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Abstract
In this paper, a holographic metasurface possessing beam scanning capability at fixed frequency is presented. The desired radiation beam is obtained by using a reference wave to excite a sinusoidally-modulated impedance surface, which is equivalent to the interference pattern between the radiation wave and reference wave. By changing the bias voltage of varactor diodes loaded on the sub-wavelength unit cells, the variation range of the modulated impedance can be tuned, resulting in the change of radiation angle. Both the simulation and experimental results demonstrate that the direction of the radiation beam can be tuned in the range from 23° to 50° at 5.5 GHz. The proposed holographic metasurface shows great potential applications in constructing planar beam scanning antenna for integrated microwave system.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the past decades, planar leaky-wave antennas (LWAs) [1] have attracted a lot of attentions, due to the characteristics of low-profile, high directivity and simplicity of integration with other circuits. This type of antennas exhibit a frequency-scanning capability since the radiation direction of the leaky beam is related to the propagation constant β. However, the frequency-dependent nature of LWAs has limited their applications in modern wireless applications, which generally operate in a certain allocated frequency bands. Usually, the beam scanning capability is realized by loading active switches, such as GaAs Monolithic microwave integrated circuit (MMIC) and varactor diodes [2–4]. Recently, electronically steerable antennas based on composite right/left-handed transmission lines (CRLH TLs) have been presented due to the increasing requirements of beam steering at fixed-frequency [5,6]. Continuous controllability of the radiation angle was achieved by tuning the bias voltage of the loaded varactor diodes. In addition, half-mode substrate integrated waveguide LWAs were presented to obtain beam steering capability with circular polarization [7,8]. The inherent limit of CRLH TLs-type LWAs is that the propagation constant β and leakage rate α cannot be independently controlled. In order to obtain the tunable radiation angle and beam width simultaneously, both series and shunt varactor diodes should be added to per unit cell [9]. Therefore, the complicated structure would bring additional energy loss and difficulties to be integrated in millimeter-wave systems.
The concept of holographic antennas is an extension of holography operating in optical realm [10]. Typical holographic antenna is composed of surface wave launcher and interference pattern. The desired objective radiation wave (leaky-wave mode) is produced by using a reference wave (surface wave mode) to feed the holographic pattern. In order to simplify the interference structure, metal strips were placed at the minimum points of the interference fields [11,12]. With the development of metasurface, sinusoidally-modulated impedance surface was proposed to design holographic antennas [13–15]. The spatial profile of the surface impedance was set to match the interference pattern between the reference wave and the desired radiation wave. A modified scalar impedance surface was proposed to obtain the circularly polarized radiation by varying the relative phase of different regions of holographic pattern [16]. Besides wave radiation in the far-field region, holographic antenna also found applications in near field focusing [17,18], generation of Bessel beam [19] and wave front modulation based on substrate integrated waveguide (SIW) [20]. Recently, a holographic metasurface is proposed to produce beam scanning with the change of frequency [21]. However, there is little study on the holographic metasurface possessing fixed frequency beam steering capability in microwave region.
In this paper, an electrically beam steering antenna based on holographic metasurface is proposed to overcome the above-stated problems of the existing tunable LWAs. Firstly, the dispersion characteristic of unit cell loaded with varactor diode is analyzed. Then relationship between spatial distribution of the surface impedance and direction of the radiation beam is analyzed to provide theoretical foundation for the beam scanning. Finally, a prototype of the holographic metasurface operating at 5.5 GHz is fabricated and measured to demonstrate the beam steering capability experimentally. Good agreements between simulations and experimental results are obtained to verify the theoretical method. Compared to previous steerable LWAs, the proposed holographic metasurface possesses a simpler structure and less energy loss due to fewer tunable elements loaded.
2. Dispersion characteristics of the tunable unit cell
The proposed tunable metasurface is composed of sub-wavelength metallic units etched on a grounded substrate, as shown in Fig. 1(a). A varactor diode is loaded in the broken central bar of the “H” structure. The sub-wavelength unit can be considered as a lumped LC circuit under the incidence of TM surface wave with polarization direction perpendicular to the substrate propagating along the metasurface. Here the equivalent-circuit model is established to analyze the resonant behavior and dispersion characteristic of the unit, as shown in Fig. 1(b). C1 indicates the capacitor between the neighbor units, and the perpendicular bar is modeled as an inductance L1. C2 is used to describe the capacitive coupling between the “H” structure and the ground. Cv denotes the capacitance of the varactor diode. It is obvious that the gap size g has a great influence on the capacitance C1, but does not affect the L1 and C2. Thus, the resonant frequency and dispersion characteristic of the unit cell can be controlled by tuning the gap size g and the capacitance of the diode Cv.
Fig. 1 Unit cell loaded with varactor. (a) Geometrical structure of the tunable unit cell. The substrate with a thickness of 3 mm and a relative permittivity of 2.65 is used in this paper. The dimensions of the unit are p = 8 mm, l1 = 10 mm, w1 = w2 = 1.5 mm, d = 1.2 mm, and varied g. The metallic part is illustrated in yellow, and the dielectric part is shown in gray. (b) The equivalent-circuit model of the unit.
In order to verify the analysis, the dispersion curves of the unit with different g and Cv are simulated by the commercial software CST Microwave Studio. The phase difference φ across the unit can be calculated by eigen mode solver when the surface wave passes through a unit cell [22,23]. And then the phase constant β is calculated by β = φ/p. Since the eigen mode solver cannot analyze a unit containing lumped elements under periodic boundary conditions, the varactor diode is replaced by a parallel-plate capacitor with same volume in simulation [24,25]. The simulation results reveal that the phase constant β increases as g decreasing and Cv increasing, as shown in Figs. 2(a) and 2(b). As is well known, the surface impedance can be defined as the ratio of the transverse electric to transverse magnetic fields near the surface [26]. When the transverse-magnetic (TM) mode wave propagating along the surface, the surface impedance can be written as:
where η0 and k0 is the impedance and wave number in the free space, respectively, and β is the phase constant of the unit cell. And then the relationships between the surface impedance and g with different capacitances Cv are calculated at 5.5 GHz, as shown in Fig. 2(c). It is obvious that, the surface impedance of the unit cell would increase with gap size g decreasing when the Cv is fixed. Therefore, different unit cells can be used to build the sinusoidally-modulated impedance surface with fixed capacitance. The distribution of the impedance would be reconfigurable by tuning the uniform capacitance loaded on the unit cells.Fig. 2 The dispersion diagram of the unit cell. (a) Dispersion relationship with different gap size g, in which Cv = 1 pF. (b) Dispersion relationship with different Cv, in which g = 0.6 mm. (c) Relationship between surface impedance and gap size g under different Cv at 5.5 GHz.
3. Operating mechanism
According to microwave holography theory, the surface impedance distribution is utilized to reconstruct the whole interference pattern as
where ψref is the reference wave, ψrad is the radiation wave, represents the conjugate operation, Xs is the average value of surface impedance and M is the modulation depth. In this design, the reference wave and radiation wave are defined by: in which the x-direction is assumed to be the direction of the reference wave, n is the effective surface refractive index and θ is the elevation angle of the radiation wave. Therefore, the generated interference pattern would be rewritten as:According to the Floquet theory, the fields above the periodic structures can be expanded in terms of spatial harmonics, which depend on the modulation period:
The space harmonic mode with m ≤ 0 can be in the fast wave region (βm < k0) by choosing suitable modulation period d as β0 is larger than k0 for incident surface mode. Generally, one single beam is desired so that m = −1space harmonic is chosen to radiate the desired beam [27,28]. Therefore, the radiation angle θ of the proposed antenna can be derived as:
It can be seen that, the radiation angle θ can be adjusted by changing the average surface impedance Xs, when the modulation period d is fixed. The active holographic metasurface will be constructed by using the unit cell loaded with varactor in order to obtain the adjustable Xs, which is determined by the distribution of surface impedance across one modulation period.
4. Design example
The schematic of the proposed beam reconfigurable holographic metasurface is shown in Fig. 3(a), which consists of microstrip transmission lines (TL), matching transitions and the sinusoidally-modulated interference pattern. Here the interference pattern is composed of 8 modulation periods and d is chosen as 64 mm. Each period contains 8 tunable units with different gap sizes g. In order to possess a simpler bias network, the bias voltage distribution of the varactor diodes is uniform. All the units are controlled by a uniform capacitance (Cv), so that the distribution of the surface impedance is tunable. Both ends of the microstrip TLs are tapered down to achieve 50 Ω impedance in order to connect to SMA connectors directly. The matching transitions [29] provide a good matching of both momentum and impedance between the microstrip TLs and the interference pattern. The diode is modeled as a RLC series circuits in the simulation, where R = 0.8 Ω, L = 0.7 nH and C is the tunable Cv.
Fig. 3 (a) The schematic diagram of the proposed antenna. (b) Normalized impedance profile in one modulation period. (c) - (e) The simulated radiation patterns with capacitances of 2 pF, 4 pF and 6 pF at 5.5 GHz.
When the desired radiation angle θ is 20° at 5.5 GHz, the average impedance Xs can be calculated as 0.65η0 by applying Eq. (6). If the modulation depth M is selected as 0.45, the surface impedance across one modulation period is set to be: [0.94, 0.86, 0.65, 0.44, 0.36, 0.44, 0.65, 0.86] *η0, which can be satisfied by different unit cells under Cv = 2 pF. When Cv varies from 2 pF to 6 pF, the values of Xs/η0 is tuned from 0.65 to 1.27 and M is changed from 0.45 to 0.48. The distribution of the surface impedance across one period under different capacitance is shown in Fig. 3(b).The simulated far-field radiation patterns are presented in Figs. 3(c)-3(e) at 5.5 GHz. It can be seen that the radiation beam angle is 21° at Cv = 2 pF, which is in accordance with the theoretical calculation. Furthermore, as the loaded capacitance sweeps from 2 pF to 6 pF, the radiation angle scans from 21° to 49°. The beam width is almost unchanged for that the modulation depth M only changes a little, as shown in Fig. 4(a). According to the theory of holographic antennas, if the varactor diode in each unit cell is non-uniformly biased, the modulation depth M would be changed and the beam width would be tunable. In order to verify the beam width tuning ability, the capacitances of the diodes loaded in a single period are set to be non-uniform. Therefore, the modulation depth M can be controlled nearly independently of average surface impedance Xs. Three samples, which possess a uniform Xs and different M, are proposed and simulated. The simulated radiation patterns are shown in Fig. 4(b), and the distributed capacitances values in one modulation period are also shown to depict the spatial distribution of capacitance. The beam width increases with increasing M while the beam direction is approximately the same for all the radiation patterns.
Fig. 4 (a) The normalized E-field radiation patterns with different uniform bias voltage distribution. (b) The normalized E-field radiation patterns with different non-uniform bias voltage distribution.
In order to further verify the theoretical design, the prototype of the holographic metasurface with bias circuits is fabricated, as shown in Fig. 5(a). The substrate in this design is chosen as F4B with the relative permittivity of 2.65 and loss tangent of 0.001. The thickness of the substrate is 3 mm. Varactor diodes (Skyworks SMV1234-079) are chosen in this work since their low parasitic series resistances. For the control of bias voltage, the upper end of each unit cell is connected to positive electrode of DC source through a λg/4 line and another λg/4 line is in parallel with the bias line, where λg is the guided wavelength of dominant mode in the substrate. The width of λg/4 line is 0.2 mm, it is equivalent to an open end for the RF signal and passway for direct current. Therefore, the RF signal is blocked from coupling to the bias line and the effect of the network on the radiation performance of the metasurface is avoided. While the lower end of the unit is connected to the negative electrode of DC source through a λg/4 line and a via-hole. The number of λg/4 line is 128 and the bias lines of every two periods are linked together. The bias voltages of all varactor diodes are uniform and can be varied in a range from 6 V to 1 V. The bias voltage distribution and the corresponding capacitance in one modulation period are list in Table 1. The measurement of S-parameters is conducted by using an Agilent N5227A microwave vector network analyzer (VNA), and the results are presented in Fig. 5(b). It can be seen that the reflection coefficient of the proposed antenna is almost below −10 dB in the frequency range of 5.1 GHz to 5.6 GHz, which means good impedance match is provided. Meanwhile, S21 is always below −10 dB indicating that little energy is transmitted to the output port. But it is difficult to separate the leakage power and internal loss of the metasurface structure. Therefore, the leakage rate α which corresponds to the leakage power along the structure, is extracted [8], as shown in Fig. 5(c). According to Eq. (7), the radiation efficiency ηrad with different capacitances are all greater than 75%.
where LA is the effective length of the metasurface. So that the internal loss is limited and the majority of energy has been radiated to space. Then the far-field pattern is measured in the anechoic chamber. A linearly polarized horn antenna is used as the receiving antenna. During the far-field measurement, a 50 Ω SMA load is connected to the output port in order to minimize reflections from the end of the antenna. The measured gain of the antenna is shown in Fig. 5(d), which shows that the main lobe direction has a good agreement with the simulation results. The radiation angle varies from 23° to 50° with the voltage changing from 6 V to 1 V at 5.5 GHz, which is in accordance with simulation results and theoretical calculations. The measured gain is about 4.9 dBi during the scanning range, which is a bit lower than the simulated results. This difference could be resulted from the fact that practical resistance of varactor diode is a little bigger than used in the simulation. Besides, the additional loss brought by manufacture error may also contribute to the loss in the realized gain. It is worth mentioning that the simulated gain at 6 V is 7.51 dBi and the corresponding measured result is 5.33 dBi. It is because that the resistance of the diode is set to be a fixed value under different bias voltage in simulation, but the practical resistance would be changed according to the datasheet of the diode. Therefore, the difference of 2.2dB may be caused by the unstable impedance characteristic of the varactor diode.Fig. 5 (a) The photograph of the fabricated antenna. (b) The measured S-parameters. (c) The extracted leakage rate α. (d) The measured and simulated gain at 5.5 GHz.
Table 1. Bias Voltage Distribution and Corresponding Capacitance in One Modulation Period
5. Conclusions
In this paper, an active holographic metasurface is used to validate beam steering at fixed frequency. The holographic metasurface is composed of sub-wavelength unit cells and itssurface impedance can be controlled by the loaded varactor diodes. The relationship between the desired radiation beam and distribution of the surface impedance is analyzed to construct the interference pattern. By tuning the uniform bias voltage, the main lobe of the radiation wave can scan from 23° to 50° at 5.5 GHz. The measured results show good agreements with the numerical simulations. Contrary to the conventional holographic antenna, the beam scanning capability is obtained by tuning the bias voltage rather than tuning frequency. Furthermore, only one varactor diode is loaded in the proposed unit cell, which means it possesses simpler structure and less energy loss. Such results ensure that the proposed active holographic metasurface has a very promising future in modern communication system.
Funding
National Natural Science Foundation of China (No.61771172, No.61571155, No.61401122, No.61371044, No. 61701141); Open project of State Key Laboratory of Millimeter Waves (K201709,K201828); China Postdoctoral Science Foundation funded project under Grant (No. 2016M600248); Heilongjiang Post-doctoral Financial Assistance under Grant LBH-Z16065.
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