A novel three-dimensional metamaterials tube is investigated to achieve passive resonance tunability. Varying its diameter, the resonance frequency shows a blue-shift from 0.75 to 1.13 THz. FDTD simulation reveals that this resonance tunability is attributed to destructive magnetic coupling among neighboring SRRs on the curved surface of the metamaterials tube. This blue-shift provides a new approach to achieve flexible resonance tunability into higher terahertz frequency. Meanwhile, the 3D solid-core metamaterials tube, wrapping the planar metamaterials against transparent sample in terahertz regime, can be applied to identify the materials by resonance shift. This ultra-sensitive sensing means can measure a refractive index change down to 0.0075.
Terahertz metamaterials have attracted much research interest in the past decade due to their unique electromagnetic properties.1–4 A split ring resonator (SRR) is one of the typical metamaterials structures. In order to extend its resonance bandwidth, terahertz metamaterials with resonance tunability were developed recently.5, 6 Previous experimental studies on tunable metamaterials are focused on active tunability by tuning the optical properties of the substrates using external sources.7–11 Passive tunability, without any external constituents, is of great significance to realize resonance tunability with simple setup and convenient operation. Structural tunability in the multi-layer metamaterials was proposed to tune the resonance frequency by the relative position of SRRs in the neighboring layers, which demonstrates a potential way to realize passive tunability.12–14
The resonance property of terahertz metamaterials is determined by the dimension of the individual SRRs, as well as the interactions among the SRR unit cells.15 The red-shift tunability methods in the previous studies were realized by increasing the capacitive components in the LC model. Realizing blue-shift tunability requires decreasing either the inductive component or capacitive component, which presents technical difficulties because either electric or magnetic coupling among the SRR unit cells is constructive rather than destructive. A recent study demonstrated blue-shift tunable metamaterials controlled by infra-red light intensity to reduce both the inductive and capacitive components.16 In recent research, flexible PEN films were used as substrates to construct metamaterials for resonance enhancement and broadband resonance.17–19 This kind of thin flexible metamaterial can make metamaterials into non-planar form, allowing more potential designs and applications than the metamaterials made on rigid substrates.
A novel three-dimensional terahertz metamaterial with passive tunability, a ‘metamaterials tube’, is made by rolling up two-dimensional planar metamaterials made on flexible substrates. The metamaterials tube presents blue-shift tunability with a tuning range of 50.6% from 0.75 (f0) to 1.13 THz as the diameter decreases, which is attributed to the magnetic coupling among the SRRs on the curved space. Further study is carried out by wrapping the 2D terahertz metamaterials against transparent materials to form a solid-core metamaterials tube. As the metamaterials tube changes from the hollow-core to the solid-core form, the permittivity of the inner environment increases, which makes the resonance frequency red-shift, which can be used as spectral signatures to identify the unknown materials. This novel terahertz metamaterials tube with passive tunability can facilitate the development of new functional terahertz devices.
The three-dimensional (3D) terahertz metamaterials tube is made by rolling up the 2D planar metamaterials into tube form with the SRR array on the inner wall. There are 5 metamaterials tubes fabricated at different diameters of 4.00, 4.50, 5.00, 5.50, and 6.20 mm. The 2D SRRs array fabricated is shown in Figure 1a. The SRR metamaterials are made of Cr and Cu at thicknesses of 5 and 200 nm, respectively. The outer dimension of the square SRR is 40 μm, the line width 6 μm, and the gap size 12 μm. An image of the flexible 3D metamaterials tube at a diameter of 4.00 mm is shown in Figure 1b. Figures 1c and d demonstrate the rolling-up process.
The 2D planar metamaterials are characterized first, with LC resonance f0 of 0.75 THz. The 3D metamaterials tubes are characterized as the terahertz wave propagates through the tubes. Due to the isotropic properties in the plane perpendicular to the axis of the metamaterials tube, the transmission spectra are kept the same when the 3D metamaterials tube is rotated around the axis. This polarization-insensitive advantage offers great flexibility by either polarized or non-polarized terahertz wave for sensing, detecting, and scanning applications.
Figure 2 shows the transmission spectra of the 3D terahertz metamaterials tubes. By decreasing the diameter from 6.20 to 4.00 mm, the resonance frequency shows a blue-shift from 0.75 to 1.13 THz with a tuning range up to 0.38 THz, equally to 50.6% f0 (0.75 THz). The frequency blue-shift with the diameter decreases can be attributed to interactions among the neighboring SRR unit cells of the metamaterials tube.
As the terahertz wave propagates through the metamaterials tube, the SRR unit cells on the plane related to the terahertz wave polarization direction can be divided into three zones, as shown in Figure 3a. Zone 1 contains the SRRs array, which is perpendicular to the magnetic field of the incident terahertz wave. These are the arrays of SRRs in the top and bottom of the metamaterials tube. The SRRs in Zone 1 contribute to the resonance, which is discussed in the following paragraphs. Zone 2 contains the SRRs array which is parallel to the magnetic field of the terahertz wave. These are the line arrays of SRRs at the left and right sides of the metamaterials tube. In Zone 2, the magnetic field is parallel to the SRR plane, and does not result in the oscillation current. Therefore, the SRRs in Zone 2 do not contribute to the resonance. For the remaining SRRs, which are classified into Zone 3, the scenarios of Zone 1 and 2 are combined together. The perpendicular component of the incident magnetic field contributes to the resonance of SRRs array in Zone 3. Besides the resonance excited by magnetic fields, the electric field also excites the resonance as it is parallel to the gap-bearing side of the SRR. The resonance induced by the electric field is at the same frequency as that induced by magnetic field.20–22 Therefore, the resonance excited by magnetic and electric fields reinforce each other, making the resonance stronger.
Based on the inductor–capacitor (LC) circuit model, the capacitive component is determined by the gap size of the SRR unit cell. For the 3D metamaterials tube, the capacitive component (gap size) is small (2 μm) and can be neglected. (The change is 0.05% relative to a diameter of 4.00 mm). Therefore, the electrical interaction among the SRRs is ignored and only the magnetic coupling will be explained in our further discussion.
Figure 3b compares the magnetic field directions of the 2D planar metamaterials and 3D metamaterials tube in Zone 1. For the 2D planar metamaterials, as the magnetic field H0 of the incident terahertz wave perpendicular to the SRRs induces the oscillation current inside each SRR. The oscillation current results in an induced magnetic field H ′, which acts on the nearby SRRs in a direction opposite to the incident magnetic field H0. In this case, the interaction between the neighboring SRRs array is weak as they are on the same plane. For the 3D metamaterials tube, the angles among the SRRs array change. The angle θ between the adjacent SRRs on the curved surface, depending on the curvature or the diameter of the metamaterials tube, makes the induced magnetic fields intersect each other. The magnetic field H0 of the incident terahertz wave at SRRL and SRRR can be decomposed into two components H⟂ and H‖. Only H‖ induces the oscillation current in SRRL and SRRR, resulting in the induced magnetic field H ′.
The resonance frequency of the 3D metamaterials tube can be expressed as:
where f0 is the LC resonance frequency of the single SRR, f0 = (L0C0)−1/2. L0 and C0 are the inductance and capacitance of individual SRR. LΣ is the magnetic interactions among SRRs, depending on the effective area between two neighboring SRR unit cells,
where S is the area of individual SRR determining its inductance and θ is the angle between the two adjacent SRRs as illustrated in Figure 3b. The effective area is determined by the projection area of one SRR to another. As nθ is less than 90°, the projection is negative, leading to a destructive magnetic coupling. Therefore, the resonance frequency shifts to the higher frequency. In the actual case, besides these three nearest SRRs interacting with each other, all the SRRs array on the curved surface contribute to the interactions.
The numerical simulation is carried out by CST Microwave studio 2009 to study the magnetic interactions among the neighboring SRRs. Three SRR unit cells at an angle θ are adopted in the simulation. Figures 4a and b show cross-sectional views of the magnetic field distributions in Zones 2 and 1 of the 3D metamaterials tubes at different diameters. The magnetic field amplitude at SRR0 in Zone 1 decreases as the diameter decreases, while the magnetic field amplitude at SRR0 in Zone 2 remains the same. In Zone 1, as shown in the magnetic field distributions in Figure 4b, the magnetic field intensity at SRR0 decreases from 21 486 to 9500 A m−1 as the angle θ increases from 0° to 2°. The oscillation current is presented in Figure 4c. As the angle θ among the neighboring SRRs increases, the oscillation current at the center SRR0 becomes weaker. This is also a proof of the destructive magnetic interactions among the neighboring SRR unit cells.
THz-TDS can be used to characterize the materials by their spectral signatures in the terahertz frequency range. However, detection of transparent materials, such as paper, polymer, and cotton, is a difficult mission from the transmission or reflection spectra of THz-TDS, although it has been used to detect liquid successfully. In this research work, a novel solid-core metamaterials tube design is proposed to detect transparent materials flexibly: cotton (Cotton Applicator, Techspray) and paper (Beautex@). 2D planar terahertz metamaterials made on flexible PEN substrates are used to wrap the samples and form a solid-core terahertz metamaterials tube at a diameter of 5.50 mm. The samples of the metamaterials tube are characterized in the same way as the hollow-core metamaterials tube. The transmission spectra are presented in Figure 5a. There are significant resonance red-shifts in these two cases as compared to the transmission spectrum of the hollow-core metamaterials tube. The red-shift amounts of the solid-core metamaterials tubes are 0.14 and 0.20 THz, respectively, due to the increase of the core materials’ permittivity. This results in an increasing capacitive component in view of the LC circuit. Figure 5b shows theoretical and experimental results of the resonance frequency of both hollow- and solid-core metamaterials tubes as a function of core diameter. As the major natural materials have a permeability of 1 in terahertz regime, the core materials’ refractive indices can be calculated by the resonance red-shift amounts. The refractive indices obtained from the experimental results match the published results very well. Our characterization can achieve the detection sensitivity of 0.5 to 1 THz/RIU (300 000–600 000 nm RIU−1). As the frequency resolution of the THz-TDS system is 0.0075 THz, a refractive index change as small as 0.00375 –0.0075 can be detected by this novel means. Such an ultra-sensitive characterization can enhance sensing capability in terahertz region. The metamaterials tube can serve as a sensitive detector to identify transparent materials in the terahertz regime.
A novel 3D metamaterials tube with a hollow core is designed and fabricated to achieve passive resonance tunability. A wide tuning range, up to 50.6% of f0, is achieved from 0.75 to 1.13 THz as the diameter decreases from 6.20 to 4.00 mm, which extends the metamaterials working range to higher frequency. This provides a new approach to cover the wide terahertz regime by combination with conventional red-shift frequency tunability. The resonance frequency blue-shift as the diameter decreases is attributed to the destructive magnetic interactions among the neighboring SRR unit cells made on the curved surface. Furthermore, the polarization insensitive property due to the symmetric tube design also offers a great flexibility of the 3D metamaterials tube for potential non-polarized terahertz wave applications. By wrapping up the 2D flexible metamaterials around the unknown transparent materials to form a solid-core metamaterials tube, unknown transparent materials can be identified by measuring resonance red-shift resulting from the refractive index changes of the core materials. This novel approach can address the challenge of conventional THz-TDS in the characterization of transparent materials. Furthermore, it can detect refractive index changes as small as 0.0075 by conventional THz-TDS for ultra-sensitive sensing applications. The metamaterials tube can realize various new functions by its resonance tunability and materials identification to further extend terahertz applications.