Electromagnetic propagation modes with an orbital angular momentum (OAM) were first studied in the context of Laguerre–Gaussian laser beam modes . The OAM mode is characterized by an intensity vortex on the beam axis and a helical phase front. It has a ejlϕ phase factor, where l is an integer indicating the OAM degree, and ϕ is the azimuthal angle measured at any plane orthogonal to the beam axis. Optical OAM modes can be used as micro-particle rotating tweezers  and for quantum key distribution , and their use in high-capacity data communications has been attempted –. Moreover, in the area of microwave wireless communications, OAM modes are considered potential candidates for increasing capacity without requiring any extra frequency resources. The advantage of OAM modes when applied to communications lies in their spatial orthogonality, which allows sharing the same frequency band, time slot, polarization, and spatial channel with other OAM modes. The key technologies of OAM-mode-based communications are associated with the mode generation and multiplexing steps. Demultiplexing is not an independent technology in itself, given that it is simply the reverse of multiplexing. There are two basic approaches to OAM beam generation and multiplexing in the microwave region. The first one is to first generate single OAM modes, and then multiplex them. Spiral phase plates (SPPs)  and helical reflectors  can be used to transform the zero OAM Hermite–Gaussian mode into finite OAM Laguerre–Gaussian modes, and vice-versa. However, a single SPP or helical reflector can only generate one OAM mode, and the several different OAM modes should be optically multiplexed—with a beam splitter, for example —before transmission or transmitted individually without multiplexing . The other approach is to generate all the multiplexed OAM modes simultaneously, using a Butler matrix and a uniform circular array (UCA) , .
A UCA is an array of N sub-antennas located along a circumference at equal spacing. The ith element is driven by a signal with a i · θl phase delay, where θl = 2π · l /N, |l| is an integer smaller than N/2 , . In these conditions, the wave front will contain the desired ejlϕ phase factor.
Figure 1 shows various simulated UCA-generated OAM beam patterns (with a 10λ UCA diameter) at a distance of 1,000λ. The element antennas are modeled as micro vertical dipole antennas. The intensity and phase vortices are clearly shown at the beam center in the l = 1 column. In the N = 4 and l = 1 box, the individual intensities are combined as in .
One advantage of the UCA approach is that each antenna element can be driven by a compound signal. Therefore, a single UCA can generate multiple OAM modes simultaneously, if driven by a suitably synthesized signal, as shown in Fig. 2.
A Butler matrix is an N × N matrix circuit widely used in beamforming networks. For each input signal, there are N output signals, with phase delays proportional to the output port number. The phase delay increment is determined by the input port; in the case of simultaneous excitation of multiple input ports, the Butler matrix outputs the necessary compound signals, which can then be fed to a UCA to generate multiplexed OAM beams. The remainder of this paper is organized as follows. Section II reviews the operations of 4 × 4 Butler matrix and the S-parameter characteristic of our 4 × 4 Butler matrix. In Section III, the measured field distribution of triple OAM modes are presented and the beam center fluctuation is analyzed. In Section IV, the transmission characteristics of our triple OAM modes are described with an indoor TV signal transmission experiment. Finally, Section V presents our conclusions.
Figure 3 shows the 4 × 4 Butler matrix circuit used in this paper, which is composed of a 90° hybrid coupler, a crossover, and a 180° phase shifter. In the 90° hybrid coupler, the coupled output is delayed by 90° than the through output. The 90° phase delay is expressed as ZN → ZN+2, neglecting the coupling magnitude factor without affecting the relative magnitudes on each path. We then have that, for integer N, ZN = − ZN ± 4 and ZN = ZN ± 8.
In Fig. 3(a), signal Z0 is input to Port 1 and the next step signals are identified in the Butler matrix circuit. The final outputs are Z8, Z6, Z4, and Z2, each one of these phase delay by −90° relative to the previous one in the list. When signal Z0 is input to Port 3 (Fig. 3(b)) all outputs are “Z2 + Z4,” which means that they all have the same phase, and when input signal Z4 is fed to Port 4 (Fig. 3(c)) the outputs are Z0, Z2, Z4, and Z6, each one of these delayed in phase by +90° relative to the previous one in the list.
The signals delayed in phase by −90°, 0, and +90° are fed to a 2 × 2 UCA to generate the −1, 0 and +1 OAM modes, respectively. When the three signals are simultaneously applied to the UCA, superposed triple OAM beams are generated (as shown in Fig. 2). The multiplexed triple OAM beams can be separated by passing the signals through the Butler matrix in the backward direction. For example, Fig. 4 shows the arrangement for multiplexing and demultiplexing the −1 mode using Butler matrices connected back-to-back. In this figure, the consecutively connected 180° phase shifter and crossover between the multiplexer (MUX) and demultiplexer (DeMUX) cancel each other, and are therefore not represented. Experimental results will be also described later.
We fabricated a WR51-waveguide-based 4 × 4 Butler matrix to operate in the 18 GHz band. Figure 5 shows a drawing of the resulting waveguide-type Butler matrix. The input and output signals are connected to the input and output ports by subminiature version A (SMA) connectors, whose inner axis pierced the waveguide wall from bottom or top. To simplify the Butler matrix structure, the 180° phase shifter in Fig. 3 is embodied by using an upward SMA in the respective output port, given that all the other three are in the downward direction. The output port crossover in Fig. 3 is implemented by crossing the coaxial cables connecting the Butler matrix and the UCA.
Figure 6 shows the S-parameter characteristics of the fabricated Butler matrix. For each input signal, there are four output signals, as in Fig. 3. Figures 6(a) and (b) show the output signals for the ±1 modes with a small and flat loss. The phase variations appear to be relatively uniform within the 17 GHz to 19 GHz band. However, the remaining (albeit small) amplitude and phase non-uniformity introduce OAM beam center fluctuations that result in degraded mode isolation in the wireless channel.
As previously mentioned, a backward-connected Butler matrix operates as an OAM mode demultiplexer. Figure 7(a) shows the MUX/DeMUX circuit implemented with Butler matrices connected back-to-back, in the reduced form of Fig. 4. The Butler matrix on the left side operates as an OAM-mode MUX, and the Butler matrix on the right side—which is connected in the backward direction—operates as a DeMUX. The internal circuits of both matrices are the same, except for the folded/not folded formats. As shown in Fig. 7(b), in the 18 GHz band the −1 mode isolation is larger than 25 dB, but the 0 and +1 modes have a slight mutual leakage, and therefore exhibit only 17 dB of isolation, which may limit the OAM mode communication distance.
Orbital angular momentum modes have a peculiar intensity and phase vortex at the beam center; a direct field distribution measurement is therefore a good method to verify OAM modes. Figure 8 shows the test setup. Each input port of the Butler matrix is driven using a vector network analyzer, and the Butler matrix outputs are fed to a 2 × 2 feeder, to radiate an electromagnetic wave. The used 2 × 2 feeder is a four-element UCA with a 2 × 2 open-ended rectangular waveguide with a 15 mm × 15 mm cross section ; a small probing antenna is used to measure the spatial field distribution by scanning a 28 cm × 26 cm area (in 1 cm steps) 25 cm away from the 2 × 2 feeder.
Figure 9(a) shows the electric field pattern 25 cm away from the feeder at 18 GHz, as simulated with the CST Microwave Studio. Assuming that the effective diameter of the 2 × 2 feeder is approximately 4 cm, the Fraunhofer distance is approximately 19 cm; the simulated patterns are therefore far-field patterns. Figure 9(b) shows the two-dimensional S21 measurement results at the same 25 cm distance.
Well-formed intensity nulls and phase vortex distributions are observable for the ±1 modes, whereas the 0 mode exhibits the typical circular intensity and phase distributions. At a 50 cm distance, the shapes did not change, but were twice enlarged. The measured combination of intensities is partially consistent with the simulation results.
The “b. c.” abbreviation in Fig. 9(b) represents the beam centers of the OAM modes—the maximum intensity position in the 0-mode case, and the minimum intensity positions in the ±1-mode cases. The beam centers vary with frequency and mode index; therefore, the beam center variation was checked in detail. To achieve that, the OAM beams were radiated by a 24 cm diameter Cassegrain antenna fed by the previously mentioned 2 × 2 feeder and measured by the probing antenna of Fig. 8, placed 2 m away from the Cassegrain antenna. Figure 10 shows the beam center variation of the three modes between 17.5 GHz and 18.5 GHz, with 1 cm resolution. The variation areas are approximately 5 cm in diameter, but can reach 2.5 m at a 100 m distance.
A more serious difficulty is the fact that the beam centers of the three modes do not coincide at most frequencies. Figure 11 shows the inter OAM beam center separations as a function of frequency—within the 17.5 GHz to 18.5 GHz band, with a 2.5 MHz spacing—as red (0 to −1 mode), green (0 to +1 mode) and blue (−1 to +1 mode) lines. The average distances are 1.6 cm (red), 1.2 cm (green), and 1.4 cm (blue). These distances correspond (respectively) to 79 cm, 62 cm, and 72 cm of average separation at a 100 m transmission distance.
The variation in the beams centers of the different OAM modes is mainly due to the non-ideal characteristics of the fabricated Butler matrix. Figure 12 shows the constellation of the four Butler matrix outputs; in this figure, the first Butler matrix output port signals are set to be 45° (located in the first quadrant) for each measured frequency.
Given that the UCA-generated OAM modes are the interference patterns of the individual antenna elements, the field distribution depends on the signals fed to the UCA. Figure 13 shows the simulated far-field pattern radiated from an N = 4 UCA (2 × 2 feeder) using ideal and real feeding signals from the fabricated Butler matrix, at 18 GHz. In the ideal case, all the OAM beam patterns are symmetric about the z-axis (the blue crossing point in the center). However, in the non-ideal case, the beam patterns show asymmetries about the z-axis and, as a result, they propagate to slightly different directions, thus introducing the beam center mismatch and some mode isolation degradation.
To use microwave OAM modes in wireless communications, a certain degree of signal to interference and noise ratio (SNIR) is required. For example, nearly 12 dB of SNIR are required for a 16 QAM, 1 GBd signal . Given that the crosstalk between OAM modes is usually the dominant source of noise, it is important to control both the received power and the mode isolation level.
In the OAM mode transmission experiment, we used the previously referred 24 cm diameter Cassegrain antenna, which was fed by the Butler matrix and the 2 × 2 feeder. We also used a camera tripod and a pointing laser for easy antenna angle alignment, both at the transmitting and receiving ends. Figure 14 shows the Tx/Rx antenna (including the Butler matrix), and Fig. 15 shows the transmission test chamber.
Figure 16 shows the test setup configuration. A E8267D signal generator was used for powering the transmission Butler matrix at 0 dBm, and a 8565EC spectrum analyzer was used to measure the received power.
Figure 17 shows the measured received power and crosstalk power at distances up to 14 m (in 2 m steps), when single-tone signals for the 0 and −1 modes are individually transmitted at frequencies near 18 GHz. The results for the +1 mode were similar to the ones of the −1 mode, and are therefore omitted. At each distance, the angles of the transmitting and receiving antennas were carefully adjusted, so as to attain both maximum signal and minimum crosstalk power. It should be noted that the obtained results are very sensitive to antenna alignment , and therefore our results constitute merely one reasonable case; other experiments could result in better or worse results.
Figure 17(a) shows the 0-channel characteristics and Fig. 17(b) shows the −1-channel characteristics. In the 0-channel case, the 0-mode power is approximately 20 dB above the crosstalk with the other two modes throughout the whole region. In contrast, in the −1 channel case, the −1-mode power reduces 10 dB per every doubling of distance, and even though it is 10 dB and 40 dB over the received 0-mode and +1-mode powers at 2 m, respectively, these margins reduce to 5 dB and 25 dB at 10 m, respectively. Therefore, to reach the required 12 dB of SINR, the 0-mode transmitted power should be appropriately reduced, as in . Table 1 shows the calculated triple OAM mode isolation, assuming that the 0-mode transmitted power is optimally reduced. In this context, mode isolation refers the difference between the signal mode power and the larger crosstalk power.
For wideband OAM signals the mode isolation level may become even worse, because of the frequency-dependent OAM beam center mismatch. In such conditions, a Butler matrix with better performance is required, to enhance the mode isolation level and the transmission distance. Figure 18 shows a TV signal transmission experiment using the ±1 modes in our laboratory.
The generation and transmission of data in triple OAM mode at a distance of 14 m is experimentally demonstrated using a 24 cm diameter Cassegrain antenna fed by a 4 × 4 waveguide Butler matrix and a 2 × 2 UCA and operating in the 18 GHz band. The generated OAM modes were verified by spatial field measurements, and demultiplexed by a reversely connected Butler matrix. The radiated OAM beam centers varied with both frequency and mode index, which resulted in mode isolation degradation; this effect is mainly due to the non-ideal characteristics of the fabricated Butler matrix. Higher levels of performance are therefore required from the Butler matrix to achieve longer communication distances. In the presented transmission experiment, the received ±1-mode power exhibited a reduction of approximately 10 dB for each doubling of distance; therefore, the mode isolation was calculated assuming an adequate reduction of the 0-mode transmitted power, and the required value of 12 dB isolation was achieved for narrow-band OAM signals at transmission distances of 10 m. For longer distances and wideband OAM mode wireless communications, high antenna gains and uniform frequency characteristics are very important issues. However, the proposed scheme constitutes a very convenient and compact method for multiple microwave OAM-mode-based communications.