1. Introduction

The accurate manipulation of electromagnetic waves has long been one of the ultimate targets for scientists on materials and electronic engineering alike. With the thriving developments of metamaterials, we are one step closer to that dream. Novel phenomena unseen in nature, most notably the negative refraction index [1], invisible cloak [2], and perfect lens [3], have all been realized in the past two decades, pushing the boundaries of human knowledge into uncharted waters, thanks to the advances in metamaterials. With customizable structures, constituents and dimensional sizes, the concept of metamaterial offers considerable freedom towards exotic properties and applications.

One of the noteworthy developments lies in the combination of metamaterials with flexible substrates. It has long been known that some of the metamaterials conventionally fabricated over rigid substrates can exhibit fine tunability. With elaborate design, such tunability could be integrated onto flexible substrates as well, offering not only the portability, deformability and extra durability while preserving original strengths, also providing intriguing potentialities for new functionalities originating from this combination [4]. With mechanical forces applied onto the flexible components, structural lattices or the shape of “meta-atoms” will experience deformation, resulting in controllable changes in the electromagnetic responses [5]. Nowadays, metamaterials over flexible substrates have demonstrated their capacities under a wide range of frequency bands, from microwave [6,7] and terahertz regions [8–11], to infrared [12,13] and visible light [14], as well as aforementioned features such as negative index metamaterials [15], chiral metamaterials [16], wavelength-selective surfaces [17], perfect absorbers [18], strain sensors [19], etc. Moreover, in an attempt to achieve better versatility and diverted functionalities, efforts have been made to extend 2D planer structures towards 3D units directly constructed from flexible materials. The use of conductive rubber as classical metamaterials unit “split ring resonator (SRR)” [20], and helical resonators made of thin copper wires for nonlinear responses [21], serve as two of such examples.

Despite the benefits, metal-based metamaterials suffer from the inherent Ohmic losses from conductive currents. That is why research attentions have been focused on the alternative approach of all-dielectric metamaterials [22,23], which employ Mie-resonance [24] to achieve strong electromagnetic coupling and light-matter interactions. Given proper design and fabrication, dielectric metamaterials can be readily utilized to obtain isotropic resonant behaviors which is much more challenging for the metallic counterparts [25]. Thanks to the rapid developments of micro/nano-fabrication technologies, such all-dielectric nanophotonic devices can be produced via laser-ablation technique [26] or electron-beam lithography [27]. However, when it comes to large-scale productions, these approaches might encounter bottlenecks from the high costs and complexities in process designs. In contrast, nanosphere lithography (NSL) is a promising method for fabricating regularly-arrayed nanoparticles [28] yet with much simplified processes and relatively good affordability, which opens up new possibilities for patterning all-dielectric metamaterials or metasurfaces. As an example, all-dielectric perfect reflectors with an average reflectance surpassing metallic mirrors have been successfully fabricated via NSL [29]. The technique may find wider scopes of applications in conjunction with flexible substrates.

In this paper, we report a flexible, all-dielectric metasurface fabricated via nanosphere lithography, and its potentialities in sensing application. The attachment of dielectric arrays to flexible substrate offers enhanced freedom and flexibility towards achieving tunability. Resonant behaviors of the metamaterial at visible wavelengths are found sensitive to the applied strain and surface dielectric environment. Numerical simulation results also conform with experimental findings. It shows that the resonant peak is the effect of coupled magnetic Mie resonance, which clarifies the underlying physical mechanism.

2. Sample fabrication and morphology characterization

Key procedures for the fabrication of the metasurface are depicted in Fig. 1. Polyethylene terephthalate (PET), a polymer commonly used for bearing complex electronic systems, ischosen as the flexible substrate, taking advantage of its optical transparency at visible wavelengths [4]. Then, a thin layer of Si is deposited on PET substrate by electron beam evaporation. After that, a monolayer of polystyrene (PS) spheres is self-assembled at the air-water interface, following the approach introduced by Rybczynski et al [30]. The PS spheres form a compactly arrayed hexagonal lattice, which could be easily transferred onto the Si surface. Next, reactive ion etching (RIE), more specifically the isotropic O₂ plasma etching, is utilized to shrink the size of PS spheres, converting the close-packed pattern into a pattern with spacing between the spheres. These downscaled PS spheres act as a mask for a second RIE procedure that follows, where SF₆/C₄H₈ gas mixture is utilized to chemically etch the exposed Si thin layer. Resulting from the protection of the PS mask, Si layer right underneath PS spheres is preserved, forming discrete cylinders without disturbance to the original hexagonal lattice. Finally, the sample is immersed in chloroform coupled with sonication to remove all remaining PS spheres. In such manner, Si metasurface can be fabricated on flexible substrates. This approach is particularly well-suited for producing regular hexagonal arrays. Desired dimensional size of a single ‘meta-atom’ can be achieved by altering the diameter of PS spheres, while spacing control is achieved through the alternation of etching parameters.

 

Fig. 1 Schematic view of the main fabricating procedures for the flexible, all-dielectric metasurface.

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Figure 2(a) demonstrates the scanning electron microscope (SEM) image of a close-packed monolayer PS spheres mask produced by self-assembly technique. The average diameter of a single PS sphere is estimated at about 350 nm. A short duration of isotropic O₂ plasma etching is found to effectively trim the edges of spheres, followed by another RIE step that fully etches exposed Si layer. The SEM image of planer hexagonal lattice of Si cylinders is shown in Fig. 2(b). A small defective area is selected to better illustrate the spatial morphology, as shown in the inset of Fig. 2(b) where the metasurface sample is tilted at around 60°. The average diameter and height of a single Si cylinder is estimated at 330 nm and 170 nm, respectively. Figure 3(c) demonstrates the remarkable flexibility of the metasurface sample. The thickness of PET substrate is about 180 μm. Interference color indicates that compactly arrayed patterns are formed, conforming with SEM observations.

 

Fig. 2 SEM images of (a) self-assembled PS spheres and (b) Si cylinders formed after RIEs. Both show regularly arrayed hexagonal lattice. The inset in (b) is the tilted view (60°) of a specially chosen defective area for better illustration of the spatial morphology. Scale bars in both images represent 1 μm. (c) Final metasurface sample demonstrates its flexibility. The interference color indicates the presence of a compactly arrayed patterns.

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Fig. 3 Measured transmission spectra of the metasurface sample with and without out-of-plane strain. The resonant peak presents a red-shift when bended.

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3. Applicability in sensing

Due to their adaptable deformability and portability, flexible metamaterials are of promising prospects for sensing applications, where special functionalities are often required under specific working conditions. A good amount of studies has been carried out in thisburgeoning field. Xu et al patterned SRR structures on polyethylene naphthalate (PEN) substrate and exploited their sensitivity towards strain, surface chemical conditions and surrounding refractive index [31]. Chuo et al developed a practical method for manufacturing mixed nanohole arrays on plastic substrate and demonstrated their potentials in low-cost bio-chemical sensors [32]. Liu et al proposed an unconventional approach to the fabrication of flexible metasurfaces that can perform functions including surface-enhanced Raman scattering (SERS) sensing and information encryption [33]. Almost all of the abovementioned studies employ the effect of plasmon resonance, where metallic materials are of great importance. In contrast, we hereby present our alternative design of all-dielectric metasurface for sensing demonstrations, where a different mechanism known as the coupled magnetic Mie resonance is exploited.

To test the sensitivity of the metasurface towards applied strain, we measured transmission spectra under conditions with and without bending. The results are shown in Fig. 3. The original length of the metasurface sample without bending is about 2 cm. After applying out-of-plane strain (as shown in Fig. 2(c)), the length shortens to 1.7 cm, and the flat surface transforms into a curved surface. When no strain is applied, the resonant peak position is located at 679 nm. After exerting external force, the resonant peak moves to 690 nm, with a net red shift of 11 nm. Here we simply use the length difference of 0.3 cm between the states of bended and non-bended to define the deformation. The strain sensitivity can be roughly estimated as 36.7 nm/cm. Despite the fact that the performance might not exceed existing plasmon resonance based sensors, such all-dielectric sensors can still find good applications under circumstances where metallic-based materials need to be avoided. For instance, when sensors need to present a profile low enough not to interfere with metal detection. Furthermore, by properly designing metasurface structures and choosing appropriate operation waveband, the performance of such all-dielectric sensors can be significantly enhanced.

It is a well-known fact that Si is compatible with the majority of collosols and solutions, which makes our all-dielectric metasurface suitable for surface sensing. To investigate the relation between the resonance behavior and surface dielectric environment, we chosepolymethyl methacrylate (PMMA), a typical photoresist that is transparent to visible light, as the material for detection. PMMA was spin-coated onto the metasurface with various spin speeds in order to form layers with different thickness. The metasurface sample was then dried in an oven at a temperature of 60°C, after which the transmission spectra was measured. By immersing in acetone and rinsing with a large amount of ethanol, PMMA can be removed and the metasurface would return to its original state. The measured transmission spectra after treatment at different speeds are shown in Fig. 4(a).The extracted resonant peak positions of each curve are presented in Fig. 4(b), in which the ‘∞’ symbol in horizontal axis denotes the state when no PMMA is spin-coated. The resonant peak positions at 2000 rpm, 3000 rpm, 4000 rpm and ‘∞’ rpm are 721 nm, 716 nm, 702 nm and 679 nm, respectively. It is clearly seen that the resonant peak position shifts towards longer wavelength with the increasing thickness of PMMA. A net shift of over 40 nm between the states with thinnest and thickest layer of PMMA can be observed. Though only the detection of PMMA is presented here, some other applications including chemical sensing may be achieved with such dielectric metasurface. For example, certain Si crystallographic planes can be functionalized with some organic compounds like benzene under certain conditions [34], which offers opportunities for such dielectric metasurface to implement chemical bond sensing capacities.

 

Fig. 4 (a) Measured transmission spectra of the metasurface sample with PMMA coating under different spin speeds settings. (b) Extracted resonant peak positions from (a). The ‘∞’ symbol in horizontal axis denotes the state at which no PMMA is spin-coated. Red-shifts of resonant peak positions are observed with the increase of PMMA thickness.

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In order to better illustrate the underlying physical mechanism, numerical simulations were carried out with the aid of the Frequency Domain (FD) solver module of CST Microwave Studio. Basic simulation configuration is shown in Fig. 5(a). Unit cell boundaries with a 60° angle between the x-axis and y-axis were employed to represent the actual hexagonal lattice. The permittivity of Si was characterized by amorphous Si dispersion model in the optical regime [35]. The refractive index of PET [36] and PMMA [31] were set to 1.57 and 1.488, respectively. Other parameters conform to those in experiments. Simulated transmission spectra with various thickness of PMMA are shown in Fig. 5(b), where ‘0 nm’ indicates the original state without PMMA. The resonant peak position experiences a red-shift when increasing the thickness of PMMA, coinciding with the measured tendency shown in Fig. 4. The resonant peaks corresponding to the state without PMMA and 150 nm of PMMA are located at 695 nm and 730 nm, respectively, with a net shift of 35 nm. Slight difference between measured and simulated results can be attributed to the lattice distortion of the Si cylinders in the experimental sample, as well as the discrepancy of dielectric properties between actual materials and standard data. Field distributions at resonance without PMMA presence are plotted in Fig. 5(c) and 5(d). Figure 5(c) demonstrates the magnetic field on the x-y plane while Fig. 5(d) demonstrates the electric field on the y-z plane. We can observe that the field patterns inside each unit cell resemble those produced by a magnetic dipole oriented along x-axis. To further explain the formation of the transmission peak, simulations withvaried distance between adjacent Si cylinders are performed. As shown in Fig. 6, the resonant peak gradually disappears when increasing the distance between each unit cell. Meanwhile, a clear transmission dip would form. Thus it is the coupling effect harnessing the overlap of near fields between close-packed resonators that leads to the shape of transmission peak [37]. The resonance behaviors of such all-dielectric cylinders or disks arrays have already been studied [38]. The manipulation of the electric and magnetic dipole modes in these dielectric resonators allows one to achieve the desired band-gap and Q factor, offering a practical approach to designing and tailoring electromagnetic responses of dielectric metamaterials.

 

Fig. 5 (a) Schematic view of the basic configurations for numerical simulations. Unit cells with 60° rhombic lattice are utilized to represent the actual hexagonal arrays. (b) Simulated transmission spectra regarding different thicknesses of PMMA coated on the metasurface. The resonant peak position experiences a red-shift with the increase of PMMA coating thickness, coinciding with the measured tendency shown in Fig. 4. (c) Simulated magnetic field distribution on the x-y plane and (d) electric field distribution on the y-z plane at resonance for the original metasurface without PMMA coating.

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Fig. 6 Simulated transmission spectra with different distance between neighbored Si cylinders. The transmission peak is suppressed when increasing the spacing, accompanied with the formation of the transmission dip.

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4. Conclusions

In summary, we have fabricated a flexible, all-dielectric metasurface via the nanosphere lithography (NSL) technique, a combination of bottom-up approach and top-down approach. Testing results demonstrate potentials of the metasurface in sensing applications. Si cylinder arrays attached to PET substrate exhibit sensitivity towards applied strain and surface dielectric environment. Simulation results indicate that the transmission peak can be regarded as a result of coupled magnetic Mie resonance between close-packed Si unit cells. Contrary to most plasmon resonance based sensors, the metasurface here adopts the Mie resonance of dielectric material for the detection of surrounding changes. This offers opportunities for designing flexible photonic devices with low-loss.