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Abstract
We proposed and demonstrated a metasurface based terahertz polarizer consisting of an optically responsive nanocomposite and a flexible base body, which fulfilled the function of linear-to-circular polarization conversion in transmission mode. Meanwhile, as the dynamic and stretchable materials enable the active manipulation of conversion points, evident frequency shifts for circular polarization transformation were discovered by applying laser irradiation and tension. Hence the modulation of conversion points covered a broadband with combination of those two external excitations. This THz polarization convertor may find its applications in polarization controls and beam steering, which also provides a low-cost and large-scale manufacturable method to achieve versatile active THz devices.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Manipulation of terahertz (THz) wave is of great significance to creating the new generation of information technologies, where 6 G wireless communication could enable new applications such as holographic communications, internet of everything, and chip-to-chip communications [1,2]. Over the past decade, great research interest has been aroused in THz manipulation [3,4] in which controlling the polarization state of THz wave plays a crucial role. Circularly polarized THz wave is considered more attractive than linearly polarized wave for their better ability to suppress multi-path interference and fading, reduce ‘Faraday rotation’ effect, and remove orientation restriction between transmitting and receiving antennas [5,6]. However, THz waves from most existing sources are linearly polarized [7]. Polarization convertors are thus indispensable to transform the linearly polarized THz wave into circular polarization.
Metasurface based THz waveplates have emerged as a promising candidate for THz wave polarization conversion [8–12]. Recently, the metasurface polarizers (MSPs) have been investigated for different applications such as spectroscopy [13,14], wireless communication [15,16], imaging [17]. Ghosh [18] proposed a tunable reflective-type MSP with a stable conversion from 3.71 to 4.93 THz by varying the chemical potential of graphene. To achieve broadband polarization conversion, Liu [19] developed a new theory and technique to realize achromatic polarization conversion in the frequency range of 0.2-1.1 THz. Nevertheless, large amounts of MSPs are in reflection mode which is difficult to prevent the interference from disturbing the output signal. As more attention is paid on transmissive linear-to-circular polarization convertors, multilayer MSPs are developed to elevate the bandwidth of conversion. Wu [20] demonstrated a double-layer MSP realizing less than −0.95 ellipticity (EP) in frequencies between 0.46 and 0.62 THz. In addition, Sun [21] designed and measured a three-layer THz quarter-wave-plate with conversion efficiency of more than 70% in the range of 1.65-1.84 THz. While diverse functions of THz MSP call for broadband polarization transformation, challenges for fabrication are upscaling as well. To address the issue, one approach is to use active metasurface, which not only implements the broadband modulation but also shows great tunability. Recently, efforts have been made on simulating graphene MSP to realize active and high-speed control of polarization state [22]. According to the simulation, phase modulation can be achieved by electrical tuning of the chemical potential of graphene, leading to broadband linear-to-circular polarization conversion. Materials with tunable permittivity, such as indium antimonide (InSb) [23] and strontium titanate (STO) [24], have been employed to achieve active MSP as well.
In our previous work [25], we made a nanocomposite which possesses tunable dielectric properties and can be easily patterned into micro-sized structures, which seems to be a potential choice to achieve active THz MSP. Based on such nanocomposite, an MSP could be demonstrated with capability of converting linear polarized THz wave into either left or right circular polarization (LCP or RCP). Here we show that such active linear-to-circular THz polarization converter can be achieved under excitations of laser and tension. Under illumination of 520 nm laser, ∼50 GHz blue-shift for the conversion frequency with EP of less than −0.95 was discovered. Meanwhile, the MSP also showed obvious shifts for both LCP and RCP conversions as the gap of the metasurface structure was elongated. With the synergic of those two excitations, a broadband linear-to-circular conversion was achieved.
2. Results and discussion
For all dielectric metasurface, meta-atoms usually have large refractive index and dielectric constant to differentiate with the dielectric background. To achieve such dielectric contrast, the meta-atoms were made by a high-index and flexible nanocomposite, which was embedded in the low-index polydimethylsiloxane (PDMS) elastomers as shown by the image in Fig. 1(a). Here the nanocomposite was obtained by in-situ reduction of HAuCl4 by PDMS monomer and followed by addition of strontium titanate particles (STOs) and curing to obtain the STOs and AuNPs filled PDMS nanocomposite (see method section) [25]. In prior, we have demonstrated that the permittivity of the nanocomposite can be tuned by the volume fraction of the STOs and dynamically changed by laser illumination due to the synergic effect of the STO and AuNP fillers [25]. The PDMS matrix material makes perfect joint between the nanocomposite meta-atoms and the dielectric background. Reprogrammable MSP polarization conversion devices can be then achieved by optical excitation of the nanocomposite meta-atoms or by mechanical stretching of the PDMS. Figure 1(a) illustrates the fabrication process and the micrographs of the MSP sample which has a total area of 10 × 15 mm2, and the parameters of MSP’s unit cell are indicated in Fig. 1(b). First, the nanocomposite meta-atoms were patterned on silicon substrate by template printing to form metasurface [25]. After that, the space between the meta-atoms and surroundings were filled by PDMS monomers and cured to embed the metasurface. The thickness of the PDMS dielectric background was controlled by a square mold as shown in Fig. 1(a). Finally, the devices were peeled off from the silicon substrate. Due to the addition of STO particles, the Young’s modulus of the nanocomposites is much larger than the PDMS dielectric background. As a result, upon application of longitudinal tension, the PDMS dielectric background was mainly stretched while the nanocomposites almost maintained its width. As depicted in Fig. 1(c), the MSP shows great flexibility due to the elastomer PDMS dielectric background, and the period of the nanocomposite stripes was well preserved during the reversible stretching. Under the manipulation of stretching, it was found that the stripes almost maintain a width of 75 μm, while the gaps between them can be pulled from 200 μm to 250 μm.
Fig. 1. (a) Schematic illustration of the MSP fabrication process; (b) the unit cell of the designed MSP; (c) micrographs of the fabricated MSP sample with and without external tension.
To design the MSP, Jones vectors [26,27] are presented for the x-polarized, LCP and RCP THz waves respectively as follow,
For stripe metasurface, the transmission matrix T0 is given for two orthogonal incident directions along x′ and y′ direction in Fig. 1(b) by:
where Tij is complex transmission coefficient of the transmitted THz polarized along the j direction relative to incident THz wave polarized along the i direction. When linearly polarized THz wave transmits along the two orthogonal directions, there exists only the diagonal T0xx and T0yy elements as given in Eq. (2), and the transmission coefficient matrix lacks orthogonal elements, which is essential for polarization conversion. To introduce non-diagonal elements, the all-dielectric metasurface was rotated with respect to the linearly polarized THz wave by θ, which gives the following form of T:To convert the x-polarized THz wave into LCP or RCP, the following equation should be satisfied at the operating frequency,
Simulations were performed using computer simulation technology (CST) microwave studio to design the MSP and study its polarization conversion properties by applying a frequency domain solver. Considering that the THz spectrum in our laboratory has its maximum amplitude at ∼0.7 THz, simulations were carried out to obtain optimized geometrical sizes of MSP operating in this near band, which gives the parameters of Fig. 1(b) as follows: w = 75 μm, p = 200 μm, and h = 100 μm.
For experimental measurement, THz time domain spectroscopy (THz-TDS) system was used to characterize the performance of MSP’s polarization conversion, as schematically shown in Fig. 2. By applying two wire grid linear polarizers (LPs) on both sides of the sample, the components of transmitted THz wave polarized in two orthogonal directions can be detected (see Method section). Experimental results were measured by the THz-TDS system by rotating LP2 and ZnTe crystal, which were then transformed to the frequency domain by fast Fourier transformation (FFT). The transmission spectrum was calculated as:
where Esam and Eref represent the electric fields of transmitted THz waves passing through MSP sample and air respectively.Fig. 2. Scheme of the THz-TDS setup for polarization conversion measurement. The inset in the lower left corner shows the relative direction of LP2 polarizer and the ZnTe crystal for measuring Txx (upper) and Txy (lower) respectively.
A sample of proposed MSP was fabricated by the template printing technique [25] and then characterized by THz-TDS system in a chamber filled with dry air (humidity < 10%) at room temperature. The measured two transmission coefficients (dotted lines) were plotted in Fig. 3(a) compared with simulated values with solid and dashed line respectively. Noticeably, a relative steady transmission of about ∼35% for Txy was obtained in a wide frequency band from 0.6 THz to 0.8 THz. On the contrary, Txx shows a decreasing trend within this band, resulting in an intersection point of Txx and Txy. Near this point, the phase of Txx (φxx) exceeds by almost 270 degrees with respect to φxy where the amplitudes of Txx and Txy are almost identical. As Eq. (5) indicates, the linear-to-circular polarization conversion occurs only when the amplitudes of those two transmission coefficients are equal and phase difference between them is odd number multiples of π/2 simultaneously. It is clear that the MSP satisfies the conditions at ∼0.7 THz leading to an LCP conversion point. In addition, the phase difference between φxx and φxy rises suddenly at ∼0.8 THz, where Txx shows a minimum. As illustrated by the inset in Fig. 3(b), the significantly enhanced azimuthal component of the displacement current and magnetic dipole at 0.8 THz are mainly localized in the metasurface, which can be ascribed to the first Mie resonance [28]. As a consequence, the sharp increase in phase difference, due to Mie resonance, contributes to another linear-to-circular polarization conversion point at ∼0.85 THz, while the phase difference has reached 450 degrees and the absolute values of Txx and Txy are roughly the same. The measured transmission properties are well fitted with the simulation values, and a slight deviation of phase difference can be found owing to structural errors of the fabricated stripes.
Fig. 3. Simulated and measured polarization conversion characteristics of the MSP: (a) Transmission amplitude of Txx and Txy and phase difference between them; (b) EP extracted from the transmission properties. The inset in (b) shows the simulated electric (left) and magnetic (right) field distribution at 0.8 THz with electric field polarized along x′ axis and magnetic field polarized along y′ axis.
To further characterize the polarization conversion efficiency, EP of the THz wave through the MSP was calculated, which can be obtained using the following equation:
where δ is the phase difference between Txx and Txy. As shown in Fig. 3(b), two conversion points located at ∼0.7 THz and ∼0.85 THz were obtained, which convert linearly polarized THz wave into LCP and RCP polarized THz wave respectively. For the experiment results, the measured EP gives a similar trend and its peaks are located at ∼0.72 THz and ∼0.83 THz. As discussed above, these consistent results manifests that the MSP is feasible and effective for polarization conversion. Moreover, with the optically active nanocomposite and flexible dielectric background materials, this MSP can achieve active tunability by either optical or mechanical stimuli, which could allow us to perform linear-to-circular conversion over a wide band range by tuning the conversion points.In our previous work [25], the optically tunable permittivity of the nanocomposite was elucidated. On account of the active nanocomposite and flexible base body, we proposed two methods to tune the polarization conversion points. Since the dielectric properties of the nanocomposite can be manipulated by 520 nm laser irradiation, the transmission spectra will shift as permittivity varies. In addition to variable permittivity, the changes in structural parameters will also lead to frequency shift. Below will demonstrate the characteristics of the active polarization converter under the excitations of laser and tension.
To verify the tunability of the polarization converter, optical excitation was firstly investigated by CST simulation. Figure 4(a) shows the EP varies with different permittivity. As the real part of permittivity (ɛ′) of the nanocomposite decreases from 12 to 10.5 corresponding to the experimental values at different laser powers [25], the conversion point shifts continuously and yields an optimal LCP conversion range in a bandwidth of ∼50 GHz under laser illumination. Moreover, the measured EP of the fabricated MSP is less than −0.95 from 0.72 THz to 0.77 THz as laser power increases from 0 W to 2.5 W, which basically agrees well with the simulation results as shown in Fig. 4(a) and (b). To provide a more intuitive description of polarized THz wave, trajectories of polarized electric fields in the incident wave plane were plotted for simulated and experimental results as shown in Fig. 4(c) and (d), respectively. The black arrow represents the electric field of the incident linear polarized THz wave with normalized amplitude. It can be found that the output THz waves were converted from linear polarization into LCP. The smaller radius of the trajectory than the incident wave indicates certain energy loss during conversion. As a result, the MSP fulfilled the function of linear-to-circular polarization conversion within 50 GHz bandwidth by laser manipulation which gives transmission of ∼35%.
Fig. 4. Simulated values with various ɛ′ and experimental results under corresponding laser powers for (a) and (b) the EPs, (c) and (d) the trajectories of normalized electric fields at polarization conversion points.
The tuning rate of the MSP converter should be in the same ballpark as the tuning rate of the dielectric constant of the nanocomposites of the same thickness. To estimate the tuning rate of the converter, a continuous nanocomposite film (∼100 μm) was measured by the THz-TDS system without laser excitation. Then the delay line of the THz-TDS system was fixed at the position corresponding to highest output voltage at the detector. Upon laser illumination, the output voltage will decrease due to the shift of the THz pulse in the time domain, which is induced by the variation of dielectric constant [29]. In three on-and-off switching cycles of laser, the output voltage at the detector was recorded at different laser powers as shown in Fig. 5(a), which gives rise and fall time of around 7 s. As a result, the tuning rate of the MSP converter is at the scale of seconds. The tuning rate could be improved by either using materials with fast heat dissipation or using ceramic fillers with fast electrical field response. Such works are in progress in our group.
Fig. 5. (a) Dynamic response THz pulse of ∼100 μm nanocomposite under square pulsed laser irradiation; (b) Schematic of effective refractive indexes with optical modulation; (c) Simulated effective refractive index in x′ and y′ directions and (d) their difference.
Effective medium theory is employed here to explain the optical tuning of the subwavelength stripe patterned MSP. According to the theory, the effective permittivity in x′ and y′ direction (ɛx′ and ɛy′) can be approximated by [30,31]:
Upon laser illumination, ɛ1 can be considered as a constant of 2.7, while ɛ2 was decreased from 12.0 to 10.5 as laser was gradually increased from 0 W to 2.5 W [25]. In this range, the variation of nx′ is negligible upon laser illumination from 0.65 to 0.75 THz as shown in Fig. 5(c), while ny′ shows a gradual decrease at higher laser power. The difference of the effective refractive index (Δn = ny′ - nx′) between the two orthogonal directions (x′ and y′ direction) can be calculated, which is decreased at higher laser power as shown in Fig. 5(d). According to Eq. (6), the linear-to-circular polarization conversion can be realized when the phase difference between x′ and y′ direction is odd number multiples of π/2, namely,
where c is the speed of light in air, f is the frequency of THz wave, and k is an odd integer. The satisfied frequency is marked by dots in Fig. 5(d). Consequently, as Δn decreases at higher laser power, the conversion point will shift to higher frequencies to maintain the phase difference. Therefore, the conversion point shifts from 0.72 to 0.77 THz as shown in Fig. 5(d).Further, the period of the stripes will also exert effects on the transmission coefficient. Apart from laser irradiation, another approach to manipulating polarization conversion points was proposed by stretching the MSP along the longitudinal direction. According to simulations, we discovered that by adjusting periodic parameters along the x′ axis marked in Fig. 1(b) the modulable polarization conversion range can be significantly broadened. According to Eq. (9) and Eq. (10), Δn will increase as the PDMS space was elongated, which shift the conversion point to lower frequency. As shown in Fig. 6(a), LCP conversion point shifts by ∼90 GHz when the structural period is elongated. More importantly, not only the incident LP wave has been converted into LCP but also the transformation of RCP becomes obvious bringing about an RCP modulation range of ∼120 GHz. In this way, the MSP sample was clamped by a fixture and then stretched to achieve structural elongation. From Fig. 6(b) we can see that either LCP or RCP conversion frequency shifted while increasing the gap between stripes, contributing to two ∼80 GHz conversion bands for both LCP and RCP which can be actively tuned by applying tension. Figure 6(c) and (d) shows the trajectories of polarized electric fields at different conversion frequencies corresponding to the extreme values extracted from Fig. 6(a) and (b). The transmitted THz waves maintained circular polarization state in a relatively broadband, exhibiting strong dynamic modulation ability. The Δn and conversion points at different elongation are illustrated in Fig. 6(e).
Fig. 6. (a) Simulated and (b) measured EPs of the MSP with different p, (c) and (d) show the trajectories of normalized electric fields at polarization conversion points; (e) Simulated effective refractive index difference.
3. Methods
3.1 Preparation of STO/AuNP/PDMS nanocomposites
In-situ synthesis method was used to generate plasmonic AuNPs working as photothermal elements. PDMS (Sylgard 184 from Dow Corning) was firstly prepared by mixing monomer and cross-linking agent at a mass ratio of 10:3, and the HAuCl4 (Sigma-Aldrich) aqueous solution with concentration of 0.01 M was then added to the premixed elastomer in a ratio of 1:9. After that, the mixture was stirred for 10 minutes to allow partial Si-H groups in the cross-linker react with HAuCl4 thus reducing gold elements which were then nucleated and grew to form AuNPs. Upon heat treatment, the vinyl groups in the PDMS monomer and the residual unreacted Si-H groups would undergo a hydrosilylation reaction in the presence of Pt catalyst resulting in a highly cross-linked PDMS with three-dimensional silicone network which ensured evenly embedded AuNPs. Furthermore, to make high-index nanocomposite, STO powders (Aladdin, particle size is ∼1.5 μm) of 40% volume fraction were introduced to the uncured AuNP-PDMS mixture followed by thoroughly stirring. Finally, the slurry was settled in vacuum chamber to remove bubbles and then transferred to a blast oven at 65 °C for 2 h to form STO/AuNP/PDMS nanocomposite.
3.2 CST simulation
The MSP was designed and the numerical simulations were realized by using the finite difference time-domain method in commercial software CST Microwave Studio. The periodic boundary conditions were applied in the x′ and y′ directions to mimic the infinite arrays, and the open boundaries are employed. Since linearly polarized THz wave transmitting along the z axis are incident on the metasurface and the transmitted signal was collected by the port boundary conditions, the corresponding transmission coefficient can be obtained.
3.3 Characterization of linear-to-circular conversion
The heart of the THz-TDS machine is an ultrafast femtosecond laser pulse, which is split into two beams. One is transformed into a picosecond pulse by ZnTe crystal to generate THz wave, another is referred as read-out pulse to collect the spectral information. Since any polarized electromagnetic wave can be decomposed into two orthogonal linearly polarized components, the polarization conversion performance of MSP can be identified by the electric field components in x and y directions accordingly. On this account, two wire-grid linear polarizers were placed on both sides of the MSP sample as shown in Fig. 2, where LP1 parallel to the x-axis was set to enhance the degree of linear polarization of the incident THz wave. More importantly, in order to collect electric fields in two orthogonal directions, LP2 was set where the transmitted THz signal went through. Consequently, when LP2 is placed parallel to either x- or y-axis, the transmitted THz wave’s component in the same direction can be measured. However, it should be noted that for the THz-TDS system based on ZnTe crystal, the intensity of detected electric field would be distorted when the polarization directions of the incident and transmitted THz waves were inconsistent. Here, it happens only when LP2 is placed perspective to x-axis. Especially in this case, ZnTe crystal for probing is supposed to be rotated by 270 degrees to obtain the actual magnitude of the detected electric field [32].
4. Conclusion
In this work, we proposed an active as well as flexible MSP which was made from optical responsive nanocomposite and fabricated using template printing method. From THz-TDS results, the ability of the MSP in converting linear polarized THz wave into circular polarization state was validated, yielding nearly perfect transmitted LCP at ∼0.72 THz and RCP at∼0.83 THz. In addition, development of its polarization conversion tunability by applying external excitations was also fulfilled. Under illumination of 520 nm laser, the LCP conversion point shifted by ∼50 GHz still maintaining EP of better than −0.95. Besides, ∼80 GHz redshifts for both LCP and RCP conversion frequencies were discovered by stretching the MSP to control the period parameters of the unit cell. In conjunction with the effects of these two incentives, a wide modulable polarization conversion band of 0.64-0.83 THz was achieved consequently. Further improvements of the insertion loss, bandwidth and tuning rate could be achieved by optimizing the dielectric meta-unit [21], material constituent of nanocomposite and tuning mechanism.
Funding
National Natural Science Foundation of China (62235004, 61831012, 62311530115, 51772045, 62171079); Sichuan Province Science and Technology Support Program (2021JDTD0026, 2022NSFSC0870).
Disclosures
The authors declare no conflicts of interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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