Manipulating polarization states of terahertz radiation using metamaterials

We present a double-ring-chain metamaterial that enables efficient polarization conversion of terahertz waves. The experimental results and numerical simulations reveal that the linear-to-linear polarization rotation and linear-to-elliptic polarization transformation are simply accomplished by altering the dimensional parameters of the metamaterial unit cells. The polarization state conversion is found to be critically related to the resonant properties of the long bars and the rings in the unit geometries and is well described by the Jones matrix. This approach promises both passive and active polarization conversion of terahertz radiation using planar metamaterials.


Introduction
Manipulation of wave polarization states is one of the essential and challenging tasks in the terahertz regime [1]. Over the last few decades, various designs of polarizers and wave plates have been proposed, including sheet polarizers using anisotropic absorption media, prism polarizers, Brewster-angle polarizers, wire-grid polarizers [2], as well as birefringence utilizing paper [3], liquid crystals [4], multi-layer meander liners [5] and chiral effect [6][7][8][9][10]. However, more convenient and flexible approaches are always desirable to completely control the polarization states [11][12][13][14][15]. This has become possible with the advent of metamaterials that promise a variety of fascinating physical phenomena, such as negative refraction [16][17][18][19], invisibility cloaking [20,21], superfocusing [22] and miniaturized antennas [23]. Here, we show that a specially designed planar metamaterial can be employed to manipulate the polarization state of terahertz waves. By altering the geometric parameters of the metamaterial unit cells, we experimentally and numerically demonstrate that the polarization of the incident linearly polarized terahertz waves can be efficiently converted.

Results and discussions
The basic building block of the proposed metamaterial is shown in figure 1(a), where each single unit cell of the structure consists of a pair of double-ring chains (DRCs). The DRC array was fabricated on a 200 nm thick aluminum film by the use of conventional photolithography and metallization processes on a 640 µm thick p-type silicon substrate. The array sample has a total 15 mm × 15 mm square area with a microscopy image shown in figure 1(b). Figure 1(c) illustrates the normal resonant transmission behavior of the metamaterial structure upon excitation with a linearly polarized terahertz wave.
The polarization-dependent terahertz responses of various DRC samples were measured by the use of terahertz time-domain spectroscopy (THz-TDS) with the help of four inserted polarizers [24,25], as shown in figure 1(d). The first polarizer is placed in front of the sample to enable a linearly polarized terahertz wave that propagates through the DRC array. The other three analyzers are placed in front of the photoconductive antenna detector with designated directions of polarization. By rotating the first analyzer (A 1 ) with horizontal (θ = 90 • ) or vertical polarization (θ = 0 • ), we then are able to obtain the transmitted terahertz wave of orthogonal components through the sample. In the experiment, the linearly incident terahertz wave is oriented horizontally along the x-axis, and the transmitted electric fields along the x ( E x x (ω)) and y ( E x y (ω)) axes are then measured with respect to θ = 90 • or 0 • , respectively. The amplitude transmissions are further achieved as and E R x y (ω) denote the electric fields through the sample (superscript S) and the reference (blank Si substrate, superscript R). The phase difference ϕ diff = ϕ x y − ϕ x x = arg(t x y (ω)) − arg(t x x (ω)) between two orthogonal polarizations is further extracted from the measured data.
To determine the polarization state of the terahertz wave through measurements, four Stokes parameters are introduced as [1] where S 0 is the relative intensity of the wave in x-linear polarization and y-linear polarization, S 1 depicts the preponderance of x-linear polarization over y-linear polarization and S 2 and S 3 represent the phase information. According to equation (1), we have the polarization azimuth α and the ellipticity angle χ as

Rotation of the polarization azimuth
The first row of figure 2(a) shows the measured amplitude transmissions |t x x | and |t x y | of the sample with structure azimuth β = 10 • , where a strong resonance is located at 0.66 THz of |t x x | = 0.89, |t x y | = 0.16 and a phase difference ϕ diff = 1 • . The measured characteristic spectral responses of the chosen structures are further supported by a full wave numerical simulation using CST Microwave Studio, as shown in figure 2(b). The unit cell shown in figure 1(a) is used as a model in the simulations with periodic boundary conditions. The silicon substrate is modeled as a lossless dielectric ε = 11.78 and Al has a conductivity σ = 3.72 × 10 7 S m −1 . The simulations reveal good agreement with the experimental results. According to equations (2) and (3), we obtain the polarization azimuth α = 10 • and the ellipticity angle χ ≈ 0 • for this sample, which indicates that the linearly polarized incident wave along the x-axis is completely rotated 10 • transmitting through the metamaterial structure, but remains linearly polarized. The extracted α and χ from the measured data are also consistent with those in the simulations. In addition, the performance of frequency-dependent polarization conversion can be further described by polarization conversion rate (PCR), which is defined as [14]  To gain insight into the linear polarization conversion of the proposed structure, we have further characterized different samples with various β. When the structure azimuth β is increased from 10 • to 30 • , it is interesting to observe that the polarization azimuth α is also increased, as shown in the second row in figures 2(a)-(d). For the sample of β = 30 • , the amplitude transmissions of two orthogonal components are |t x x | = 0.69 and |t x y | = 0.40 with ϕ diff = 1 • at the resonance frequency, while PCR reaches 0.37. In this case, the measured α and χ are equal to 30 • and 0 • , respectively. Further increasing β to 45 • , we obtain |t x x | = 0.47, |t x y | = 0.49 and a small phase difference ϕ diff = 5 • with an increased PCR value to 0.51 at resonance frequency. In this case, we have α = 46 • and χ ≈ 0 • . The overall qualitative agreement between the experimental and simulation results is quite good. Figure 2(d) visualizes the polarization conversion processes.
So far, we found that a linear-to-linear polarization conversion of polarization azimuth α could be achieved based on the proposed metamaterial structure with an equal structure azimuth β, namely α = β. Hence, an arbitrary linear-to-linear polarization conversion could be achieved through appropriate structure designs. To elucidate the underlying mechanism of these polarization conversion characteristics, the field distributions at the resonance frequency for the sample of structure azimuth β = 30 • , as an example, are given in figure 3. For either the horizontal incidence along the x-axis ( figure 3(a)) or the vertical incidence along the y-axis ( figure 3(b)), the resonant fields are both found to be mostly concentrated in the middle of the long bar. Therefore, the long bar in the chosen structure plays a key role in the polarization conversion process. In particular, we notice that the component of the electric field perpendicular to the bar makes a major contribution to the resonance excitation [26]. As a result, if a plane wave of linear polarization is incident on the structure, there is a tendency for the transmitted wave to be predominantly polarized perpendicular to the bar. When the structure is further rotated, the polarization of the transmitted wave would be changed with the polarization vector perpendicular to the long bar.
An alternative approach based on the Jones matrix gives an apparent and straightforward description of the polarization conversion of the proposed DRC structure. We consider the incident electric field vector as and after normalization, it is written as E in = ( 1 0 ), and A out B out = g 11 g 12 g 21 g 22 where E out = ( A out B out ) is the transmitted field, and G = g 11 g 22 is the equivalent Jones matrix of the chosen metamaterial structure. Here, G can be estimated as where the coefficient ζ is 0.92 for the proposed structures.

Transformation of the polarization state
In addition to the evidence that the proposed structure could realize the linear-to-linear polarization rotation at resonance frequencies, we found that such a design can also be utilized to achieve transformation of the polarization state. While the other dimensional parameters are fixed as those in the above structure of β = 45 • , we increase the radius of the rings in the DRCs to r = 12 µm and the distance of two chains to a = 34 µm. If the distance of two rings b is varied, we observe that the transmitted wave is elliptically polarized from linear polarization with different phases. Figure 4(a) shows the measured amplitude transmissions |t x x | and |t x y | of various samples. If we set b = 40 µm, then |t x x | and |t x y | are 0.815 and 0.324 at the resonance frequency of 0.66 THz, but differ in phase by about 68 • . The corresponding polarization azimuth and ellipticity angle are α = 10 • and χ = 20 • , respectively. This indicates that the linearly polarized incident wave is to be left elliptically polarized with the principal axis azimuth of 10 • and ellipticity angle of 20 • . The measured results are in accordance with the simulations, as shown in figure 4(b). According to PCR, it reaches the peak value of 0.25 at 0.66 THz, as shown in figure 4(c). The emergent states are shown visually in figure 4(d).
The distance between two rings, b, is further increased to 48 and 56 µm, and the measured and corresponding simulated transmission spectra are represented in figures 4(a) and (b), respectively. With b = 48 µm, |t x x | = 0.62 and |t x y | = 0.44 with ϕ diff ≈ 89 • at the resonance frequency, PCR reaches 0.42. The measured polarization azimuth and ellipticity angles are α = 1 • and χ = 35 • , indicating that an elliptically polarized transmitted wave is realized. Further increasing b to 56 µm, we have |t x x | = 0.43, |t x y | = 0.46, ϕ diff ≈ 84 • and PCR = 0.42 at resonance frequency, with measured values α = −29 • and χ = 42 • . Since sin 2χ = 0.995 ∼ 1.0, the corresponding linearly incident wave is now almost circularly polarized [21].  It can be seen from figure 4 that the ellipticity angle χ experiences a significant increase with increasing b. When b is increased from 40 to 56 µm, sin 2χ is enhanced from 0.637 to 0.995, which means that the linearly polarized incident wave is converted into elliptically polarized or even circularly polarized wave after transmitting through the metamaterial structures.
The underlying mechanism in this situation can also be elucidated in the electric field distributions. Taking the sample of b = 48 µm as an example, fascinating features are observed, as shown in figure 5. Most of the energy is concentrated not only in the middle of the long bar ( figure 5(a)), but also in the cross section of DRCs ( figure 5(b)), although they have different phases. Therefore, both the long bar and circular rings contribute to the resonance of the structure, and the interactions of the linearly polarized incident wave with both of them thus lead to elliptical polarization conversion of the transmitted wave.

Further systematic experiments
Furthermore, we investigate additional structures of different dimensional parameters, which can realize the linear-to-linear rotation, as well as the linear-to-elliptic transformation at various resonance frequencies. Figures 6(a) and (b) show the measured amplitude transmissions although a serious of DRCs with dimensional parameters is listed in table 1. It is seen that these structures could realize the polarization conversion at different resonance frequencies.

Conclusions
We show that a DRC structure enables efficient manipulation of terahertz polarization. The linear-to-linear polarization rotation and the linear-to-elliptic polarization transformation have been experimentally and numerically demonstrated. The polarization of the incident wave after transmitting through the proposed metamaterial structures can be well modulated at resonance frequencies. The resonances of the long bar and the circular rings in the unit cell play a key role in the polarization conversion process. The interactions of the linearly polarized incident wave with both unit elements thus lead to rotation or transformation of the polarization state. Hence, one could manipulate the polarization state simply by altering the resonance behaviors through appropriate geometric designs. This approach offers a new way of implementing polarization conversion of terahertz waves using metamaterials, and such a design may also be extended to higher frequencies.