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We present a method to design and fabricate a kind of converters based on flexible metasurfaces which can change the polarization state of an incident terahertz beam. The metasurface consists of a two-dimensional array of rectangular metallic antennas that can abruptly change the phase of the incoming terahertz beam. Experimentally demonstrated half-wave plates generate 0.1 THz beam with a π/2 polarization rotation. By slightly changing the structure of the converter, an elliptically or circularly polarized beam is expected to be obtained. These flexible terahertz converters may have many potential applications in terahertz technology.
© 2016 Optical Society of America
1. Introduction
Polarization is an important property of light wave, change of which may have lots of applications in optical science and technology. Conventional approach to change the polarization state is to use a birefringent crystal which can cause different phase delays along two orthogonal axes. Yet this approach may have some disadvantages such as low efficiency, bulky volume, frangibility, long propagation distance and narrow bandwidth.
Terahertz (THz) wave consists of the electromagnetic waves between infrared light and micro waves. Thus it has many properties of both infrared light and microwaves. THz technology has made a great progress in recent years, and many functional THz devices have been developed [1,2]. However, controlling the polarization state of THz wave remains a big challenge due to lack of suitable natural materials. Manipulating the polarization state of THz wave is of vital importance because it may have potential applications in THz imaging, communication and sensitive detection [3–8]. So far, many studies have been focused on changing the polarization state of THz wave [9–11].
Recently, metasurfaces, a kind of two-dimensional artificially designed devices, continuously attract a great deal of attention due to their special ability. That is, metasurfaces can abruptly change the amplitude and phase of the incident beam, while nature materials cannot. Metasurfaces can be designed to work at different frequency on a subwavelength scale. V-shaped antennas, C-shaped antennas, rectangular patches have been reported to control the propagation of the incident beam [12–17]. Over the past years, a number of metasurface devices have been designed such as flat lens, vortex beam generator, polarizer and beam splitter [18–37]. In order to tune the polarization of light more freely, many works have been done [38–40]. It has been demonstrated that a broadband quarter-wave plate was made based on plasmonic metasurfaces working from λ = 5 to 12 μm, thus offering a great way to control the polarization of light wave from middle infrared to far infrared [41]. Designing and fabricating metasurfaces to realize a kind of polarization converters working at THz waveband is of great significance to the development of THz functional devices.
In this paper, we present a method to design and manufacture metasurfaces based on metallic antenna arrays that can abruptly create the phase delay of an incoming THz wave. Numerical simulations demonstrate that such metasurfaces can be used for THz polarization converters to realize linear-to-linear, linear-to-circular or linear-to-elliptical conversion. In particular, we fabricate several samples working at 0.1 THz and experimentally demonstrate that one of them can use as a half-wave plate. Our work provides a way to fabricate a kind of ultrathin flexible THz polarization converters.
2. Simulation and design
Let us firstly consider a unit cell, schematically depicted in Fig. 1(a). It is composed of an Ag nano rectangular rod (i.e., antenna) and an Ag ground plane separated by a 0.2 mm Polypropylene spacer, one kind of flexible materials. The height of the antenna is 10 μm and the thickness of the Ag ground plane is 0.45 mm. The unit cell is square with side length L = 1.5 mm. When illuminated by an incident beam, electric currents will be created both in the antenna and the ground plane. The two currents show an anti-symmetric distribution. Then a magnetic resonance can be generated because of the near-field coupling between the rod and the substrate at particular frequency. This magnetic resonance can be affected by the geometric and material’s parameters of the unit cell. That is why we can manipulate the THz wave by changing the size of the antennas. The reflection property of the unit cell is investigated at THz waveband via numerical simulation based on the well-known finite difference time domain (FDTD) method with periodic boundary conditions.
Fig. 1 (a) Schematics of the unit cell. It is composed of an Ag (yellow) nano rod and an Ag ground plane separated by a 0.2 mm Polypropylene (grey) spacer. The spacing distance L is 1.5 mm. The thickness of Ag rod Ta is 10 μm. (b) The structure of the line array A (B) that is includes 8 unit cells in a row, in which the antennas have the same values of Lx (Ly) and different values of Ly (Lx).
Let Lx and Ly denote the two side lengths of the rectangular antenna, respectively. The reflection property is simulated when the unit cell is normally illuminated by a continuous plane wave (0.1THz) polarized at 45 degrees to x-axis. Figures 2(a) and 2(b) show the calculated Ly dependence of the amplitude and phase of the reflected field components Ex and Ey. The results show that the amplitude of Ex and Ey does not change with Ly, while the phase of Ey changes with Ly but the phase of Ex keeps unchanged. That means the antenna in the unit cell becomes resonant when we change the length Ly. The amplitude of Ex and Ey keeps stable because of the small resonance absorptions on the metasurfaces [42]. The Lx dependence is also calculated, but not shown here. All the results demonstrate that the phase of the x- and y-polarization reflection wave is sensitive to the variation on the antenna size Lx and Ly, respectively.
Fig. 2 The calculated amplitude and phase of the reflected field components Ex and Ey when the unit cell is illuminated by a normally incident 0.1 THz beam polarized at 45 degrees to x-axis. (a) and (b) The Ly dependence for Ex and Ey, respectively. The Lx dependence is not shown here. (c) and (d) Eight unit cells from #1 to #8 are considered and each cell is calculated individually. The calculated results of the eight unit cells are put all together for Ex and Ey, respectively. The Lx and Ly of the antenna in the unit cell from #1 to #8 are Lx = 0.32 mm and Ly = 0.7, 0.84, 0.87, 0.9, 0.92, 0.94, 1.0, and 1.3 mm, respectively.
We then consider eight unit cells. The antenna in each cell has the same values of Lx and different values of Ly, i.e., Lx = 0.32 mm and Ly = 0.7, 0.84, 0.87, 0.9, 0.92, 0.94, 1.0, and 1.3 mm, respectively. The amplitude and phase delay of the reflected field components Ex and Ey for each cell are calculated individually when this cell is normally illuminated by a plane wave (0.1THz) polarized at 45 degrees to x-axis. Note that the phase delay means the delay between the reflected wave and the incident wave, and the phase of the incident wave is the same for each case. The calculated results for the eight cells are put all together in one figure, and Figs. 2(c) and 2(d) show the results for Ex and Ey, respectively. For the case of Ex, both amplitude and phase delay are nearly the same for each cell. For the case of Ey, however, the amplitude is nearly the same for each cell, while the phase delay is different. In particular, each additional cell can provide π/4 phase increment, thus allowing a full phase control from 0 to 2π if the eight cells are strung into a line array. Based on this, we have the reason to consider to construct a line array A (B) that is includes eight unit cells in a row, for which the antennas have the same values of Lx (Ly) and different values of Ly (Lx), as shown in Fig. 1(b). The array A (B) provides the ability to tailor the phase of Ey (Ex) from 0 to 2π.
The reflection property of the line array A as a whole is simulated with periodic boundary conditions, as shown in Fig. 3. When A is under the incidence of a normally incoming THz beam polarized at 45 degrees to x-axis, the incident beam is anomalously reflected and the wavefront of Ey is changed. However, the wavefront of Ex remains unchanged as we expect. An efficiency of conversion is defined as the intensity ratio of the reflected wave to the incident wave. When the line array A is illuminated by an incident wave polarized along y axis, the conversion efficiency is very high, almost 80%. When illuminated by an incident wave polarized at 45° to x-axis, the conversion efficiency is almost 40% as a whole because Ex normally reflects from the surface as can been seen in Fig. 3. Also, if the line array B is illuminated by the same incident beam, the wavefront of Ex will change and the wavefront of Ey remains unchanged (not shown in Fig. 3). Reflection angle θr of the extraordinary beam can be calculated via the following equation [14]:
which can be derived from the generalized Snell’s law:where λ0 is the vacuum wavelength of the incoming beam, θi is the incident angle, θr is the reflection angle, nr = ni = 1. and p is the length of the line array.Fig. 3 The simulated reflected field patterns on x-z plane when the liner array A is under the incidence of a normally incoming THz beam polarized at 45 degrees to x-axis.
Based on the calculation, simulation and analysis above, and inspired by the literature [41], we now present an idea to design a kind of metasurfaces as shown in Fig. 4(a). This metasurface consists of six A line arrays and six B line arrays. A and B are interlaced arrangement along y direction with an offset distance d between them in the x direction which can cause the abrupt phase delay between the line arrays A and B. When a THz beam is normally incident on such a metasurface, considering the existence of the arrays A and B which can redirect Ey and Ex respectively, the reflected beam could be understood to include two beams: beam A and beam B. The coupling between beams A and B may allow the metasurface to be of an ability to convert a linearly polarized beam into an extraordinary beam with different polarization states for different values of d.
Fig. 4 (a) The structure of the deigned metasurface consisting of the line arrays A and B which are interlaced arrangement along y direction with an offset distance d between them in the x direction. (b) The calculated Lissajous figure for the deigned metasurface, which shows the different polarization state could be obtained by changing the distance d with d = 0, d = p/8, d = p/4, d = 3p/8, and d = p/2.
In order to check the ability described above, the Lissajous figure of the reflected wave is calculated when the metasurface is normally illuminated by a 0.1 THz plane wave linearly polarized at 45 degrees to x-axis. A series of monitors in the far-field with different distances from the metasurface are used to measure the electric field. Then this collection of measures are used to build the Lissajous figure, as depicted in Fig. 4(b). The square in Fig. 4(b) represents the projection of the electric vector on x-y plane of the far-field which can show the polarization state of the reflected beam. As expected, the polarization state of the incident wave can be tuned from the linear polarization state to the other polarization states depending on the offset distance d. In particular, the cases of d = 0, d = p/8, d = p/4, d = 3p/8, and d = p/2 are considered, and the linear, circular or elliptical polarization state should be achieved.
3. Experimental demonstration
In order to experimentally confirm our design idea, we made several metasurfaces via the photolithography and electron beam evaporation technology, as shown in Fig. 5(a). The height of the metallic antenna is 150 nm which is thicker than the skin depth of the THz wave. A source Tx is used to generate a continuous linearly polarized THz beam at 0.1 THz, and a receiver Rx is used to detect the THz beam, as shown in Fig. 5(b). Lens A is used to collimate the THz beam generated by Tx, and Lens B is used to collect the reflected THz wave. The receiver is put on a rotator to detect the signal with different rotation angles so as to see the polarization state of the wave. The receiver Rx is sensitive to linearly polarized THz wave. A Lock-in amplifier connected to the receiver is used to show the relative intensity of the signals. When we rotate the receiver, the intensity of the signal will change because the polarization state of the signal will mismatch with the receiver.
Fig. 5 (a) The microphotograph of the part of one fabricated metasurface. (b) The experimental setup. Tx is a 0.1 THz source and Rx is a receiver.
Two samples with d = 0 and d = p/2 are tested when the samples are normally illuminated. The experimental results demonstrate that the polarization state of the reflected beam keeps unchanged relative to the incident beam for d = 0, while rotates π/2 for d = p/2, as shown in Figs. 6(a) and 6(b), in which the red triangle represents the decreasing of the signal’s intensity compared with the maximum intensity of the THz wave when the receiver is rotated with different angles. The reflection angle is 15° for the both samples, which is the same as simulated. The measured reflection signal is almost 5.5 mV and the measured incoming signal is almost 20mV. As a result, the conversion efficiency is more than 27.5%, close to 40% that is the theoretic value expected above. A mirror is used as a comparison. When the position of the receiver Rx is kept unchanged but the sample is replaced by the mirror, any signals cannot be detected because the reflection angle is 0° for the mirror. These results mean that the samples can redirect the incoming beam and change its polarization state, and that the sample with d = p/2 can work as a half-wave plate at 0.1 THz.
Our experimental results confirm that the designed metasurfaces can convert a linearly polarized THz beam into an extraordinary beam with different polarization state for different values of d.
4. Conclusion
In conclusion, we design and analyze a kind of ultrathin flexible THz polarization converter based on metasurfaces and demonstrate experimentally a half-wave plate working at 0.1THz. Our work provides a way to design and fabricate the devices to change the polarization state of THz wave, which may have good applications in THz technology. Such converters can work at other THz wavebands through appropriately adjusting the structure parameters of the metasurface.
Acknowledgments
Funding: National Natural Science Foundation of China (NSFC) (1157410 and 61177095), and the Wuhan Applied Basic research project, China (20140101010009).
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