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Abstract
A flexible all-dielectric metamaterials composed of single-layer ceramic microspheres embedded in elastomeric medium is proposed and experimentally demonstrated in terahertz (THz) range. The THz waves are strongly confined in the high-permittivity and low-loss ceramic (ZrO2) microspheres resulting in remarkable Mie magnetic resonances, which can be effectively tuned with strained elastomeric medium. The first resonance mode would experience red shifts with the increased strain along magnetic field direction, while it would experience blue shifts with the increased strain along electric field direction. These properties are well explained by dipole-dipole coupling theory. This work provides an easy and cheap method to obtain tunable all-dielectric metamaterials in THz range.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The term “metamaterials” refers to artificially structured medium whose electromagnetic properties can be described by effective parameters such as effective permittivity and effective permeability. With its exotic properties which are usually not found in nature, like negative refractive index [1], perfect lens [2], invisibility cloak [3] and perfect absorber [4], metamaterials, especially metallic metamaterials, have been widely investigated in various frequency ranges. Although much progress has been made during the past years, metallic metamaterials have also some drawbacks, such as serious Ohmic loss and anisotropic property [5–7]. Recently, all-dielectric metamaterials based on the Mie resonances have gained considerable attention owing to their low intrinsic loss [8–16]. During the past few years, much progress has been made in all-dielectric metamaterial based photonic devices and considerable applications have been reported.
Recently, the all-dielectric metamaterials in THz ranges have also investigated by several groups [12–15]. Usually, once the geometric and material parameters are designed, the corresponding optical responses are determined. From the viewpoint of practical application, the capability of actively tuning their optical properties becomes increasingly important. While various tunable all-dielectric metamaterials have been reported in microwave and optical ranges, tunable all-dielectric metamaterials in THz range are rarely reported, except for the strontium titanate (STO) all-dielectric metamaterials [15].
Here, we investigate a flexible all-dielectric metamaterials in THz range. It is composed of single-layer ceramic microspheres embedded in elastomeric medium. With the help of THz-TDS system, the strain-dependent responses are measured and analyzed to demonstrate its good tunability. It should be noted that the tunable metallic metamaterial based on strained elastomeric medium has also been reported by Li [17].
2. Design and preparation
The simplified process for the flexible all-dielectric metamaterials, sketched in Fig. 1, begins with the fabrication of micro zirconia (yttria-stabilized) spherical particles. The reason why we select micro-zirconia (yttria-stabilized) spherical particles is because of their easy fabrication. In addition, they are also commercial available. The zirconia (yttria-stabilized) spherical particles are prepared by inorganic sol–gel process, which has been reported by Belov [16]. To prepare flexible all-dielectric metamaterials, a stainless steel container is fabricated by traditional mechanical machining method (Fig. 1(a)). A piece of tape is used and spherical particles are placed on it to make sure that single-layer spherical particles are attached to the tape firmly. Then, the tape is turned over to remove the redundant particles to obtain nearly single-layer all-dielectric metamaterials on it. The tape-based all-dielectric metamaterials is then placed on the bottom of stainless steel container while keep the particles face upward (Fig. 1(b)). To transfer these particles into flexible substrate, the polydimethylsiloxane (PDMS) polymer is casted into the stainless steel container and the particles are embedded in PDMS (Fig. 1(c)). After cured for 24 hours, the PDMS film and particles are peeled off. Finally, flexible all-dielectric metamaterials is obtained, as shown in Fig. 1(d). Figure 2 shows the fabricated flexible all-dielectric metamaterials. As provided in Fig. 2(a), using inorganic sol–gel process method, nearly uniform micro zirconia (yttria-stabilized) spherical particles with a diameter of 70 μm can be prepared. Figure 2(b) shows the SEM photograph of flexible all-dielectric metamaterials, where the spherical particles are embedded in the PDMS. The side view of flexible all-dielectric metamaterials is provided in Fig. 2(c), where one can find that single-layer spherical particles are arrayed in the PDMS. The photograph of flexible all-dielectric metamaterials is shown in Fig. 2(d).
Fig. 1 The process flow of flexible all-dielectric metamaterials: (a) Fabrication of stainless steel container. (b) Single layer of micro zirconia (yttria-stabilized) spherical particles is placed on the container. (c) Casting PDMS into the container to form all-dielectric metamaterials. (d) Peeling the flexible all-dielectric metamaterials from the container.
Fig. 2 The fabricated flexible all-dielectric metamaterials: (a) The photograph of micro zirconia (yttria-stabilized) spherical particles. (b) The top view of flexible all-dielectric metamaterials. (c) The side view of flexible all-dielectric metamaterials. (d) The photograph of flexible all-dielectric metamaterials. (e) The measured transmission spectrum of flexible all-dielectric metamaterials, the inserts are the magnetic field and electric field distribution at the transmission dip, respectively.
3. Results and discussion
The fabricated sample is characterized by a photoconductive switch-based THz-TDS system, which has been reported by Yang et al. [14]. The transmission spectrum under no strain is shown in Fig. 2(e), where one can find that a remarkable transmission trough appears at 0.801THz, corresponding to the first Mie resonances of spherical particles. To give deep insight into the underlying physics of this transmission, simulations based on the finite-element soft, CST Microwave studio, are carried out to obtain the corresponding magnetic field and electric field distribution. As is shown in this picture, one can find that linear magnetic field and circulating electric field are induced in the particle, confirming the magnetic resonance.
The transmission spectrum measurements based on THz-TDS system are performed to demonstrate the tunability of prepared metamaterials. The transmission spectrums are conducted under mechanical strain, both applied uniaxially along the E direction and H direction, as shown in Fig. 3. To introduce mechanical strain, the sample is fixed on a custom-built stage. The mechanical strain can be produced by moving the graded micrometer screw. Here, the mechanical strain can be described as (l-l0)/ l0 × 100%, where l0 is the initial length of fabricated sample.
Fig. 3 The strain-dependent response of flexible all-dielectric metamaterials. (a) The response with strain direction along electric field. (b) The response with strain direction along magnetic field.
When the strain direction of applied mechanical strain is along E direction, the measured transmission spectrum is provided in Fig. 3(a). Various applied mechanical strains, namely 0%, 2%, 4%, 6%, 8% are considered in our study. As shown in Fig. 3(a), as the applied mechanical strain increases along E-direction, the transmission troughs shift towards to high frequency. Quantitatively, it can be found that as the applied mechanical strain increases from 0% to 8%, the first transmission trough shifts from 0.801 THz to 0.764 THz, namely 0.037THz tunability. When the strain direction of applied mechanical strain is along H direction, the measured transmission spectrum is provided in Fig. 3(b). As shown in this figure, the first transmission trough shifts towards to high frequency. Quantitatively, it can be found that as the applied mechanical strain increases from 0% to 8%, the transmission trough shifts from 0.801 THz to 0.845 THz, namely 0.044THz tunability.
To give a deep insight into the underlying physics of mechanical strain dependent transmission trough, one can use dipole-dipole coupling theory model [18]. The level scheme of coupled dipoles (for example, two coupled dipoles) is plotted in Fig. 4, which includes transverse and longitudinal coupling. As for transverse coupling, two cases can be considered. The first one is that the dipoles are coupled as antisymmetric mode, in that case the dipoles would attract each other, thus reducing the restoring force and leading to a lower frequency. In contrast, another one is that the dipoles are coupled as symmetrical mode, where the dipoles would repulsive each other, thereby enhancing the restoring force and leading to a higher frequency. In the case of longitudinal coupling, the coupling effect is similar. When the dipoles are coupled as antisymmetric mode, the dipoles would repulsive each other, resulting in a higher frequency. In contrast, when the dipoles are coupled as symmetrical mode, the dipoles would attract each other and bring out a lower frequency. With the dipole-dipole coupling theory model discussed above, the mechanical strain dependent transmission trough can be explained easily.
Fig. 4 The underlying physics of strain-dependent response of flexible all-dielectric metamaterials. (a) The level scheme of coupled dipoles. (b) The simplified model for flexible all-dielectric metamaterials. (c) The case for strain direction along magnetic field (d) The case for strain direction along electric field.
For simplify, we assume that the particles are well ordered in x and y directions (with periodic lattice in x and y directions, dx and dy, respectively), as shown in Fig. 4(b). In such case, the magnetic resonance mode is equal to magnetic dipole and only symmetrical coupled mode occurs due to the symmetrical structure. When the applied strain is along magnetic field, dx would increase and dy would decrease. As a result, the transverse coupling effect would be enhanced and the longitudinal coupling effect would be reduced, both of which would make the magnetic resonance shift to higher frequency. In contrast, when the applied strain is along magnetic field, dx would decrease and dy would increase. Consequently, the transverse coupling effect would be reduced and the longitudinal coupling effect would be enhanced, both of which would lead to a red shift of magnetic resonance.
Simulations are carried out to corroborate the theory used above based on the CST and finite element modelling (FEM). Firstly, the mechanical simulations are performed to obtain the deformation of ceramic microsphere/ PDMS composite with various strains along x- direction. As provided in Fig. 2(a), it can be found that the filling fraction of ceramic microsphere is about 60%. As a result, the composite can be equivalent to a metamaterial, which is composed of periodically arrayed ceramic microspheres imbedded in PDMS (the diameter of microsphere is 70 um and the periodic lattice is 80 um, respectively). The 800 um × 800 um (x × y) PDMS substrate with density of 965 kg m−3, Young’s modulus of 20 MPa and Poisson’s ratio of 0.40, is employed. The Young’s modulus and Poisson’s ratio of microsphere are 210 GPa and 0.30, respectively. The simulated deformations with various strains (2%, 4%, 6%, 8%) along x-direction are shown in Fig. 5 (b) - (e). Meanwhile, the obtained changes in unit cell size with strain along the x-direction are shown in Fig. 5(f). Clearly, the simulated deformations are in agreement with the ones predicted above. Based on these results, the simulated strain-dependent responses of flexible all-dielectric metamaterials are shown in Fig. 6. As is shown this picture, when the strain increases, the magnetic resonance shifts to lower frequency with strain direction along electric field while it shifts to higher frequency with strain direction along magnetic field. These results are in agreement with the experiment ones, confirming the feasibility of dipole-dipole coupling theory model used above.
Fig. 5 (a) The equivalent all-dielectric metasurface used in the simulations. (b) - (e) The simulated deformation with various strains (2%, 4%, 6%, 8%) along x-direction. (f) The change in unit cell size with strain along the x-direction.
Fig. 6 The simulated strain-dependent response of flexible all-dielectric metamaterials. (a) The response with strain direction along electric field. (b) The response with strain direction along magnetic field.
4. Conclusion
In conclusion, we have demonstrated a kind of flexible THz all-dielectric metamaterials, which is composed of single-layer ceramic microspheres embedded in elastomeric medium. It is shown that remarkable magnetic resonance can be induced in the high-permittivity and low-loss ceramic (ZrO2) microspheres. We have found that the magnetic resonance can be effectively tuned by mechanical strain, which can be explained by dipole-dipole coupling theory. It is expected that it provides an easy and cheap method to obtain tunable all-dielectric metamaterials in THz range.
Funding
National Natural Science Foundation of China (NSFC) Grants 61774020 and 51402163; National Key Research and Development Program of China Grant 2017YFB0406300; Director Funds of Beijing Key Laboratory of Network System Architecture and Convergence.
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