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Abstract
Terahertz (THz) all-dielectric metasurfaces made of high-index and low-loss resonators have attracted more and more attention due to their versatile properties. However, the all-dielectric metasurfaces in THz suffer from limited bandwidth and low tunability. Meanwhile, they are usually fabricated on flat and rigid substrates, and consequently their applications are restricted. Here, a simple approach is proposed and experimentally demonstrated to obtain a flexible and tunable THz all-dielectric metasurface. In this metasurface, micro ceramic spheres (ZrO2) are embedded in a ferroelectric (strontium titanate) / elastomer (polydimethylsiloxane) composite. It is shown that the Mie resonances in micro ceramic spheres can be thermally and reversibly tuned resulting from the temperature dependent permittivity of the ferroelectric / PDMS composite. This metasurface characterized by flexibility and tunability is expected to have a more extensive application in active THz devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
Chuwen Lan, Di Zhu, Jiannan Gao, Bo Li, and Zehua Gao, "Flexible and tunable terahertz all-dielectric metasurface composed of ceramic spheres embedded in ferroelectric/elastomer composite: erratum," Opt. Express 26, 19043-19043 (2018)https://opg.optica.org/oe/abstract.cfm?uri=oe-26-15-19043
1. Introduction
Metamaterials or metasurfaces, made of arrayed subwavelength structures, have drawn increasing attention in recent years. This can be attributed to their fantastic properties like negative refractive index and zero index [1], as well as fruitful applications such as perfect lens [2], invisibility cloak [3] and perfect absorber [4]. Usually, the metallic structures are used as the fundamental block building. Over the past years, these structures have been widely investigated and employed to obtain vast of devices from microwave to optical ranges. However, they usually have some drawbacks, which have restricted their practical applications. For example, these metallic structures usually suffer from high ohmic loss, especially in optical ranges. Although some effort has been made [5,6], it still remains a problem. A promising method to solve this problem is using Mie resonances in high-index and low-loss resonators. According to the Mie theory, various resonances including magnetic and electric ones can be induced in these subwavelength particles. Because of their low loss and compability with complementary metal oxide semiconductor (CMOS) process, these all-dielectric metamaterials are of considerable interest and various applications have been investigated [7–9].
Recently, increasing attention has been paid to the all-dielectric metasurface in THz range, a unique frequency range which has plentiful potential applications. Over the past few years, THz all-dielectric metasurface has been reported by several groups and various devices such as grating [10], mirror [11], absorber [12] and lens [13] have been demonstrated. Usually, once the materials and geometrical parameters are chosen, the electromagnetic responses of all-dielectric metasurface are fixed. As a result, obtaining tunable all-dielectric metasurfaces becomes quite important. Several tunable all-dielectric metasurfaces have been proposed and demonstrated. For example, Němec has demonstrated a thermally tunable THz all-dielectric metasurface based on STO rods [14]. Moreover, by covering the silicon based all-dielectric metasurface with STO film, a tunable electromagnetic response has been observed by Qu [15]. In addition, our group has obtained a mechanically tunable all-dielectric metasurface with ceramic microspheres embedded in polydimethylsiloxane (PDMS) [16].
Here, we proposed and experimentally demonstrated a simple method to obtain both flexible and tunable THz all-dielectric metasurface. In this metasurface, micro ceramic spheres (ZrO2) are embedded in strontium titanate (STO) / elastomer (PDMS) composite. It is found that the Mie resonances in micro ceramic spheres can be thermally and reversibly tuned as a result of the temperature dependent permittivity of STO/ PDMS composite. Compared to previous tunable THz all-dielectric metasurface [14, 15], this metasurface has advantages of flexibility and inexpensive fabrication.
2. Design and preparation
Figure 1 shows the simplified fabrication process flow for the flexible and tunable THz all-dielectric metasurface. Firstly, the micro yttria-stabilized (0.003Vp) zirconia spheres are prepared using sol-gel process according to literature [17]. The micro yttria-stabilized zirconia spheres are chosen due to their high permittivity and low loss. Here, uniform yttria-stabilized zirconia spheres with diameter of 80 μm are used. A piece of Kapton tape is used to stick the prepared ceramic spheres and then spheres arrayed with nearly a single layer (Fig. 1(a)). Then, this tape is placed in a stainless steel container (Fig. 1(b)). A composite ink made from dispersing Nano-STO powders uniformly in PDMS polymer is casted into the container and cured at 120 °C for 1 h (Fig. 1(c)). The composite is then peeled off to obtain a flexible all-dielectric metamaterials (Fig. 1(d)). Figure 1(e) shows the scanning electron microscope (SEM) photograph of fabricated flexible all-dielectric metamaterials. It is obviously that spherical particles are embedded in the STO/ PDMS composite, with a volume filling factor of about 13%.
Fig. 1 (a)- (d) The fabrication process of all-dielectric metasurface. (e) The scanning electron microscope (SEM) photograph of fabricated sample. The insert is the SEM picture of a single-layer spheres on the Kapton tape.
To predict the THz response, the effective parameters of STO/ PDMS composite are calculated. According to previous work [18], the refractive index of STO/ PDMS composite can be expressed as:
where is the refractive index of PDMS and is the one of STO. is the volume fraction of STO. Here, the refractive index of PDMS is nearly temperature independent () [19]. Unlike PDMS, the THz response of STO is temperature dependent [20]. The relative permittivity of STO in THz range can be expressed as:where is the high-frequency bulk permittivity of STO, and is the oscillator strength. and are the angular frequency and soft mode frequency, respectively. is the damping factor. According to reference [20], the relative permittivity of STO at temperatures of 300 K, 320 K, 340 K, 350 K and 360 K can be calculated as 362, 300, 251, 223, and 200, respectively. It should be noted that the loss angle tangent is about 0.01- 0.02. In this paper, the loss angle tangent at all temperatures is assumed as 0.015. Table 1 shows the calculated permittivity of STO/ PDMS composite at various temperatures with volume fraction of STO increasing from 5% to 20%. It can be found that the permittivity of STO/ PDMS composite increases with the volume fraction of STO. In addition, the permittivity decreases dramatically with the increasing temperature.
Table 1. The calculated permittivity of STO/ PDMS composite at different volume fractions of STO and temperatures.
3. Results and discussion
Simulations, based on CST microwave studio (finite difference-time domain), are carried out to predict the THz response of this metasurface. Firstly, the transmission spectrum is simulated. Here, the volume fraction of STO is 10%. According to Table 1, the permittivity of STO/ PDMS composite is 3.2812 at 300 K. The permittivity and loss tangent of micro yttria-stabilized zirconia spheres are 33 and 0.015, respectively [21]. According to the volume filling factor of spheres, the sample can be considered as a metasurface with a diameter and lattice constant of 80 μm and 200 μm, respectively. The result is shown in Fig. 2, where two remarkable transmission dips can be observed at 0.643 THz and 0.774 THz. The corresponding magnetic fields are simulated and provided in this figure, where these two dips correspond to the first magnetic resonance and the first electric resonance, respectively. With a photoconductive switch-based terahertz time domain spectroscopy system, the terahertz transmission spectrum is obtained and plotted by red dash line. Clearly, good agreement has been obtained between the simulated and experiment results.
Fig. 2 The simulated and measured transmission spectrum of specimen. The volume fraction of STO is 10%.
To confirm the thermal tunability of this metasurface, temperature dependent transmission spectra are achieved by increasing temperature from 300 K to 360 K, as shown in Figs. 3(a) and 3(b). In the simulations, the temperature dependent relative permittivity of STO/ PDMS composite is set according to Table 1. It can be found that the magnetic resonance remains nearly unchanged when the temperature increases. Unlike magnetic resonance, the electric resonance shows remarkable thermal tenability, and the electric resonance has a blueshift of 0.005 THz. The obtained transmission spectra demonstrate the tunability of the prepared metasurface by using a THz-TDS system. The sample is mounted on a hot plate, which has an aperture to make the THz beam transmit through it. The temperature of the sample can be precisely controlled by a heating system. In the measurement, the THz pulse illuminates the sample under normal incidence and the time dependent transmission is measured. Through Fourier transforming the time domain spectroscopy, the frequency dependent transmission spectra are achieved, as shown in Figs. 3(c) and 3(d), where the frequencies of the dips exhibit remarkable temperature dependence. When the temperature increases from 300 K to 360 K, the magnetic resonance keeps nearly unchanged. On the contrary, the electric resonance shifts from 0.813 THz to 0.817 THz (a blueshift of 0.004 THz). The tuning figure of merit (FOM), defined as tuned frequency/ full wave at half maximum (FWHM) × 100 %, can be calculated as 14.3%. Clearly, the experiment results are in good agreement with the simulated one, confirming the feasibility of the proposed method.
Fig. 3 The simulated and measured transmission spectrum at different temperatures. The volume fraction of STO is 10 %. (a) Simulation. (b) The enlarged picture of (a) near the second resonance. (c) Experiment. (d) The enlarged picture of (c) near the second resonance.
Actually, the performance of tenability is dependent on the volume fraction of STO, and simulations are performed with the volume fraction of STO increasing from 10% to 15%. Compared to results in Fig. 3, both the magnetic and electric resonances shift to lower frequencies when the volume fraction of STO increase to 15%, as plotted in Figs. 4(a) and 4(b). In addition, the electric resonance shows strong temperature dependence. The electric resonance frequency experiences a blueshift of 0.01 THz (from 0.706 THz to 0.716 THz). However, the electric resonance has a redshift of 0.004 THz (FOM=14.3%) when the volume fraction of STO is 10%, which suggests that the tunability can be effectively improved by increasing the volume fraction of STO. Experimentally, the electric resonance frequency experiences a blueshift of 0.007 THz (from 0.776 THz to 0.783 THz) (FOM=28.2%). The experiment results are in good agreement with the simulated ones. To demonstrate this tuning is reversible, we have repeated the temperature variation in 10 cycles, which can confirm this property obviously (see Fig. 5(a)). It should be pointed out that the temperature range in aforementioned results is only 60 K and the tunability performance can be improved by increasing the temperature range. To demonstrate the prediction, simulations are carried out at temperatures of 250 K and 400 K (ΔT = 150 K). The volume fraction of STO is 15% in the simulations. According to Eq. (1) and Eq. (2), the permittivity of STO/PDMS composite at temperatures of 250 K and 400 K is calculated as 4.43 and 4.03, respectively. The simulated transmission is shown in Fig. 5(b), where the electric resonance reveals remarkable temperature dependence while the magnetic resonance remains nearly unchanged. The resonance frequency for the electric resonance shifts from 0.719 THz to 0.699 THz, a redshift of 0.02 THz. The modulation depth (MD) is also calculated at 0.719 THz. Here, MD = (T(250 K) - T(400 K))/T(250 K)× 100 %. The value of MD reaches 88.6 % at 0.719 THz. Particularly, the FOM reaches 98.6%. The good tunability and modulation performance demonstrate the robustness of proposed method. It is worth mentioning that the stability of this tunable metasurface is higher than the one of our previous work [16].
Fig. 4 The simulated and measured transmission spectrum at different temperatures. The volume fraction of STO is 15 %. (a) Simulation. (b) The enlarged picture of (a) near the second resonance. (c) Experiment. (d) The enlarged picture of (c) near the second resonance.
Fig. 5 (a)Temperature variation of the second resonance in 10 cycles (b) The simulated transmission spectrum of all-dielectric metasurface at temperatures of 250 K and 400 K.
4. Conclusion
We have proposed and experimentally demonstrated a simple approach to obtain flexible and tunable THz all-dielectric metasurface. In this metasurface, the micro ceramic spheres (ZrO2) are embedded in ferroelectric and elastomer composite. The results reveal that Mie resonances in micro ceramic spheres can be thermally and reversibly tuned because of the temperature dependent permittivity of STO/ PDMS composite. With the properties of flexibility and tunability, this metasurface may find various applications in active THz devices.
Funding
111 Project and Director Funds of Beijing Key Laboratory of Network System Architecture and Convergence (B17007); National Natural Science Foundation of China (NSFC) (61372109, 51402163); Shenzhen Science and Technology Projects (XCL201110009, JCY201110096, JSE201007200050A); China Postdoctoral Research Foundation (2013M530042, 2017M620693).
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