1. Introduction

During past few years, electromagnetic metamaterials have undergone rapid development, due to unique properties especially effective parameters below unity or even zero [1]. The extension of effective parameters not only enriches the understanding of interaction between matter and wave but also allows to design unique devices to control electromagnetic/optics wave, such as negative refraction lens [2], cloaking [3], metasurface [4], etc.

However, due to the inherent resonant nature, limited bandwidth has been always considered as the top issue to overcome, as early as the first demonstration of metamaterials. From the effective equivalent circuit point of view, operation frequency of metamaterials relies on effective capacitance and effective inductance. Thus, various efforts to frequency tunability have been employed via varactor diode [5–7], mechanical geometry tuning [8–12] and liquid crystal (LC) [13–33]. Importantly, nonlinear metamaterial, whose resonance frequency can be shifted with incident power intensity, has been considered as an effective tuning approach, because it provides more freedom to control electromagnetic response of metamaterial but also promotes the potential applications [5–9]. Compared to those approaches to frequency control, liquid crystal has been considered as one of most promising materials to change environmental dielectric condition so as to vary resonance state, due to its large birefringence and easy approach to be incorporated [13–33].

Up to now, various efforts have been given on the tunability of different microstructures including split ring resonator (SRR) [13–15], cut-wire pair [21], fishnet [16,22] via liquid crystal incorporation. Under external field excitation, it is possible to reorientate LC molecular director such that the effective dielectric permittivity can be altered. Very recently, on the basis of frequency tuning ability, LC allows metamaterial based principle-of-proof device to show reconfigurable properties, for instance, beam control metasurface [24,29,30]. Among various tunable microstructures based on LC, SRR is the most difficult prototype to engineer as its complex distribution of local electric field [18]. In this paper, we investigated an isolated SRR deposited by a seesile droplet of nematic LC. By utilizing a relatively low static electrical field excitation for the alignment LC, a reversible frequency shift in resonance dip was observed due to LC molecular alignment transformation from random state to obeying local field. A maximum frequency tuning range up to 237MHz, is experimentally observed. The frequency tuning ability is significantly correlated with droplet height. More importantly, transmission phase is also modulated.

2. Results

Figure 1 illustrates schematic views of tunable metamaterial unit, which consists of a copper SRR with two identical gaps etched on the surface of a 0.5-mm-thick Teflon fiberglass slab. A nematic LC droplet is deposited on the surface of SRR. Two thin conducting wires are connected to SRR arms to provide bias voltage. To measure the electromagnetic response of isolated SRR, a pair of monopole antenna, which is made from conventional coaxial cable via removing shielding layer and dielectric substrate but keeping the inner conductor, are employed as the transmitter and receiver of electromagnetic wave. Thus, an incident beam is propagated with magnetic field mainly perpendicular on surface of SRR due to the near field distribution of electromagnetic wave. Thus, SRR is expected to be excited by external magnetic field, even electric field may play minor contribution. In this paper, commercial LC, TEB30A, with a moderate birefringence Δn = 0.08 (ordinary index, no = 1.65, and, extraordinary index ne = 1.73) is employed. Compared to birefringence at optical range, smaller value is due to dielectric permittivity dispersion [21].

 

Fig. 1 (a) Top view and (b) side view of single SRR covered by liquid crystal droplet. (c) Photograph of SRR sample with lead wire. (d) Schematic view for SRR electromagnetic response measurement setup via a pair of monopole antenna. The geometrical parameters of SRR are as follows: l = 5.00, w = 1.00, g = 0.50, t = 0.50 (unit: mm).

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The scattering parameters were measured and recorded via a Vector Network Analyzer (VNA) AV3629D in free space. The transmission spectra for a bare Teflon substrate without metallic SRR was used as calibration reference. Figure 2(a) gives transmission spectra of SRR deposited by a nematic LC droplet with a height of 3.0 mm under different bias voltage. It can be seen that, without bias voltage, SRR exhibits a pronounced transmission dip at 11.34 GHz, around which magnetic resonance is presumably excited. However, the transmission dip continuously shifts down to 11.103 GHz, as the bias voltage increases from 0 V to 120 V, then followed by tuning saturation even the bias voltage is further enhanced, as shown in Fig. 2(c). It is noting that such tuning activity is reversible. In total, tuning range of 237 MHz is observed experimentally.

 

Fig. 2 (a) Experimental transmission magnitude of SRR covered by nematic LC under different voltage. (b) Simulated transmission spectra versus various permittivity of LC. Inset shows circular current distribution around SRR resonance dip. (c) Experimental operation frequency of SRR versus bias voltage. The droplet has 3.0 mm in height.

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Figure 3 shows the transmission phase variation as a function of bias voltage. The phase experiences abrupt drop around transmission dip, which is in accordance with magnetic resonance characteristics. More importantly, frequency tuning property enables transmission phase to be modulated. At some given frequency point, taking f = 11.29 GHz for instance, the transmission phase of SRR experiences a remarkable increase from −176.5° to −58°, accounting for nearly 118° variation, indicating the potential application as elementary unit for metasurface to control electromagnetic beam deflection.

 

Fig. 3 Transmission phase of SRR covered by nematic LC under different voltage (a) and simulated with various permittivity of LC (b). The droplet has 3.0 mm in height.

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To understand frequency tuning behaviour, full wave numerical calculations were carried out. A pair of monopole antenna operating in free space were modelled to calculate the electromagnetic response of SRR covered by nematic LC droplet. To mimic LC molecular reorientation influence on SRR resonance, effective permittivity change of LC was calculated. At the first stage without bias field, nematic LC molecules are randomly distributed inside droplet, leading to an average permittivity as follows [32,33],

Obviously, such average effective permittivity, ε_m = 2.81, is in between the permittivity along long and short axes of LC molecules. As bias electric field is applied, such effective permittivity is expected to increase due to the nematic LC reorientation. It is noting that effective permittivity variation is limited by the permittivity along long axis, ε_e = n_e2 = 2.99. Therefore, the influence of LC permittivity varying from ε_m to ε_e is calculated to analyse transmission magnitude and phase of SRR, as presented in Figs. 2(b) and 3(b), respectively. From the comparison between experimental and numerical results, an excellent agreement is achieved, confirming the frequency redshift of SRR with increasing external electric field (permittivity of LC). Slight discrepancies of resonance frequency and tuning range are probably due to minor fabrication error.

Furthermore, droplet size of LC plays an important role on the frequency tuning range of SRR. Maximum frequency shift of SRR under different size of LC droplet is investigated and given in Fig. 4. Covered by a smaller LC droplet with a height of 0.75 mm, SRR resonance dip can be shifted as much as 128 MHz. However, tuning range increases dramatically with large droplet size and reaches a maximum value of 237 MHz for droplet height of 3.0 mm. The numerical simulation reproduces similar result to experimental data.

 

Fig. 4 (a) SRR covered by LC droplet with different size (b) Maximum frequency tuning range of SRR as a function of droplet height.

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Magnetic resonance of SRR is verified by the circular distribution of surface currents, as shown in the inset of Fig. 2(b). It has been found that magnetic resonance frequency is determined by $f=\frac{1}{2\pi \sqrt{LC}}$, where L and C are the effective inductance and capacitance of SRR. Obviously, LC reorientation only disturb dielectric condition and capacitance. To look insight, the underlying physics of LC droplet influences on SRR resonance, local electric field inside the plane perpendicular to SRR gap is monitored at the resonance dip. As shown in Fig. 5, due to the extremely thin thickness for metal layer, t = 0.03 mm, fringing fields inside LC layer and Teflon substrate are rather remarkable compared to that inside the gap. Hence, the total gap capacitance of one gap, Cg, can be expressed by including all the components,

 

Fig. 5 Schematic view of nematic LC molecular reorientation around SRR gap (a) without and (b) with bias electric field.

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where C_p, C_LC and C_sub represent the capacitance inside metal sides of gap, fringing capacitances inside LC droplet and Teflon substrate, respectively. C_p can be calculated directly by the parallel-plate model, while fringing capacitances, C_LC and C_sub, mainly depend on the permittivity and the thickness of LC and Teflon substrate, respectively. In the initial state, LC molecules are randomly dispersed inside droplet, time-varying local electric field experience the average effective permittivity, ε_m = 2.81. However, under static electric field inducement, LC molecules begin to be reoriented with their directors (long axis) parallel to the local field directions. As bias field approaches to threshold voltage of 120 V, ideally nearly all the molecular directors obey the static electric field distribution, hence, time-varying local electric field experiences effective permittivity of ε_e for nematic LC. During LC molecular reorientation process, the effective permittivity of LC increases gradually from ε_m to ε_e. As a consequence, the capacitance inside the gap, C_p, and fringing capacitance within LC droplet, C_LC, enhances while fringing capacitance, C_sub, inside Teflon substrate remains, resulting in a remarkably increase on total capacitance of SRR, as well as a visible blueshift of magnetic resonance of SRR.

3. Discussions

To provide clear illustration for gap capacitance dependence on the height of LC droplet, numerical electrostatic calculation of SRR capacitance including fringing components was carried out via electrostatic solver of CST EM studio, as shown in Fig. 6. It can be seen that, no matter either reorientation state of LC, the overall capacitance of SRR, one half value of single gap capacitance due to the serial connection of two gaps, increases rapidly with the droplet height until it reaches the threshold around h = 3.5 mm. Furthermore, SRR capacitance difference between random state and reorientation state of LC, ΔC, experiences remarkable enhancement from 0.0005 pF to 0.0020 pF as the droplet increases from 0.5 mm to 3.0 mm, which well explains experimental frequency shift with droplet height, as stated previously. The capacitance difference saturation for droplet height, clearly indicates that fringing field strength above 3.0 mm height away from SRR surface is rather weak that can be negligible.

 

Fig. 6 Total capacitance of SRR varies as a function of different LC droplet height. Effective permittivity of 2.81 and 2.99 refer to LC initial state without bias voltage and saturated reorientation state with threshold bias voltage.

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4. Conclusions

In summary, an electrically tunable electromagnetic behaviour for single SRR covered by nematic LC droplet is investigated experimentally. A maximum frequency tuning range of 237 MHz is observed under bias voltage applied by 120 volts, due to significant enhancement of SRR fringing capacitance from LC molecular director reorientations. Tuning ability increases rapidly with the droplet size and saturates till droplet height exceeds 3.0 mm due to total capacitance reaches its threshold. Tuning ability of single SRR provides more flexible design to bulk devices, such as metasurface, to control electromagnetic/optic wave.