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Abstract
In this paper, a nematic liquid crystal (NLC)-based tunable terahertz (THz) plasmonic metamaterials (MMs) with large modulation depth (MD) and low insertion loss (IL) is designed and experimentally verified at THz frequencies. The proposed structure includes two-layered MM that is immersed in LC. The metal MM is used directly as electrode. The tunable device with a 46×46 array of sub-wavelength circular air loops was fabricated on a quartz glass substrate, with 2×2 cm2 area and 220 µm thickness. The obtained results show that the amplitude MD and IL for normally incident electromagnetic (EM) waves are about 96% and 1.19 dB at 421.2 GHz, respectively, when the bias voltage applied to the NLC layer varies from 0 to 16 V. Meanwhile, the transmission peak frequency gradually decreases from 421.2 to 381.8 GHz, and the frequency tunability (FT) of the proposed structure is greater than 9.35%. This study provides a potential solution for THz modulators, filters, and switches.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, the terahertz (THz) technology has received considerable attention due to its potential applications in next-generation computing and communication systems [1], biological and medical sciences [2], food safety testing [3], and space sciences [4]. Numerous functional devices in the THz regime, such as phase shifters [5,6], filters [7], modulators [8], absorbers [9], switches [10], lens [11], wave plate [12], and polarization converter [13] have been proposed. Currently, the control mechanisms of THz modulators are mainly mechanical, electrical, or optical [14].
An electromagnetic (EM) metamaterial (MM) is an artificial composite material that can exhibit several extraordinary physical properties, such as negative magnetic permeability, negative refractive index, and an inverse Doppler effect, which are not found in natural materials [15,16]. MMs typically consists of periodic arrays of sub-wavelength metallic structures that are integrated into a dielectric or semiconducting substrate. One possible method for fabricating a dynamically tunable MM is to control the permittivity of the constituent materials. The orientation of nematic liquid crystals (NLCs) molecules can be changed by applying an electric or magnetic field, thus changing the dielectric constant of the LC [17,18]. The liquid crystals (LCs) can be used to construct tunable THz devices due to high birefringence and tunable dielectric properties [19,20]. Recently, many LC-based tunable THz MM devices have been reported. However, most of the reported devices are based on single-layer plasmon-induced transparency metamaterial [21,22]. For example, an electrically tunable MM device consisting of a periodic array of crossed elements embedded in NLC has been proposed in [23]. J. Wang et al. designed an electrically tunable THz modulator with LC MM and demonstrated through simulations that the modulation depth beyond 90% and insertion loss below 0.5 dB were achievable at normal incidence [24]. In addition, some novel THz devices with two metallic structures have recently been reported. Rely on two MM structures, the tuning speed of the device is faster due to the small thickness of the LC layer. For example, the tunable properties of a THz fishnet MM enhanced with a nematic LC layer and two fishnet metallic structures have been theoretically investigated, and a frequency tunability (FT) higher than 150 GHz is predicted [25]. A THz quarter-wave plate with double layers of graphene grating and a layer of LCs was proposed by Y. Y. Ji et al [26]. In 2019, an active THz resonance switch was experimentally demonstrated by S. T. Xu et al, and the results show that its extinction ratio at 0.82 THz exceeds 30 dB [27].
This paper presents the application of LC for a tunable metamaterial-LC-metamaterial (MLM) structure at frequencies around 420 GHz. The proposed device includes two-layered MM, which is sub-wavelength circular air loops array and immersed in LC with thickness of 45 µm. The metal MM is also directly used as electrode. The THz MLM structure provides EM transmission through propagating surface plasmons (PSPs) coupling excited by two layers of the metal microstructures [28], and the energy of the coupled field is primarily concentrated in the LC layer. The experimental results show that when the bias voltage applied to the LC layer changes from 0 to 16 V, the amplitude modulation depth (MD) and insertion loss (IL) of the device at 421.2 GHz are 96% and 1.19 dB, respectively. A large depth modulation and low IL of terahertz radiation with low bias voltage is achieved in the process.
2. Design and manufacture
The 3D schematic diagram of the unit cell of the designed NLC-based tunable THz MM structure is shown in Fig. 1(a). The unit cell is primarily composed of two parallel quartz glass substrates and two same patterned copper layers embedded in an intermediate NLC layer. The upper and the lower patterned copper layers act as a resonant structure and are also used as an electrode for applying a bias voltage. In order to control the orientation of the LC molecules in the absence of a bias voltage, the inner surface of each patterned copper layer was spin-coated with a thin polyimide (PI) alignment layer and was mechanically rubbed along a selected direction on the surface of PI alignment layer. In the unbiased state (ɛ⊥), the long axis of the LC molecules is aligned parallel to the mechanical rubbing direction due to the static action of the PI alignment layer. When driven at saturation bias voltage, the long axis of the LC molecules is aligned parallel to the direction of the electric field, and the dielectric constant of the LC reaches its maximum value (ɛ//). The dielectric constant of the LC in the NLC-based electronically controlled THz MM is tunable based on its voltage dependence.
Fig. 1. (a) 3D schematic diagram of a unit cell. (b) Top view of the metal resonance unit cell. (c) Side view of the unit cell.
The transmission characteristics of the device were calculated by CST Microwave Studio. The unit cell is applied periodic boundary condition in the x-axis and y-axis directions and illuminated by a linear polarization and normal incidence plane wave. Each metal MM array layer consisting of 46×46 unit cells was printed on the inner surface of the upper and lower quartz glass substrates. The conductivity of the copper layer is set to 5.8 × 107 S/m. Both the upper and the lower substrates are each a 220 µm thick quartz glass plate, with the relative dielectric permittivity and loss tangent of ɛQL = 3.78 and tanδQL = 0.002, respectively. The geometric parameters of the unit cell presented in Figs. 1(b) and 1(c) are as follows: p = 309 µm, R1 = 128 µm, R2 = 144 µm, w = 12 µm, Tq = 220 µm, Tp = 45 µm, Tc = 0.5 µm, and Ti ≈ 90 nm. The NLC is filled with an LC mixture (HFUT-HB01), whose characteristic parameters in the frequency range of 330 to 500 GHz are as follows: ɛ⊥ = 2.547, tan(δ⊥) = 0.02, ɛ// = 3.65, and tan(δ//) = 0.02 [17]. Since the unit cell has a symmetric structure, the proposed device is polarization independent.
The amplitude MD and the IL of the proposed tunable THz MM structure can be calculated as:
Where Tmax and Tmin are the maximum and the minimum transmittance of the structure at a certain frequency, respectively. The numerical analysis is carried out assuming ideal homogeneous LC layers, whose permittivity continuously varies between ɛ⊥ and ɛ//. The assumption of isotropy and homogeneity for each state of permittivity of the LC layer may produce small simulation errors in MD and IL of THz wave. Figure 2 shows the simulation results of the proposed device. It can be seen from the Fig. 2(a) that as the dielectric constant of the LC increases from 2.547 to 3.65, the transmission peak on the right gradually redshifts from 416.7 to 378.9 GHz. The frequency point 416.7 GHz corresponds to the maximum amplitude MD of 97% and the minimum IL of 1.09 dB (according to Eqs. (1) and (2)). The effects of the LC layer thickness on MD and IL were analyzed at 416.7 GHz. As shown in Fig. 2(b), the THz device has the best MD and IL when the thickness of the LC layer is 45 µm.Fig. 2. (a) Transmission spectra of the designed MLM structure at different LC dielectric constants. (b) The effects of the LC layer thickness on MD and IL.
Figure 3(a) shows the proposed tunable MM array with a 46×46 array of sub-wavelength circular air loops that was fabricated using an ultraviolet lithography process. A photomicrograph of the manufactured sample is shown in Fig. 3(b), while Fig. 3(c) shows the experimental setup for characterizing the fabricated sample. A vector network analyzer (Agilent N5224A) and a mm-wave module extender (VDI) with 330 to 500 GHz frequency range were used to measure the spectral response of the sample in dry air. Two pairs of lenses were used to focus the THz beam. During measurements, a 1 kHz square wave voltage was used as the bias electric field in order to prevent electric charge from accumulating in the sample.
Fig. 3. (a) Fabricated prototype. (b) Microscopic image of a group of unit cells. (c) Experimental setup for the characterization of the sample.
3. Experimental results and discussions
Figure 4 shows the transmission spectra of the manufactured sample at different bias voltages. Because the device was not illuminated by an ideal linear polarized wave in the test, the experimental results has different with the simulation results. It can be seen from the figure that the transmission peak on the right gradually decreases from 421.2 to 381.8 GHz when the applied bias voltage increases from 0 to 16 V, and the FT of the manufactured structure is greater than 9.35%, which is calculated by the following definition:
Where fH and fL are the resonant frequency points corresponding to the unbiased and biased states, respectively. And the maximum MD and the minimum IL are 96% and 1.19 dB, respectively, at 421.2 GHz. The comparison of Fig. 4 and Fig. 2 shows that the initial resonance frequency point of 4.5 GHz observed in the measurement is larger than the simulated value, which may be caused by dimensional manufacturing and test error. However, the evolution of the spectrum of the fabricated sample is consistent with the theoretical analysis over the entire design frequency range. The rotation speed of LC molecules, which is independent on testing frequencies, is mainly determined by bias voltage. The response time of the LC is about 200 ms by measuring voltage-transmission curves in transparent test cells with 45 µm LC layer [29].The transmittance and the amplitude MD of the sample at 421.2 GHz as are also extracted a function of bias voltage. Figure 5(a) shows that the transmittance of the sample is nearly constant because the applied bias voltage is less than 1.5 V, which is the threshold voltage required for reorientation of the LC molecules. However, when the applied bias voltage increases from 1.5 to 10 V, the transmittance of the sample monotonically decreases. Meanwhile, the Q factor of the sample increases monotonically, which is defined by the following formula:
Here fr is the resonant frequency, fRH and fLH are the upper and lower cut-off frequencies (${T_{{f_{RH}}}} = {T_{{f_{LH}}}} = \frac{{\sqrt 2 }}{2}{T_{{f_r}}}$), respectively. At bias voltage greater than 10 V, the transmittance of the sample gradually stabilizes because the LC molecules are oriented nearly parallel to the direction of the electric field. Figure 5(b) shows that the sample can be modulated at the operating frequency of the sample while a bias voltage is applied.Fig. 5. (a) Transmittance of the fabricated sample at an operating frequency of 421.2 GHz under different applied voltages. The Q factor of the fabricated sample at different applied voltages is shown in the inset. (b) Amplitude modulation depth of the fabricated sample at 421.2 GHz under different applied voltages.
In order to obtain better understanding of the mechanism governing the operation of the device, the electric field and the surface current distributions in the device are analyzed at 416.7 GHz under biased and unbiased states. The simulated results are presented in Fig. 6. Figures 6(a) and 6(d) show the electric field distribution in the MLM structure at 416.7 GHz for unbiased and biased, respectively. It can be clearly seen that the transmittance of THz waves along the positive z direction while unbiased is significantly greater than that while biased. Figures 6(a) and 6(d) show that the NLC-based THz MLM structure provides EM transmission through propagating surface plasmons (PSPs) coupling excited by two layers of metal microstructures, and the energy of the coupled field is primarily concentrated in the intermediate dielectric layer. Figures 6(b, e) and 6(c, f) show the surface current distributions in the MLM structure at 416.7 GHz while unbiased and biased, respectively. It can be seen in Figs. 6(b) and 6(e) that the surface currents in the upper and the lower patterned copper layers are primarily concentrated on the edge of the air ring when the device is unbiased. The surface currents in the upper and the lower patterned copper layers are antiparallel and flow along the direction of the electric field of the incident EM wave. Meanwhile, Figs. 6(c) and 6(f) show that the surface current distributions in both biased and unbiased cases are similar, although the amounts of surface current in both cases are significantly different. These results indicate that the THz incident wave excites the surface plasmon polaritons (SPPs) on the metal surface. The THz wave energy is coupled into the metal microstructure in the form of SPPs and is confined to the metal surface.
Fig. 6. Electric field and surface current distributions at 416.7 GHz while biased and unbiased. (a) Electric field distribution while unbiased (x = p/2). (b) and (e) Surface current distributions in the upper and the lower patterned copper layers, respectively, while unbiased. (d) Electric field distribution while biased (x = p/2). (c) and (f) Surface current distributions in the upper and the lower patterned copper layers, respectively, while biased.
Strong localization of the THz wave is recognized. The extinction or attenuation length is on the order of the wavelength of the incident THz wave. The THz radiation transmitted through multiple layers in the plasmonic MMs can be tuned by controlling the refractive index of the NLC sandwiched between the two MM layers. The THz transmittance is enhanced due to the coupling between the surface EM waves in the metal/dielectric multi-layers with a periodic array of sub-wavelength elements. Meanwhile, the relatively thin thickness (about 486 µm) of the device reduces the attenuation of the terahertz signal. The metal microstructure is immersed in the NLC layer. The evanescent field provides coupling between the MM layers and will propagate in the NLC layer. Therefore, the NLC layer in the MLM structure has a strong influence on the transmission spectrum. The results presented above validate that a large amplitude MD and a small IL can be obtained by adjusting the bias voltage and changing the dielectric constant of the LC layer.
4. Conclusions
In this paper, a tunable MM in the THz frequency range is designed, fabricated, and tested. The EM transmission is investigated through the NLC-based double-layered metal hole-loop arrays while the device was irradiated at normal incidence with THz EM waves. The tunability of the device is verified by performing transmittance measurements of the device at different bias voltages (0 - 16 V). The experimental results show that the amplitude MD and IL of the fabricated sample are 96% and 1.19 dB, respectively, at 421.2 GHz. The proposed device can be used as a THz modulator, filter, or switch.
Funding
National Natural Science Foundation of China (51607050, 61871171); Science and Technology on Electronic Information Control Laboratory Fund.
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