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Abstract
Orbital angular momentum (OAM) is an intrinsic property that all electromagnetic waves can carry. Interesting properties of OAM beams have enabled many novel applications. But broadband OAM generator has rarely been investigated, especially in the millimeter wave frequency band. In this work, a broadband OAM generator applying a metallic reflective metasurface operating from 59 to 70 GHz is designed, simulated, fabricated and measured. Both simulation and experiment results demonstrate that broadband millimeter wave OAM beams with good quality can be reliably launched by the designed metasurface. The proposed broadband OAM generator alleviates malfunctions caused by dispersion and provides new possibilities of multiplexing for millimeter wave communication applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic beams carrying orbital angular momentum (OAM), also referred to as vortex beams, feature a helical wavefront [1]. Since discovered in 1992, considerable research endeavor has been devoted to developing new methods to generate OAM beams and exploring novel applications of OAM beams [2–4]. OAM beams in different frequency ranges have been investigated, such as optical domain [5–7], millimeter wave [8], microwave [9] and RF regime [10]. Various interesting applications of OAM beams have been demonstrated, among which the most extensively studied one is boosting data capacity by OAM mode number multiplexing [11]. Other interesting applications of OAM beams have been found in particle trapping [12], beam focusing [13], measurement of rotational Doppler effect [14] and imaging [15], to name a few.
To engender the helical wavefront of an OAM beam, a plethora of methodologies have been reported in literature, most of which rely on first generating a planar phase front featured by an azimuthal variation represented by ejmφ (m is OAM mode number and φ is azimuthal angle) and the helical wavefront is then formed via propagation of the beam [5,8]. Spiral phase plate made of dielectric materials has been first applied to generate optical OAM beams [16,17] and subsequently utilized in microwave and millimeter wave range [11]. But the performance of spiral phase plates is degraded by big beam divergence angle and reflection at air-dielectric interface [18,19]. Antenna arrays are also employed to launch OAM beams in microwave frequency range [20]. However, the major drawback of the antenna array mechanism is the demanded complicated and expensive feeding system, especially for radiating higher-order OAM beams that inevitably needs more antenna elements. Flat spiral phase plate is also proposed as an alternative to spiral phase plate [8], but still suffers from the reflection problem [18,19]. Metasurfaces, two-dimensional counterpart of metamaterials, are robust in tailoring phase fronts and intensity patterns of electromagnetic waves in various unprecedented approaches [21–24] and thus suitable for launching OAM beams [25–29], which has been the subject of intense research activity. In addition, metasurfaces can be engineered to enable high transmission efficiency to circumvent the reflection deficiency of spiral phase plates and flat spiral phase plates [30–32].
Besides exploring novel mechanisms to engender OAM beams with improved quality and advanced functionalities [18,33–35], broadening operation bandwidth of OAM beams is also very meaningful for reducing dispersion-induced distortions and developing novel applications, such as broadband OAM imaging [15] and broadband object detection or identification [36,37]. Another potential application is combining OAM multiplexing and frequency-division multiplexing to further enhance data capacity in communications. Recently, some groups have investigated broadband OAM generators in the microwave region (2.1-2.7 GHz in [3], 6.95-18 GHz in [4], 6.25-10.5 GHz in [38], and 7.5-10.5 GHz in [39]) and optical regime (1500-1600 nm in [40] and 532-780 nm in [41]). However, broadband OAM generator operating in millimeter wave regime has rarely been reported in literature and achromatic OAM launcher immune to dispersion for millimeter wave applications is still lacking, except for one work covering the lowest fraction of millimeter wave band (28.4-36.8 GHz in [42]). Exploration of the underutilized millimeter wave region has profound implications for a multitude of applications, such as increasing available spectrum and enhancing spectrum efficiency for wireless communications and enhancing spatial resolution for imaging and object identification. In this work, we propose design, simulation and measurement of a metasurface-based OAM generator working in a broad millimeter wave range from 59 to 70 GHz (a fractional bandwidth of 17%). Detailed design procedure of metasurface unit element is provided, which renders the resultant phase shift exhibit proper features required for broadband OAM beams. Simulation of a metasurface containing different unit cells corresponding to different phase shift is carried out. The metasurface plate is then fabricated and characterized. Good measured phase and amplitude results undoubtedly validate the broadband feature of the OAM beam generator.
2. Design methodology
Although dielectric metasurface is superior to metallic metasurface due to their lower loss, more sophisticated fabrication technique is demanded to implement dielectric metasurface, especially for scenarios involving more than one kind of dielectric materials and small element sizes [43]. As a consequence, metallic metasurface is adopted in this work to demonstrate the design, simulation, fabrication and measurement of a broadband OAM launcher operating in millimeter wave domain.
Structure of a unit cell of the utilized metasurface is composed of two closely coupled parallel metallic dipoles of identical rectangular shape, shown in Fig. 1(a). The metallic dipoles are sitting on a dielectric substrate backed by a layer of metallic ground, resulting in a reflective type metasurface. The substrate is made of a cost-effective material F4B (dielectric constant is 2.2 and loss tangent is 0.002) with a height of h = 0.63 mm. Polarization conversion of the reflected fields with respect to the incident fields, which is beneficial to suppressing interference between the incident and reflected fields and boosting signal-to-noise ratio of the reflected OAM beams [40], is achieved by tilting the two dipoles 45° with respect to the unit cell edges. As a result, x- or y-polarized incident fields can induce currents on the dipoles containing components in the other direction that effectively produce the reflected fields also in the other direction. This is better illustrated by an example with an x-polarized incident field described in Fig. 1(b). It can be decomposed into two field components parallel and perpendicular to the dipoles, respectively, which are depicted in Fig. 1(b) as and . Once reflected, the corresponding two reflected field components and have near unity amplitudes and are approximately out of phase in the design bandwidth from 59 to 70 GHz, shown in Figs. 1(c) and 1(d). Here, the 180° phase difference between the two reflected field components is acquired via appropriately adjusting dimensions of the dipoles. As observed in Fig. 1(b), combining and can yield a y-polarized total reflected field and polarization conversion is thus accomplished. By the same manner, a y-polarized incident field can be proven to generate an x-polarized reflected field.
Fig. 1 (a) Schematic of the proposed metallic metasurface. (b) Schematic of the polarization conversion from an x-polarized incident field to a y-polarized reflected field using two decomposed components, where component 1 is assumed to maintain its direction while the direction of component 2 is reversed because of the 180° phase difference. (c) Amplitude and (d) phase of the reflected two components. Parameters used to obtain (c) and (d) are a = 0.8 mm, b = 1.6 mm, d = 3 mm, g = 0.38 mm.
Proper adjustment of dimensions of the dipoles in a unit element can alter phase of the reflected cross-polarized field from 0 to 2π. Therefore, a reflected wave with customized phase pattern can be accomplished by the applied metasurface with engineered distribution of different unit elements. To generate an OAM beam featured with a helical wavefront or azimuthally dependent phase pattern represented by ejmφ, a metasurface with unit elements forming a similar azimuthally varying pattern can be employed, which is called flat phase plate [44]. The phase for an OAM beam of order m in Cartesian coordinates, in which the metasurface resides, can be written as:
To engender a broadband OAM beam, or maintain the phase pattern in Eq. (1) in a frequency band rather than at a single frequency point, is more challenging and has not been reported in millimeter wave regime (to the best of our knowledge). The mechanism used to generate a broadband Bessel beam [45], which is based on metamaterial structure bearing effective permittivity independent of frequency, is not suitable for the current broadband OAM launcher since this method cannot guarantee frequency-independent phase shift. The strategy adopted in this work is designing a metasurface consisting of several segments exhibiting a fixed phase difference between each two adjacent segments and largely maintaining the phase difference in the targeted frequency band to achieve a broadband OAM beam.An OAM beam with mode number m = −1, which corresponds to the ideal azimuthally decreasing phase profile given in Fig. 2(a), is designed as an example and configuration of the applied metasurface is shown in Fig. 2(b). The metasurface is split into eight triangular regions and each region results in different phase shift in the reflected cross-polarized field that can be expressed as:
where N is the number of total regions that is set to 8 in this study and [z] results in the maximum integer no greater than z. As defined in Eq. (2), the phase of region 1 is set to 0 as a reference. For the case m = −1, the phase linearly decreases from 0 in region 1 to −7π/4 in region 8 counterclockwise with a fixed decrement of −π/4, shown in Fig. 2(c). Therefore, continuous phase variation along the azimuthal direction in Eq. (1) is implemented in a discrete manner in Eq. (2) to greatly simplify the design process. The eight distinct phase shifts in the eight regions are then realized by tuning dimensions and directions of the dipoles. As observed in Fig. 2(b), dimensions of the dipoles increase gradually from region 1 to region 4. In addition, dipoles in regions 5 to 8 are respectively identical to those in regions 1 to 4 while rotated by 90°. The unit cells on the interfaces between regions 1 and 2, 3 and 4, 5 and 6, as well as 7 and 8 use the ones same as those in region 1, 3, 5, and 7, respectively. It is worth mentioning that an ideal OAM beam can only be launched by a generator with an infinitely large dimension, which is not practical and a truncated generator is always applied for implementation in reality.Fig. 2 (a) Ideal phase profile of an OAM beam with m = −1. (b) Schematic of the designed OAM generating metasurface with different dipole configurations in eight different regions. Gray rectangles represent metal dipoles. (c) Discrete phase profile of an OAM beam with m = −1 used in this work.
Broadband feature of the spiral phase profile is obtained by further optimizing dimensions of the dipoles and gaps between the dipoles using commercial software package CST microwave studio [46]. Adopted criterion for the optimization is making the phase difference between each two adjacent regions to be approximately −π/4 when sweeping the frequency in the operation band, which can be described as:
where i is the index of region and j is the index of swept frequency point from 59 to 70 GHz with 1 GHz step. Goal of the optimization carried out by CST is actually confining the phase difference in Eq. (3) in the interval of [−π/3, −π/6]. The optimized parameters of the unit cells in different regions are listed in Table 1. The unit cell period is chosen to be d = 3 mm. Phases and amplitudes of the reflected cross-polarized fields for the unit cells in eight regions are simulated and plotted in Fig. 3 as a function of frequency from 59 to 70 GHz. All the regions bear normalized amplitudes above 0.72 across the operation bandwidth, except for regions 1 and 5 recording 0.5 at 59 GHz. Despite this issue, the overall average amplitude of all the regions across the entire operation bandwidth is above 0.87, implying good polarization conversion efficiency. The corresponding efficiency of the metasurface, defined as the ratio of the power in the generated cross-polarized OAM beam over the total power of the incident beam, is calculated and given in Fig. 9, which records a minimum of 0.7 at 59 GHz and a maximum of 0.81 at 70 GHz. The phases shown in Fig. 3(b) are obtained by setting the phase of region 1 to be zero so that it can serve as a phase reference at each simulated frequency. The plotted phase profile exhibits good linearity, which implies that the phase differences are well confined in a small interval around −π/4 in the operation bandwidth. As a consequence, both the simulated amplitude and phase results can ensure the generation of broadband millimeter-wave OAM beams.
Table 1. Optimized Parameters of Unit Cells in Different Regions
Fig. 3 Simulation results of (a) normalized amplitude and (b) phase of the cross-polarized reflected waves applying optimized unit elements in the eight regions.
3. Simulation results
Based on the optimized geometries of dipoles in the eight regions, a metasurface containing 50 × 50 elements is simulated to numerically evaluate its ability of broadband OAM beam generation. The total dimension of the square metasurface plate is 150 mm × 150 mm. The plate is fed by a circular waveguide antenna 10 cm away from it facing its center. Phase and amplitude information of cross-polarized fields are recorded 20 cm away from the metasurface at frequency points 59, 63, 67 and 70 GHz in the design bandwidth. As shown in Fig. 4, all the simulated phase profiles exhibit apparent spiral nature corresponding to a m = −1 OAM beam and all the amplitude pattern bear an obvious singularity at the center. This is also the case for the generated OAM beams at other frequencies in the design frequency band. The spiral phase pattern is actually a combined effect of the ideal OAM phase pattern shown in Fig. 2(a) and the spreading of the OAM beam as it propagates away from the generator [19]. Mode spectra are also calculated to quantify purity of the m = −1 mode as well as crosstalk between different modes of the generated OAM beams [39]. It can be clearly seen from Fig. 4 that the m = −1 mode is predominant for all the four frequencies. Defining mode purity as ratio of the power in the dominant mode over the overall power distributed in all the modes, as expressed in Eq. (4) with denoting the magnitude of the ith mode, the recorded mode purity for the four frequencies are 87.9%, 87.3%, 84.3% and 79.4%, respectively.
The maximum crosstalk occurs between the dominant mode and the second strongest mode, defined in Eq. (5) with representing magnitude of the second strongest mode, which is calculated to be −12.3 dB, −13.1 dB, −12.0 dB, and −11.6 dB for the four frequencies, respectively.Metasurface OAM beam generator with very good quality is thus demonstrated in the operation band. It is worth mentioning that the field recording plane is not too far away from the metasurface due to the limit in available computational resources. Another thing deserves clarification is that the middle parts of the phase profiles in Fig. 4 start to rotate at different angles for different frequencies. But this is not detrimental to the purpose of this work because the essence of broadband OAM beam generation is maintaining the desired helical phase front or spiral planar phase distribution in a broad frequency band, which only poses a requirement on the relative phase distribution at each frequency rather than the absolute phase value.Fig. 4 Simulation results of phase, normalized amplitude and mode spectra of the cross-polarized electric fields of the generated m = −1 OAM beam at different frequencies: (a), (b) and (c) 59 GHz; (d), (e) and (f) 63 GHz; (g), (h) and (i) 67 GHz; (j), (k) and (l) 70 GHz. The first column shows phase results (in degree), the second column shows amplitude results (in dB scale) and the third column shows mode spectra.
4. Experimental results
To experimentally demonstrate the designed broadband OAM generator, a metasurface plate with 74 × 74 elements and a dimension of 222 mm × 222 mm is fabricated on a 0.63-mm-thick F4B printed circuit board. Photo of the front side of the fabricated metasurface plate is shown in Fig. 5(a). Near-field planar scanning method is applied to characterize the produced OAM beams in the operation bandwidth. Setup of the experimental system is shown in Fig. 5(b). Both transmitting and receiving antennas are linear-polarized circular horn antennas with working frequency from 50 to 75 GHz. The transmitting antenna and the plate are separated by 30 cm. The receiving antenna detects the reflected millimeter wave and performs near-field scanning in a 300 mm × 300 mm square region parallel to the plate with a scanning step of 2.5 mm by a mechanical scanning stage. The scanning is first performed in a plane 50-cm away from the plate and then further distances of 100 and 150 cm are used. The transmitting antenna radiates vertically polarized wave while the receiving antenna probes horizontally polarized wave to form the required cross-polarization measurement setup. A vector network analyzer (VNA, Keysight technologies, N5227A) connecting to the two antennas implements the measurements up to 67 GHz, which is the upper frequency limit of the VNA.
Fig. 5 (a) Photo of fabricated metasurface plate using 0.63-mm-thick F4B PCB board. (b) Experimental measurement setup.
Phase and amplitude results measured at different scanning planes are respectively provided in Figs. 6 and 7. It is observed from Fig. 6 that phase distributions sampled at different scanning locations and different frequencies in the design bandwidth all display correct spiral feature associated with a m = −1 OAM beam. All amplitude distributions exhibit a ring-shaped pattern with an obvious null at the center and the recorded amplitude decreases as the scanning plane is further. It is also found that the measurement results obtained at the same scanning plane show a good resemblance between different frequencies, unambiguously demonstrating the broadband nature of the millimeter-wave OAM generator. Some deficiencies can be observed in the phase distributions recorded on the first scanning plane (50-cm away), which is caused by the fact that part of reflected wave is obstructed and scattered by the transmitting antenna and the metallic post used to fix it (shown in Fig. 5(b)). Such obstruction also induces a gap in the ring of the amplitude pattern obtained on the first scanning plane. As the OAM beam propagates, number of turns of the spiral phase profile in a fixed scanning region becomes less and the ring-shaped amplitude pattern is gradually expanded, which is attributed to the diffraction of the OAM beam during propagation. In addition, the deficiencies in the phase and amplitude patterns are gradually mitigated as the OAM beam propagates further, which are thus not harmful for practical applications. Associated mode spectra are shown in Fig. 8 and quantified mode purity and maximum crosstalk for different cases are summarized in Table 2. The obtained higher than 75% mode purity and less than −10 dB crosstalk undoubtedly corroborate the high quality of the measured OAM beams in the design bandwidth and are sufficient for most practical OAM applications. Efficiency of the metasurface-based OAM generator is also obtained by measuring the entire power reflected by the metasurface plate, including power carried by both the cross-polarized and co-polarized fields. Propagation attenuation of the millimeter wave is also accounted for in the calculation of the efficiency. The obtained efficiency from measurements is shown in Fig. 9, with a minimum of 0.64 at 59 GHz and a maximum of 0.71 at 64 GHz, better than that reported in [39]. Good agreement between the simulated and measured efficiencies is also validated. Therefore, reliable broadband feature of the metasurface-based OAM generator is corroborated at different scanning locations.
Fig. 6 Measured phase distributions of the cross-polarized electric fields of the generated m = −1 OAM beam at different frequencies and different scanning planes. (a), (d) and (g) are obtained at 59 GHz. (b), (e) and (h) are obtained at 63 GHz. (c), (f) and (i) are obtained at 67 GHz. (a), (b) and (c) are obtained at the 50-cm-away scanning plane. (d), (e) and (f) are obtained at the 100-cm-away scanning plane. (g), (h) and (i) are obtained at the 150-cm-away scanning plane.
Fig. 7 Measured amplitude distributions of the cross-polarized electric fields of the generated m = −1 OAM beam at different frequencies and different scanning planes. (a), (d) and (g) are obtained at 59 GHz. (b), (e) and (h) are obtained at 63 GHz. (c), (f) and (i) are obtained at 67 GHz. (a), (b) and (c) are obtained at the 50-cm-away scanning plane. (d), (e) and (f) are obtained at the 100-cm-away scanning plane. (g), (h) and (i) are obtained at the 150-cm-away scanning plane.
Fig. 8 Calculated mode spectra of the generated m = −1 OAM beam at different frequencies and different scanning planes. (a), (d) and (g) are obtained at 59 GHz. (b), (e) and (h) are obtained at 63 GHz. (c), (f) and (i) are obtained at 67 GHz. (a), (b) and (c) are obtained at the 50-cm-away scanning plane. (d), (e) and (f) are obtained at the 100-cm-away scanning plane. (g), (h) and (i) are obtained at the 150-cm-away scanning plane.
Table 2. Mode Purity and Maximum Crosstalk of Measured Broadband OAM Beams
5. Discussions and conclusions
Table 3 lists detailed comparison of this work with previous similar works on broadband OAM in terms of some pivotal factors. It can be seen that this work is the first one covering the 60 GHz millimeter wave band and exhibits both high power efficiency and mode purity. Although the relative bandwidth of the proposed OAM generator is narrower than some previous works, its measured efficiency is the highest. Moreover, given measurement technique available, it is possible to extend the bandwidth of the current work to higher frequency since the efficiency and mode purity are very likely to maintain at a high level even above 70 GHz.
Table 3. Comparison with Previous Works in terms of Pivotal Factors
Several measures can be adopted to further improve performance of the proposed broadband millimeter wave OAM launcher. First, multilayer metasurface can be exploited to boost the polarization conversion efficiency of such reflective type metasurface, similar to the method applied to enhance transmission efficiency of transmission type metasurfaces [30–32]. Second, substrate with even lower dielectric loss at millimeter region can reduce the loss and increase the overall efficiency. Third, a smaller unit cell is likely to result in better approximation to an artificial atom and finer interaction with electromagnetic fields [47], but at the cost of requiring more sophisticated fabrication technique. Last but not least, more segments of different unit cells can help to make the phase variation from 0 to 2π more smoothly [48].
In summary, design method, simulation study and experimental characterization of a broadband millimeter wave OAM beam generator are reported in this work. The generator is implemented by a metallic reflective metasurface with subwavelength unit elements, which are appropriately designed to enable broadband spiral phase front generation. The designed metasurface is validated by both simulation and experiments, which obtain broadband millimeter wave OAM beams with high quality. Quantitative information of the simulated and measured OAM beams, such as power efficiency, mode spectra, mode purity and crosstalk, are provided to validate the performance of the designed generator. This work may pave the way to a new method of multiplexing for using OAM beams in millimeter wave wireless communications that can combine frequency-division multiplexing to the conventional OAM-mode-number multiplexing to further boost data capacity. Other applications can also be benefited, such as imaging and target detection based on OAM beams. In addition, this work may provide a paradigm for designing broadband metasurface-based devices in the millimeter wave range and hold potential to be scaled up to higher frequencies.
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