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Abstract
In this paper, a composite planar spiral antenna consisting of an eight-arm equiangular spiral antenna and eight Archimedean spiral antennas has been designed to radiate electromagnetic wave carrying tunable angular momenta in a wide band. A tunable eight-way Wilkinson power divider network is used to offer three kinds of feeding modes for the equiangular spiral antenna, and thus the composite antenna can radiate the electromagnetic waves with angular momenta of the modes l=1, 2, and 3, respectively. The Archimedean spiral is introduced to improve the gain of the composite antenna in the case of the angular momentum of l=3. By analyzing axis ratio (AR) of the proposed antenna, the generated angular momentum of l=1 is spin angular momentum (SAM), and the angular momenta of both l=2 and 3 include SAM and orbital angular momentum (OAM). Simulated and measured results are given to demonstrate good performance including tunable modes, good purity and wide band.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As is well known from Maxwell’s equation, electromagnetic radiation carries energy and momentum. The momentum may have linear momentum and angular momentum. The angular momentum has a characteristic helical phase fronts, and can be separated into spin angular momentum (SAM) associated with field direction, i.e., polarization, and orbital angular momentum (OAM) associated with field distribution [1]. In 1992, L. Allen et al. theoretically and experimentally distinguished the OAM from the SAM by using Laguerre-Gaussian laser with a helical phase dependence of ejlφ, in which φ is the azimuthal angle and l is the mode index [2].
The recognition of the OAM as a new degree of freedom of the field promotes its wide application in various fields [3] including quantum [4], optical tweezer [5], imaging [6], [7], radar pulse [8], and synthesis of radiation patterns [9], etc. In recent years, the OAM has been introduced in wireless communication to enlarge channel capacity due to its unlimited orthogonal eigenstates [10], [11]. Various approaches including spiral phase plate (SPP) [12], circular antenna array [13], [14], metasurface based reflectarray [15–18] and transmitarray [19], etc. have been developed to generate the OAM wave. However, these implementations are space consuming. More importantly, when the antenna arrays are used as receivers and transmitters, simultaneously, the resulting performance in a OAM based radio communication is similar to the traditional multiple-input-multiple-output (MIMO) communication method [20], [21]. Therefore, some antenna elements including dielectric resonant antenna (DRA) [22], circular microstrip antenna [23], and concentric microstrip antenna [24], etc., were proposed to radiate the OAM vortex wave. But these antenna designs only operate in a narrow band. In [25], a water loaded ring microstrip antenna was designed to radiate an OAM wave with tunable modes in a wide band. But the mode purity of the OAM degrades with the increase of the frequency. Spiral antennas as a class of frequency independent antennas have been widely used in wideband communication systems [26]. Some spiral antennas have been designed to radiate the OAM wave [27], [28]. However, the different OAM modes are generated at different frequencies in these designs.
In this paper, a composite planar spiral antenna composed of an eight-arm planar equiangular spiral antenna and eight planar Archimedean spiral antennas has been proposed to radiate the wave carrying the angular momentum in a wide band. The motivation of this paper has two folds: one is to radiate the angular momentum wave including the SAM and the OAM in a wide band, which distinguishes the previously reported antenna designs for generation of the OAM in a narrow band; the other is to dynamically manipulate the SAM and the OAM with good mode purity. Theoretical analysis of the planar spiral antenna for generating the angular momentum is given. Simulation and measurement results show that the proposed composite spiral antenna can flexibly radiate the waves carrying the SAM and the OAM in a wide overlapped band from 2.35 GHz to 2.91 GHz with a good mode purity of over 90%.
2. Spiral antenna design for angular momentum wave
2.1 Operation mechanism of spiral antenna for angular momentum
The expression describing a single-arm equiangular curve is ρ=ρ0e-aφ (0≤φ≤2mπ), in which the constant a determines the rate of wrapping and ρ0 is the radius of the start point of the spiral, which can be determined from the initial value of φ. Here m is the number of the turn. The equiangular spiral curve has the property that at any two points the angles between the tangent and the radial vectors are equal [29]. The n-arm equiangular spiral structure can be obtained by rotating the single-arm structure by (i−1)2π/n (i=1,2,…,n) around the origin. With the rotational symmetry in azimuth, the radiation field of the n-arm equiangular spiral antenna depends on the feeding phase arrangement [30]. There are n modes for the n-arm structure. A general excitation can be expressed as a summation of n modes with complex amplitudes. When a signal fed into the spiral antenna is constant in magnitude, and of progressive phase variation of 2lπ/n from arm to arm, the radiation field of the lth mode which is of circular polarization and has a phase dependence of ejlφ is excited. According to the multimode analysis, the far field of the lth mode can be solved as [31], [32]
Here Kl is a parameter proportional to the mode radiation resistance, Il is the magnitude of the mode current, and Jn is the n-order Bessel functions of the first kind. It can be seen from (1) that the radiation field of the n-arm spiral antenna has the angular momentum carrying l per photon, when the lth mode is excited. Note that the angular momentum includes the SAM associated with the field polarization and the OAM associated with the field distribution.
2.2 Design of composite spiral antenna
As shown in Fig. 1, the proposed composite planar spiral antenna is composed of two parts, i.e., a radiator and a feeding network. The radiator consisting of an eight-arm planar equiangular spiral antenna and eight planar Archimedean spiral antennas is fabricated on a circle-shaped, top F4B substrate with relative permittivity of 2.2 and a thickness of h1=1 mm. The feeding network is an eight-way Wilkinson power divider network fabricated on a circle-shaped, bottom F4B substrate with a thickness of h2=1 mm. A metallic ground plate etched with eight circle holes is placed on the top of the bottom F4B substrate. Eight cylinder-shaped metallic probes with a radius of 0.5 mm are used to connect the feeding network with the radiator through the holes. An air gap of 10 mm is located between two substrates. Here the use of the air gap is to decrease the effect of the feeding network on the spiral antenna and thus improve its impedance matching and gain.
Theoretically, the planar equiangular spiral antenna has an infinite frequency band when it has an infinitely large aperture. According to band theory [29], the radiation occurs where the circumference of the antenna is iλ. The maximum dimension of the spiral determines its low frequency cutoff, while the feed region size typically sets the high frequency limit. When truncating the equiangular spiral antenna, the current on the spiral reflects from the terminal of the antenna, thus deteriorating its radiation performance. To reduce the truncation effect, the Archimedean spiral structure are loaded at the end of the equiangular spiral antenna. The Archimedean spiral has a constant arm width and constant separation between arms through the entire aperture. The polar coordinate equation of the Archimedean curve is given as ρ=bφ+ρ1 (φ1≤φ≤ φ2), in which b is the growth rate, and ρ1 is the starting radius. Here an eight-arm equiangular spiral structure and the eight Archimedean spiral structures are designed. The optimized geometric parameters of ρ0=4.3 mm, a=0.37 and m=1 for the equiangular spiral structure and ρ1=48.64 mm, b=0.049, φ1=3π, and φ2=4.2π for the Archimedean spiral structure are used to obtain good radiation performance. The whole dimension of the composite antenna is R=205.89 mm.
The PIN diode (CD4148WTP) is inserted into a F-shaped microstrip line used to connect each arm of the equiangular spiral with the corresponding Archimedean spiral, as shown in Fig. 2(a). In the DC bias circuits for the PIN diode, the inductor of 200 nH for the RF choking and the capacitor of 20 pF for the DC blocking are used. By controlling the ON/OFF states of the PIN diodes, the Archimedean spiral antenna is connected with the equiangular spiral antenna or not such that the radiation performance of the proposed antenna is improved.
Fig. 2. Views of the radiation structure and the feeding network. (a) Radiation structure. (b) Feeding network.
In the eight-way Wilkinson power divider, the resistor of 185.12 Ω is used for isolations between the output ports. In each pair of the output ports there are eight PIN diodes. By controlling the ON/OFF states of the PIN diodes, there are three operating states, as shown in Table 1. As shown in Fig. 2(b), two outputting signals from the ports 5 and 6 have different phase difference when passing through two paths with the different lengths. According to Fig. 3, in the three operating states, the phase differences between the ports 5 and 6 are 45°, 90°, and 135°, respectively, and thus the phase variation for the eight ports covers 360°, 720°, and 1080°, respectively. In the three states, the transmission magnitude variations between the different ports are less than 2 dB, and the isolation between the different ports are better than −15 dB. It is worthwhile pointing out that in the state III, PIN 0 used to connect the equiangular spiral antenna with the eight Archimedean spiral antennas is in the ON state, while in both states I and II, PIN 0 is in the OFF state. Figure 4 shows the gain patterns of the proposed antenna in xoz and yoz planes at 2.75 GHz. In the states I and II, the gains of the proposed antenna are 7.26 dB and 4.58 dB, respectively. In the state III, the gain of the planar equiangular spiral antenna without the Archimedean spiral antenna is −1.4 dB. By using the Archimedean spiral, the gain can be increased as 5.09 dB.
Fig. 4. The gain of the proposed composite spiral antenna in xoz and yoz planes at 2.75 GHz in the (a) states I and II and (b) state III.
Table 1. Reconfigurable SAM and OAM Modes In Different States
3. Simulation and measurement results
The proposed antenna has been fabricated, as shown in Fig. 5. In the experiment, the states of the PIN diodes were controlled by the applied voltage, which was provided by four 5-V lithium batteries. The simulated and measured S11 of the spiral antenna in the three states are given in Fig. 6. In the state I, the measured operating band for S11≤−10 dB covers 2.25∼3.25 GHz, in good agreement with the simulated one of 2.25∼3.15 GHz. In the state II, both the simulated and measured operating frequency bands are from 2.35 GHz to 2.91 GHz. In the state III, the measured band of 2.25∼3 GHz agrees with the simulated one of 2.25∼2.98 GHz. The overlapped band for the three states is 2.35∼2.91 GHz with the fractional band of 21.3%.
Figure 7 demonstrates the normalized patterns of the proposed antenna at 2.75 GHz in xoz and yoz planes, respectively. It can be found that the measured results are in good agreement with the simulated ones in the three states. The slight discrepancy between them occurs at the back direction. This is because the DC bias circuit is placed at the back side of the spiral antenna.
Figure 8 shows the simulated phase and magnitude of the proposed antenna at 2.75 GHz on an observation plane at a distance of 1 m. It can be seen that in the three states, the helical phase distributions can be observed. It is worthwhile pointing out that in the state I, there is not a null amplitude in the broadside direction, as shown in Figs. 7 and 8. This is because in the state I, a circular polarized (CP) plane wave is radiated instead of the OAM wave. Figure 9 gives the axis ratio (AR) of the proposed antenna in the three states. The AR for the state I in the operating band is less than 3 dB and thus the CP wave is radiated. In the state II, the AR slightly larger than 3 dB is obtained and thus the elliptically polarized (EP) wave is generated. In the state III, the larger AR is achieved due to the use of the Archimedean spiral antenna, and thus the EP wave is radiated. In the three states, the radiated wave carries the SAM. Hence in the states I, II and III, the radiated waves carry the OAM with the mode index of l=0, 1, 2, respectively. The measured phase distributions of the proposed antenna at 2.75 GHz in the three states are shown in Fig. 10, in good agreement with the simulation results. Here the observation plane with a size of 600 mm×600 mm is located at a distance of 800 mm from the antenna, and the sampling space of the z-component of the electric field is 0.4 mm.
Figure 11 shows the measured phase distributions of the proposed antenna at 2.3 GHz, 2.75 GHz and 3.2 GHz, respectively, in the state I. It can be seen that in the wide operating band, the helical phase can be achieved. Similar results can be obtained in the states II and III. Figure 12 shows the measured mode purity of the proposed antenna in the three states at 2.75 GHz. The purities of over 90% can be obtained.
Fig. 11. Measured phase distribution of the Ez of the proposed antenna at different frequencies in the state I.
4. Conclusions
A composite planar spiral antenna composed of the planar equiangular spiral antenna and the planar Archimedean spiral antenna has been designed for radiating the electromagnetic wave carrying the angular momentum in a wide band. By switching ON/OFF states of the PIN diodes between two radiation structures and in the eight-way Wilkinson power divider network, the waves carrying the angular momentum including the SAM and the OAM of the modes l=1 and 2 can be radiated. Simulated and measured results show that the proposed antenna has good radiation performance including wide band, good gain, and tunable modes with good purity.
Funding
Shaanxi Outstanding Youth Science Foundation; National Natural Science Foundation of China (61771359).
Disclosures
The authors declare no conflicts of interest.
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