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Abstract
In this paper, an approach to achieve wide-angle beam scanning in the terahertz (THz) band with frequency sweeping was proposed based on a metasurface structure. To widen the scanning angular scope, a coherent enhancement mechanism for improving the mode competition efficiency of the high-order diffraction mode was first implemented. A systematic method was firstly developed for the design of practical frequency-controlled beam scanning quasi-optics in THz band, in which the optimization of scanning range, linearity, and the avoidance of beam blocking are comprehensively considered. The proposed concept and approach was verified by the measured wide-angle beam scanning at the 0.18-0.22THz frequency band, with a diffraction efficiency of the main lobe as high as 88 percent. The good performance of the device paves the way for potential applications in THz imaging, moving target detection, and communication.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves are generally referred to the spectrum from 0.1 and 10 THz, which lies in a special transition of the electromagnetic (EM) spectrum [1]. Unlike optical and infrared radiation, THz waves offer the property of being able to ‘see through’ obscuring materials such as clothing, cardboard, and wood with relatively little loss. Compared to microwave and lower radio frequency wave, THz wave has shorter wavelength which results in better spatial resolution. Above unique advantages make THz imaging and sensing promising for plenty of applications, such as personal screening and surrounding surveillance for safety [2–7] and non-contact and non-destructive materials testing [8,9].
So far in THz band, mechanical steering scheme is commonly employed to realize the target location or detection for most of imaging systems [2–5], which inherently have the limitation of low frame rate. To reduce the imaging time and obtain high frame rate, electrical beam steering controlled by phased arrays is promising, whereas limited by the difficulty of develop phase shifters in THz band. An alternative approach is to realize beam steering by the frequency sweeping, which is referred as frequency-controlled beam scanning devices.
In the frequency band above 0.1THz, few of the works on the frequency scanning antennas have been reported [9–11]. And most of them employed the concept of leaky wave antenna. For example, a dielectric waveguide-based antenna with metal strips on its top side has been fabricated at 212GHz [9]. And a dielectric waveguide with periodic corrugations as the leaky structures has been developed at 97-103GHz [10]. Furthermore, a micro-fabricated slotted-waveguide with fast waves propagation and radiation has been realized at the frequency band of 130-150GHz [11]. Above structures are all fed at one end with fast waves mode excited and propagating down their axis to create the simultaneous leaky radiation.
Recently, THz metasurfaces, which are 2D equivalents of volumetric metamaterials, have been explored with extensive interests to arouse new concepts in physics and produce exotic electromagnetic functionalities in THz band [12–16], including high-efficiency THz modulators, low-loss polarization conversions, and the abnormal reflections and transmissions of THz waves. The method to realize beam scanning with micro-fabricated waveguide arrays and diffraction metasurface have also been proposed [17,18] recently in THz band. However, the useful angular scope of beam scanning is quite limited by the low transfer efficiency from incident THz wave to high-order diffraction, the poor linearity of the scanning angle to the frequency sweeping, and the lack of optimization for the topology of metasurface based quasi-optics system.
In this paper, the approach to achieve frequency-controlled beam scanning with wide angular scope was studied in THz band. It was achieved by effectively transferring the incident THz waves to higher-order diffraction based on a well-designed metasurface. A coherent enhancement mechanism was implemented to suppress the unwanted modes and improve the coupling efficiency of the main mode. A comprehensive method was studied to optimize the scanning range, linearity and to avoid beam blocking, to design a practical THz beam scanning system, which including both the THz metasurface and the relevant quasi-optics. With the proposed concepts and methods, a wide-angle beam scanning quasi-optics with good scanning linearity was designed and fabricated in 0.18-0.22THz band. The measured beam scanning range of the main lobe is about 135% wider than that of the conventional first-order mode, with mode transferring efficiency of the main lobe up to 88 percent, which verify the effectiveness of unwanted mode suppression. The good performance of the device paves the way for potential applications in THz imaging, moving target detection, and communication.
2. Design of the wide-angle beam scanning system with THz metasurface
2.1. Basic principle of the frequency-controlled beam scanning with THz metasurface
The metasurface is a planar 2-D periodic structure. The frequency-controlled beam scanning device is designed based on the metasurface. Figure 1 shows the schematic diagram of the beam scanning device, which is formed by metal layer, medium layer and periodic metal gap. The XOY plane is periodic surface, and XOZ plane is the incident plane, where θ0 is the incident angle. when the incident wave illuminates the metal gap surface, the periodic structure will generate diffraction wave and reflection wave, as shown in Fig. 1.
Figure 2 shows a unit of the beam scanning device, who contains two subcells which are H size’s metal chip, medium layer and metal layer. Dx is periodic length along the X direction and Dy is Y direction’s periodic length.
Floquet theorem is the best way to analyze the property of the periodic structure. As shown in Fig. 1, the periodic structure can generate different modes’ diffraction waves according to the Floquet theorem [19,20]. The grating function is constructed based on the Floquet theorem as
where k0 is free space wave number, m is the harmonic order, θm is the diffraction angle of the mth-order space harmonic called as mth-order mode.The propagation constant of the mth–order space harmonic along the X direction is given by
According to the period theorem, only the fast wave can radiate when , so to satisfy the relationship, m must be 0 or positive.
2.2. Design of the wide-angle beam scanning system
To achieve frequency-controlled beam scanning with wide angular scope, it’s an effective way to transfer the incident THz waves to higher-order diffraction based on a well-designed metasurface. However, one can found from Eq. (2) that, as the order of the main diffraction mode become higher, more other modes may become leaky and mode competition problem may become more complex to ensure high coupling efficiency of the main mode.
Comprehensively considering above aspects, the 2nd order mode are chosen as the main diffraction mode, which makes good compromise between the angular scope and the coupling efficiency. To minimize the modes competition, the unit length along X direction must satisfies
where λ is free space wavelength, θ0 is incident angle.In Eq. (3), the left side of the inequality means the 2nd order diffraction mode have to be leaky to achieve beam scanning, the right side of the inequality means the 3rd order and −1st order diffraction modes are both non-leaky modes. Hence, only the unavoidable 1rd mode and specular reflective mode may contribute to the mode competition. In this paper, a coherent enhancement mechanism is implemented to efficiently suppress these two unwanted modes, and ensure the high efficiency to couple the incident THz wave to the 2nd order diffraction mode. The detail of the method was given in Part C of this section. In Y direction, to avoid grating lobe, the unit length Dy should satisfy
In this paper, the metasurface with 2nd order diffraction mode for beam scanning was implemented as the fundamental component to achieve wide-angle scanning for frequency band 0.18-0.22THz. To develop a practical system (as schematic show in Fig. 1) consists of a feed horn, a lens and the metasurface, comprehensive design method has to be investigated to optimize the unit cell, the incident angle, the beam scanning linearity, and to avoid beam blocking resulted from the overlapping of the incident wave and different diffraction modes. To avoid the 2nd order mode overlaps the incident wave (feed blockage), the length Dx satisfies
In this paper, TE wave with electric field along Y direction was generated by the feed horn. A hyperbolic polyethylene lens with aperture diameter 7cm was used to collimate and focus the beam onto the metasurface which is at the distance of 30cm. Hence, the span angle of the incident beam is about 13.5°, which is referred as θs in this paper. From Eq. (3), one can found that the 2ndorder mode can’t be excited with small incident angle. Additionally, the grazing incidence with large incident angle approaching 90° should be avoided. So the incident angle θ0 is reasonably set in the scope of 25°~65°.
Figure 3(a) and 3(b) show two possible beam scanning topologies for the cases of large and small incident angle, respectively. In Fig. 3(a), the 2nd order mode diffraction beam is on the right of the incident THz beam, while in Fig. 3(b), the 2nd order mode diffraction beam is on the left. The angle between the beam centers of the incident wave and 2nd order mode is referred as θ20, and the angle between the beam centers of the 1st and 2nd order mode is referred as θ21.
From Eq. (1), the diffraction angle of 2nd order mode and 1st order modes can be derived as following
and the diffraction angle of 1st order mode is given by
To avoid the beam overlaps of the main mode with the incident and the unwanted leaky mode, the following two relations have to be satisfied for the whole band of the beam scanning system.
Here, the angular width of the diffraction beam is assumed to be same as the incident beam in our system topology, which is agree with the later experimental results. Based on the combination of Eq. (3), (8), and (9), the value of Dx is limited to a certain scope for each different incident angle θ0. Figure 4 gives the corresponding results in the Dx-θ0 plane. Only the shaded region with red and green color satisfy all the above requirements, and can be chosen as the valid parameters. The red region is corresponding to the small incident angle case as shown in Fig. 3(a), while the green region is corresponding to the large incident angle case in Fig. 3(b).
From Fig. 4, it’s found that the valid incident angle is confined to 25°~35° and 55°~65°. The suitable values of Dx are in the table below in which the Dx is every 0.01mm and the is every 1° considering the machining precision and angle accuracy.
For a frequency-controlled beam scanning device, another important property is the scanning linearity. Because the scanning angle is frequency-dependent, the scanning linearity shows the linear relationship between the diffraction angle and the frequency. To quantitatively characterize the linearity of the 2nd order mode, the first order derivative of scanning angle θ over frequency f can be obtained to describe the localized variation rate, however, considering the frequency is stepping, the angle difference between the adjacent frequency is more meaningful to characterize the linearity of the 2ndmode. In mathematics, variance is a measure of the degree of discretization of a set of data, so the linearity of the 2nd order mode can be measured by the variance of the angle difference between the adjacent frequency, as given in Eq. (10)
where n is the point number of the frequency, θj is the scanning angle of the first j frequency point, and is the average of all frequency point scanning angles.From Eq. (10), it can be seen that the variance value is more less, the linearity of the beam scanning angles is much better. Figure 5 shows the linearity of the 2nd order mode according to Table 1 and Eq. (10). In the Fig. 5, Each column has a different shape and color representing a different Dx value. The smaller the value of Dx, the larger the variance. It’s found that the smallest variance value is 0.1817 generated at θ0 = 55° and Dx = 2.25mm.
Table 1. Values of Dx Corresponding to Different Values of the θ0
In summary, by taking the beam blocking, the scanning linearity and the higher mode suppression problems into account, the incident angle and the unit cell period along X direction has been successfully optimized to be θ0 = 55° and Dx = 2.25mm, to ensure the good beam scanning performance at the frequency band 0.18-022THz. Additionally, with Eq. (4), the value of Dy is set as 0.8mm.To obtain high transferring efficiency from the incident THz wave to the main mode, the unavoidable mode competition from the unwanted 1rd mode and specular reflective mode must be carefully deal with based on the further optimization of the unit cell structure. This is important to ensure the radiation efficiency of the scanning beam and is studied in the following part.
2.3. Coherent diffraction enhancement with multiple subcells for the second order diffraction
In this part, a coherent diffraction enhancement method is implemented to ensure the high transfer coefficient from the incident THz wave to the 2nd order diffraction mode. Unit cells with multiple H shaped subcells was chosen to realize the coherent enhancement. Different dimensions of the subcells correspond to different diffraction phase, and the subcells’ sizes and distance in between are essential to the enhancement of the 2nd order diffraction mode. Unit cell with two subcells is chosen as shown in Fig. 6. The medium is ROGERS 5880 whose thickness is 0.254mm. Incident wave illuminates subcells and excites 2nd mode diffraction beam. The transfer phase from the incident wave into 2nd order diffraction mode can be obtained by numerical simulation with commercial software HFSS. Assuming the transfer phase of the subcell 1 and subcell 2 is φ1 and φ2, respectively, and d is the distance between the subcell 1 and subcell 2, the 2nd order mode can be coherently enhanced if the parameters satisfy following relationship
The optimized unit cell dimension is listed in Table2, and the simulated transfer phase for subcell 1 and 2 are given in Fig. 7. The phase difference changing from 220°to 195° over the frequency band 0.18-0.22THz, and the relationship of Eq. (11) are well satisfied over the whole band.
Table 2. Optimized Parameters of Unit Cell
3. Simulation and experimental verification of wide-angle beam scanning with artificial electromagnetic structure in terahertz band
With the optimized parameters obtained in Section 2, a planar metasurface was fabricated based on the laser fine etching technology. The laser fine etching technology is to focus the high-quality and low-power laser beam into a very small spot, and form a high power density at the focal point to vaporize the material instantly to form the hole, gap and slot. It has many advantages, such as non-contact processing, high degree of flexibility, fast processing speed, non-noise, small zone affected by the heat and good focus performance. To cover the focused beam from the lens as shown in Fig. 3, the planar metasurface includes 20 units in x direction and 55 units in y direction, and measures totally about 45mm × 44mm.Fig. 8(a) gives the photograph of the fabricated device. The magnified view of the unit cell with multiple subcells can be found in the insets of Fig. 8(b).
To characterize the designed metasurface and to measure the performance of the whole beam scanning system, an experimental setup was developed, as schematically shown in Fig. 9. The setup is mainly composed of three parts, including the THz transceiver, the computer controlled near field scanning platform and the beam scanning system developed in this paper for measurements. The THz transceiver was implemented with a microwave Vector Network Analyzer (VNA), THz multiplier and heterodyne receiver to couple the THz signal into the feed horn of the beam scanning system and to extract the field information from the probe in the near field scanning platform. The schematic diagram of the THz transceiver is shown in Fig. 10. Ku-band radio frequency (RF) and local oscillator (LO) continuous wave swept sources with 3.33 GHz bandwidth and fixed frequency difference of 25 MHz are provided by the VNA. The RF signal is upconverted with a × 12 multiplier and become RF1 signal in 0.2 THz band. Then the RF1 signal is divided into two branches by a coupler, one of which is directly transmitted by the transmitting horn. The LO signal is also upconverted and divided into two branches. One branch signal is mixed with the signal coupled from RF1 and subsequently input to VNA as the reference IF signal. Another branch signal is mixed with the received signal from the probe and input to VNA as the measured IF signal. After the coherent demodulation based on the reference and measured IF signals inside the VNA, the resulted field distribution information in 0.2 THz band are transferred to a computer for data processing. In this paper, the far field radiation pattern was obtained based on the field extrapolation method [21,22] with the measured amplitude and phase distribution by the scanning platform. Figure 11 shows the main part of the experimental setup.
In the experiment, the near-field scanning measurement covers a two-dimensional aperture with 600mm in horizontal direction and 400mm in vertical direction. The center of the scanning aperture is aligned with the center of the metasurface. Based on the measured data and the near-far field transformation, the normalized main lobe radiation patterns (corresponding to the 2nd order diffraction mode) for different frequency points in the band 0.18-0.22THz are obtained and shown in Fig. 12. It’s seen that, the beam scanning range of the main lobe covers from −41.4° to −23.1°, which is much wider than that of the first-order mode (as given later in Fig. 15). The 3dB beam width is about 2°-3° for the system in this paper, and can be changed by modifying the parameter of the illuminating beam with the dimension of the metasurface. For comparison, the simulated results of the radiation pattern is also given in Fig. 13. Since the whole beam scanning system including both the electrically-large components (such as the lens) and the fine structures (the unit cell structures), it’s not easy to conduct a full wave simulation. In this paper, an approximate method with two step was developed to numerically analyze the characteristics of the beam scanning device. In first step, a periodical-boundary simulation was implemented to extract the surface field distribution of the unit cell under the illumination of ideal THz planar wave with the incident angle as optimized in Section II. Then, the field at the surface of the whole metasurface with fabricated dimension was approximately derived according to the Floquet theorem. Finally, the far field radiation pattern was derived based on the surface field of the whole metasurface. It’s seen that, the experimental and simulation results agree well which validate the effectiveness of the simulation method with approximation but high efficiency.
Figure 14 give the comparison between the measured, simulated and theoretical diffraction angle for the 2nd order mode at the frequency band 0.18-0.22THz. Figure 15 shows the comparison between the measured, simulated and theoretical diffraction angle for the 1st order mode at the frequency band 0.18-0.22THz. It’s seen that, the measured results are close to the theoretical and simulation results with just a small deviation. For the 2nd order mode, the diffraction angle scans from −41.4° to −23.1° as the frequency changing, while for the 1st order mode, the diffraction angle scans from 4.5° to 12.3° as the frequency changing. This indicates the 135% improvement of the scanning angle is accomplished based on the proposed method with the successful mode competition of the high order mode. From the measured results, the minimum angle gap between the 2nd order mode and incident beam is 13.5°, and the minimum gap between the 2nd order mode and the 1st order mode is 27.6°. So the beam blocking problem can be completely avoided in the whole beam scanning systems.
Fig. 14 The measured results of the 2nd order mode wave compared with the theoretical and simulated results.
Fig. 15 The measured results of the 1st order mode wave compared with the theoretical and simulated results.
The mode competition was also quantitatively investigated based on the measured results. Table 3 gives the ratio of the main mode to the 1st order and the specular reflection beam. The ratio of the main mode to the specular reflection beam is all higher than 9dB and the ratio of the main mode to the 1st order mode is all higher than 7.5dB throughout the whole band, which validate the effectiveness of the coherent enhancement method developed in this paper. To study the efficiency of the main mode radiation, the metasurface is replaced with a smooth metal reflector. The ratio of the main mode radiation to the beam reflected by the metal was also given in Table 3.
Table 3. The Measured ResultsofDifferent Modes
4. Conclusion
In this paper, the approach to realize frequency controlled wide-angle beam scanning with artificial metasurface was proposed. The wavelength dependent diffraction with high order mode are produced based on the interaction of the metasurface with the incident THz wave. To design a practical beam scanning system including the metasurface and quasi-optics, a comprehensive optimization procedure was developed to determine the appropriate incident angle of the exciting beam and the unit cell dimensions, by taking into account the scanning range, linearity, and the avoidance of beam blocking. To achieve high mode competition efficiency for the main high order mode, a coherent enhancement mechanism was implemented to suppress the unwanted but unavoidable leaky modes, and to improve the radiation efficiency of the main mode. A wide-angle beam scanning quasi-optics with planar metasurface was designed and fabricated in 0.18-0.22THz band. With successful mode competition of the high order mode based on the proposed method, 135% improvement of the scanning angle is accomplished in experiment, with quite good scanning linearity. Additionally, the measured diffraction efficiency of the main lobe is up to 88% and average above 85% over the whole band, which indicates the remarkable inhibition of the unwanted diffraction. The good performance of the device paves the way for potential applications in THz imaging, moving target detection, and communication.
Funding
National Key Research and Development Program of China (2017YFA0701004), the National Natural Science Foundation of China (61671432 and 61731020), and Key project of equipment preresearch Fund (6140413010401).
Acknowledgments
It’s also noted that the first two authors contributed equally to this study and share the first authorship.
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