces especially that it can be a scalable design.