Fabrizio TAMBURINI, et al.

RF Vorticity

Vortex RF ( Orbital Angular Momentum ) can transmit multiple channels on one frequency: infinite potential

March 2, 2012

Vortex radio waves could boost wireless capacity “infinitely”


Sebastian Anthony

After four years of incredulity and not-so-gentle mocking, Bo Thide of the Swedish Institute of Space Physics and a team in Italy have finally proven that it’s possible to simultaneously transmit multiple radio channels over exactly the same wireless frequency. In theory, according to Thide, we could potentially transmit an “infinite number” of TV, radio, WiFi, and cellular channels at the same time over the same frequency, blasting apart our highly congested wireless spectrum.

Thide’s approach is rather simple. Basically, electromagnetic waves can have both spin angular and orbital angular momentum (OAM). If you picture the Earth-Sun system, spin momentum is the Earth rotating on its axis (producing the day-night cycle), and orbital momentum is the Earth rotating around the sun (producing the seasons). In standard wireless communications — radio, TV, WiFi — we only modulate the spin angular momentum of waves. For years, Thide had theorized that orbital angular momentum could also be added to wireless signals, effectively creating a spiral signal that looks like fusilli pasta; or, in the words of Thide, a “radio vortex.”

Now, in an experiment in Venice, Thide and his Italian colleagues have transmitted two signals at the same time, on the same frequency, over a distance of 442 meters (1450ft). Pictured on the right is the antenna that the team used. No, your eyes don’t deceive you: To create these radio vortices, all you have to do is make a cut in a standard parabolic reflector and twist it slightly. If you imagine a corkscrew of radio signals being continuously transmitted from the outside edge of the antenna, that’s effectively what’s occurring. On the receiving end, there are two “normal” TV antennae (Yagi-Uda) set apart by the same angle as the break in the transmitter. These antennae “decode” the vortex, and voila: Two radio signals transmitted over the same frequency.

It is hard to put into words just how significant Thide’s discovery could be. If the vortex preserves other aspects of wireless communications, such as multiplexing, then in the short term we could be looking at a wireless spectrum that can carry 10 or 20 times as much data. In the long term, as our understanding of orbital angular momentum grows, our wireless spectrum could effectively be infinite. To be honest, this is such a huge twist for wireless communications that the full repercussions are not yet known.

With radio and TV, and now cellular networks, wireless spectrum is one of humanity’s most valued resources. It is because airwaves are so clogged that companies like Verizon or Vodafone pay billions of dollars for just a few megahertz. If Thide’s discovery pans out, not only would wireless spectrum lose most of its value, but the trouble and strife surrounding LightSquared, international roaming, LTE rollout, white space wireless, and digital TV simply cease to be.

Video : //

 Here  [MP4, 23 MB ]
New Journal of Physics, Volume 14 ( March 2012 )

[ Excerpts ]

Encoding many channels on the same frequency through radio vorticity: first experimental test

Fabrizio Tamburini, Elettra Mari, Anna Sponselli, Bo Thidé, Antonio Bianchini1 and Filippo Romanato


We have shown experimentally, in a real-world setting, that it is possible to use two beams of incoherent radio waves, transmitted on the same frequency but encoded in two different orbital angular momentum states, to simultaneously transmit two independent radio channels. This novel radio technique allows the implementation of, in principle, an infinite number of channels in a given, fixed bandwidth, even without using polarization, multiport or dense coding techniques. This paves the way for innovative techniques in radio science and entirely new paradigms in radio communication protocols that might offer a solution to the problem of radio-band congestion.

1. Introduction

The first radio signal transmitted and received by Guglielmo Marconi on 8 December 1895 started the wireless communication revolution [1]. Now information is mostly exchanged through wireless channels and the rapid increase of the use of mobile devices has led to congestion in the available radio bands even after the application of dense coding and channel sharing techniques [2]. Therefore, it is important to try to develop new methods that make it possible to utilize the electromagnetic (EM) spectrum better.

One way is to exploit fundamental physical properties of the EM field that hitherto have not been utilized in radio communications. To this end, we recall that the EM field can carry both energy and momentum. Whereas the Poynting vector S and the concomitant linear momentum (rational units) are associated with force action and therefore with translational dynamics, the angular momentum is a conserved physical observable (constant of motion) that is associated with torque action and thus with rotational dynamics [3]. In a beam geometry as used in radio communications, the total angular momentum can be conveniently expressed as the sum of two components: J = S + L. The component S represents the spin angular momentum (SAM), related to the polarization of the individual EM waves of the beam and thus with photon helicity. The component L represents the lesser-known orbital angular momentum (OAM) associated with the helicoidal phase profile of the EM beam in the direction orthogonal to the propagation axis. In a quantum picture L can be described as a superposition of discrete photon quantum eigenstates, each with a well-defined OAM value lhbar,l = 0,±1,±2,... [4–7]. Hence, not only in mechanics but also in electromagnetism, OAM is a fundamental physical quantity that spans an infinite state space [8]. It offers, in addition to the conventional translational linear momentum and polarization (SAM) rotational degrees of freedom, which spans only a two-dimensional (2D) state space, additional rotational degrees of freedom that are distinctly different from SAM. Without increasing the frequency bandwidth, the OAM states can be used as a new, very large set of communication channels that are mutually orthogonal to each other in the OAM state space.

Here we report the results of real-world, outdoor radio experiments in the 2.4 GHz WiFi band that demonstrate the feasibility of increasing the wireless information transfer capacity over large distances by exploiting the OAM states [8] of EM waves. Our findings extend previous indoor laboratory test experiments in which the transmission of optical OAM states of coherent laser [9] and radio [10] beams was demonstrated. The results reported here show that OAM and vorticity are preserved throughout the long-distance propagation over long distances and can indeed be utilized in radio communication.

Unlike already existing radio communication protocols that use the spatial phase distribution generated by a set of antennae to artificially increase the transmission bandwidth, the immediate advantage provided by a protocol based on the physical OAM states as independent communication channels is that of using the peculiar spatial phase distribution of each of these states as a reference pattern to generate, modulate and detect them in a better way.

OAM has found practical applications in many other fields such as radar [11], nanotechnology [12], quantum experiments [13] and also astronomy and space sciences [14–18], improving the resolving power of diffraction-limited optical instruments [19] and facilitating the detection of extrasolar planets [20] and Kerr black holes [21].

2. Transmitting with radio vortices

To date, there has been no report on the transmission of twisted radio beams in a real-world experiment. The results from our outdoor radio vorticity experiments demonstrate that when using a given radio frequency bandwidth around a fixed carrier frequency, the inherent orthogonality (in a Hilbert sense) of the denumerably infinite OAM state space can ideally provide, without increasing the frequency bandwidth, an arbitrarily large set of independent OAM transmission channels, each characterized only by its peculiar topological property. This new technique can be described as topological diversity.

In our radio vorticity communication experiments, we generated and detected two orthogonal OAM channels within a given fixed frequency band: one untwisted with OAM l = 0 and the other with an l = 1 OAM twist. Two identical WiFi FM transmitters, each with an output power of 2 W and driven by a signal generator, were tuned to the carrier frequency of 2.414 GHz to feed two antennae. In an FM transmission the amplitude and intensity of the EM wave remain constant in time; only the carrier frequency is modulated. The signal-to-noise ratio of the WiFi modules was 38 dB for the video channel and 45 dB for the audio band. The receiver sensitivity was -90 dBm, i.e. 10-9mW. The transmitted signal bandwidths of both signals were 15 or 27 MHz, like those used in video signals.

The l = 0 source was radiated with linear polarization by a commercial 16.5 dBi gain Yagi–Uda antenna [22]. To generate the l = 1 vortex beam, we mechanically modified a 26 dBi commercial off-axis parabolic antenna, with diameter D = 80 cm, to attain an off-axis spiral parabolic-shaped phase mask reflector. The expected beam waist, given by the diffraction limit of the antenna, is dphiv = 1.22?/D ˜ 10.9°, where ? is the radio wavelength. The half-power beam width (HPBW), i.e. the angular separation between the points on the antenna radiation pattern at which the power or, equivalently, the linear momentum, drops to half its maximum value is ? = k?/D = 8.75°. The characteristic parameter of the antenna, k, is a factor that depends on the shape of the reflector and the method of illumination. This l = 1 beam was also linearly polarized. Additional technical details of the experiment can be found in the appendix...

4. Radio transmission with orbital angular momentum

The purpose of the second stage of the experiment was to transmit, using the same set of antennae, on the same frequency of 2.414 GHz, and within a fixed given bandwidth, two mutually orthogonal OAM modes at a distance of 442 m (3536?) from the phase-detecting interferometer. After having verified that the phase properties of the twisted beam were preserved, by analysing the beam shape with an intensity/spectrum analyser, we transmitted the two OAM modes from the lighthouse of San Giorgio Island in the direction of the balcony of Palazzo Ducale in Venice (Italy), where they were received. The HPBW diameter of the parabolic antenna at that distance was 67 m. During the experiment, we measured a maximum signal power Pmax = 30.7 dBm, with a background noise of -87 dBm generated by external radio sources. The noise background that we characterized with the help of a digital spectrum analyser was dominantly caused by external sources (see table A.4 in the appendix).

At the phase singularity point we expected the intensity to drop almost to zero, as found in experiments at optical frequencies. The narrow zone where the central singularity was located, defined by a 10 dB (i.e. tenfold) drop in the mean field intensity, had a diameter of about 2?. This small region was contained inside a wider zone with a diameter of ~190 cm (~15?) where a 3–5 dB drop in the mean field intensity was observed. Outside this region, at distances larger than 2 m (~16?) from the singularity, the field intensity was found to be more stable and flatter. The measured signal intensity was only 3 dB lower than expected from a non-helicoidal parabolic antenna with the same diameter and focal length.

Due to propagation effects, the signal intensity near the singularity, where the electric field tends to zero, exhibited a more uniform and flatter intensity profile than expected from a coherent beam with a Laguerre–Gaussian profile. The phase distribution of the entire antenna lobe was preserved. This actually resembles the behaviour of incoherent beams carrying OAM. Such beams preserve the phase profile but the region of the lobe in which the singularity is located appears much more filled by the signal because of the large width of the transmission band and, in our case, probably also because of the shape of the transmitting antenna. The only insignificant variable interference effects noted during the experiments were due to reflections of the beam from the water surface of the lagoon that varied with the tidal height of the sea.

By using an interferometric phase discrimination method we were able to separate the two OAM modes by identifying their 'phase fingerprints' [10, 11, 21, 23, 24]. The receiving station consisted of a commercial off the shelf (COTS) frequency-modulation (FM) radio module receiver fed by two identical 16.5 dBi Yagi–Uda antennae (hereafter called antenna A and antenna B) connected together with 180°-phase-shifted cables through a beam adder module, in order to obtain a phase-difference interferometer. We decided to use such directive antennae to spatially reduce any possible background interference due to the presence of other WiFi sources. The antenna parameters are given in the appendix. Antenna A was mounted on a mechanical translator oriented towards the direction of the transmitting station to select one of the two channels by exploiting the spatial phase front properties of different OAM states present in the two beams, whereas antenna B could be moved mechanically in the orthogonal horizontal direction only.

The interferometer measured the phase difference between the two antennae, A and B, and therefore characterized the spatial phase properties of the beams that are the fingerprints of the vorticity OAM states of the field. To discriminate between the two different spatial modes of the EM field, we aligned antenna A, antenna B and the field singularity along a line parallel to the horizon, and the singularity was positioned in the middle of the segment delimited by antennae A and B (see the scheme in the appendix, figure A.6). If the setup were perfectly aligned, the twisted EM wave with l = 1 would have produced an exact 180° azimuthal phase difference between the two antennae, subsequently compensated for by the cable electric delay, thus producing an intensity maximum. The untwisted beam, with 0° azimuthal phase difference, would have produced an intensity minimum for the same settings.

EM waves with wavelength ?, propagating along the two paths from the source to the two receiving antennae A and B, acquired a total phase difference phgr that depends on the angle ? between the incident plane wavefront and the interferometer baseline, the relative azimuthal term between the two receiving antennae phgrl due to the beam vorticity (phgrl = 0 when l = 0 and phgrl = p when l = 1) and a generic additional spatial/temporal phase term phgr0 introduced by the experimental setup (e.g. cable delay, imperfect parallelism of the receiving antennae, etc). This total phase difference can be approximated by *** where d is the separation of the two antennae. The signal was collected equally by antennae A and B in phase and the signal of antenna A arrived at the signal adder 180° out of phase with respect to that of antenna B because of the electric ?/2 cable delay, resulting in a difference signal configuration, |A - B|, such that

where V 0 is the voltage measured at the antenna cable end (receiver input). The bearing to the transmitter is, in the ideal case, determined by a minimum or total absence of signal. A maximum is obtained when phgr = (k + 1)p and k is an integer.

By adding a phase delay to the signal from antenna A, one can change the pointing direction of the antenna system in such a way that the segment A - B, delimited by the two antennae, would effectively rotate rigidly around the field singularity in the direction orthogonal to the propagation of the EM signal, with the result of moving the position of the null interference fringes and compensating for the presence of additional phases and the inclination of the interferometric base with respect to the direction of the source. Alternatively, a similar compensation is obtained by moving antenna A along the direction of the source by a quantity ?x = ?n/2p. Consequently, the phase difference between the two paths can be written as ***.

The parameter n can be adjusted to improve the tuning of the receiving system and read a signal minimum in the exact direction to the transmitting antenna. Here, n is negative when antenna A is moved towards the source.

If the beam carries OAM, the phase distribution of the wavefront arriving at antennae A and B will exhibit a characteristic topological signature. In the simplest case, when the centre of the vortex coincides with the centre of the interferometer, the two antennae will experience a phase gap due to the OAM of the EM wave phgrl = lp and a maximum of the signal is obtained when the phase factor is ***
where is the set of all integer numbers. When l = 1, a maximum for the vortex is achieved when n = 0 and k = 0. Because of destructive interference the l = 0 signal intensity will at the same time experience a minimum. On the other hand, a maximum for the l = 0 mode will be obtained when n = -?/2, corresponding to a minimum for the vortex. Following these considerations, we aligned the interferometer so as to have the field singularity at the midpoint of the line joining the two receiving antennae (i.e. the interferometer baseline) and obtained a phase gap phgrl = p between the two antennae expected during the reception of the l = 1 vortex. To better optimize the interference fringe structure we oriented the baseline by an inclination ? ~ 10° with respect to the balcony in order to be orthogonal to the incoming beam. During the experiment, the main practical difficulty was that of positioning the singularity at the midpoint between the two Yagi–Uda antennae: this problem was solved with the find-and-track direction method, also known as the 'fox-hunting' method [25], commonly used to locate a radio transmitter with high precision.

In order to have a simple, straightforward and practical method to discriminate between the two orthogonal OAM channels, transmitted on the same carrier frequency, we frequency modulated them with constant-level audio signals at different modulation frequencies (400 and 1000 Hz for the untwisted and twisted waves, respectively) by injecting a -5 dBm monophonic audio signal into the video band of each transmitter. The thus-modulated radio signals were received by the two Yagi–Uda antennae, summed by a 3 dB power splitter/combiner (Mini-Circuits ZX10-2-42 +) and then demodulated in the FM receiver into monophonic audio signals that were subsequently digitally sampled, recorded and analysed in real time with 32-bit resolution. Each dataset so produced was 22?870?008 bytes long.

The total signal loss measured in the receiving line of the interferometer was 6 dB. In order to reduce the power of the signal we inserted a calibrated 10 dB attenuator into the receiving line, so that the audio digitizer connected to the receiver output would not saturate due to overvoltage. In a conventional single-antenna receiver setup that detects linear momentum only, the two radio signals were audible simultaneously. By mechanically moving the antenna A with respect to B to select one of the two orthogonal OAM beams, one signal was alternately suppressed with respect to the other due to the different spatial phase signature of the two OAM states. We adjusted the baseline in order to optimize the discrimination of the two different OAM channels by moving antenna A.

Since an FM transmission has the property of generating a constant amplitude output, we adjusted the output of the two transmitters to measure the same receiver output voltage, 1 volt in continuous current (VCC) for each channel. In this way, we were able to characterize the transition between equal-intensity twisted and untwisted channels. Figure 2 shows the maximum positive voltage of the signal measured at the output of the antenna receiver and amplifier. The untwisted beam (line marked 'o') showed destructive interference in the interval 8.5–9.4 cm (approximately 0.7?–0.8?) from the initial antenna position. In the corresponding audio track, the carrier disappears and the 400 Hz tone is suddenly replaced by white noise, which appears louder due to the automatic gain control (AGC) of the receiver. This is a clear indication of destructive interference. Similar behaviour was observed in two other smaller regions and is possibly due to the effects of the secondary Yagi lobes that were not considered in our autocorrelation analysis. The twisted beam (red continuous line), on the other hand, presented a richer forest of alternating maxima and minima; only near the initial position of the antenna (0.4–1.6 cm) was a wide region of total destructive interference observed.

Figure 2. Diagram of the monophonic audio recordings of the twisted/untwisted beams. The output of the two transmitters was adjusted to ensure the same maximum input voltage of 2 V when both channels were present, and 1 VCC max for each individual channel. The first minimum is found at about 1 cm of antenna shift for the l = 1 mode (continuous line). Here the l = 0 channel (marked with the symbol 'o') has a maximum and the associated audio tone is clearly audible. The same was found for the l = 0 mode around the 9 cm antenna position. The inner boundaries of the two minima regions are separated in distance by half the radio wavelength. Between these positions there was a forest of minima of the l = 1 mode, a phenomenon due to the sampling of the field from a finite-sized antenna. Beyond the minimum located at 9 cm, two additional alternating signal minima due to the cross-talk of the two Yagi–Uda antennae were found....

An audio recording, split into three MP3 files of the tuning between the two OAM channels, is provided as additional material, available at The first audio file (movie 1) is the recording of the spatial tuning of the channel without OAM only. One can hear the main tone at 400 Hz and then strong white noise at the position where antenna A, moving in the direction of the source with respect to antenna B, reaches the point where the signal is cancelled by the interferometer. The second file (movie 2) shows that the twisted beam has a much richer spatial structure than that of the untwisted beam. Finally, the third file (movie 3) is the recording of the vortex tuning between the two different OAM states transmitted simultaneously on the same frequency and used in the data analysis reported in figures 2–4.

Already with this setup, one can obtain four physically distinct channels on the same frequency by additionally introducing the use of polarization (SAM), which is independent of OAM. A further five-fold multiplicative factor from implementing multiplexing would yield a total of 20 channels on the same frequency. The utilization of multiport techniques (e.g. MIMO) could increase the capacity further.

5. Conclusions

Our experimental findings that EM OAM can be used for increasing radio transmission capacity without increasing bandwidth is likely to open up new perspectives on wireless communications and radio-based science. History tells us that Marconi invented the wireless telegraph and from that the communication world spread its branches in all directions [1]. All current radio communication services are based on various forms of phase, frequency and/or amplitude modulation of the EM radiation in the form of EM linear momentum (i.e. integrated Poynting vector or energy flux). In order that many different broadcasting stations are able to transmit simultaneously without overlapping their radio signals, Marconi suggested that the total available spectrum of radio frequencies be divided into many non-overlapping frequency subbands [23]. Now, the wide use of wireless communication has unavoidably led to the saturation of all available frequency bands, even after the adoption of artificial techniques that increase band capacity. We have experimentally shown that by using helicoidal parabolic antennae, the use of OAM states might dramatically increase the capacity of any frequency band, allowing the use of dense coding techniques in each of these new vortex radio channels. This might represent a concrete proposal for a possible solution to the band saturation problem.

Moreover, our experimental findings demonstrate that the spatial phase signature was preserved even in the far-field region and for incoherent non-monochromatic wave beams. These results open up new perspectives not only for wireless communication but also for physics and astronomy, including the possible detection of Kerr black holes in the test general relativity [21].


[ PDF ]

Applicant: UNIV PADOVA



As is well known, if common techniques of channel multiplexing are not considered, TV and radio broadcasting is limited by the fact that only two independent signals, one for each polarization state of the EM field, can be transmitted for each carrier frequency.

With current technology and international standards, the available frequencies for the transmission of radio signals, each identified by their carrier frequency and bandwidth, are confined to a relatively narrow spectrum, which accordingly limits the number of signals that can be transmitted independently within a given geographical region.

Telecommunication methods and systems that exploit a further characteristic quantity of the EM waves, the orbital angular momentum, for increasing the capacity of transmitting information, have been recently proposed.

The orbital angular momentum (OAM) is a fundamental physical property of the EM field. The simplest example of an EM field in a pure OAM eigenstate, independent of frequency, is a paraxial beam of light propagating in vacuum along a z axis. In this case, the complex amplitude of the EM field, measured in the plane orthogonal to z, Uf <G>p, can be described, in terms of a Laguerre-Gaussian mode in a cylindrical reference frame r,-&, z , by:


where i describes the number of twists of the helical wavefront (OAM mode, topological charge), p the number of radial nodes of the mode, w the beam waist, L<e> (x) is an associated Laguerre polynomial.
More in general, the amplitude of a field carrying OAM state can be described in an apparatus of spherical coordinates as the factorization of two parts: the first, Ae(r,-&,q>) , depends on the spatial coordinates and the OAM mode while the second, exp(-/ ) , gives the phase dependence, according to the following relation:
Uf-<G> {r, ,<? ) = Af {r, ,<? )exp{- m) A superimposition of different OAM states can generate non-integer OAM states, i.e. a beam endowed with a phase dependence exp(z<'>ccd) corresponding to a non-integer OAM value . A non-integer OAM state can be represented as a series superimposition of integer OAM modes, according to the following relation:
expO'ccfl ) = <[pound][chi]> ( <[pi][alpha]>)<8[iota][eta]>(<[pi][alpha]>) y expQ<'> ft)
[pi] f ^[infinity] - [pound]

An EM wave is therefore characterised by a set of OAM modes, which are naturally quantized and can ideally be infinite.

OAM eigenstates, each identified by a unique integer, are quantised by nature and can therefore be superimposed into various bit patterns that can be resolved at the receiving end. Each OAM mode may be tagged with an integer number (known as "quantum number") I that identifies the corresponding state of vorticity of the propagating EM wave. The quantum number I of an OAM mode may be positive or negative depending on the vorticity type (left-handed or right-handed) with respect to the propagation direction of the EM wave.

OAM modes are independent of the polarization state of the EM field, i.e. they may exist for any type of polarization of the EM wave.
A beam of EM waves on a given carrier frequency can be encoded with an OAM spectrum in term of pure, integer OAM eigenstates.

OAM eigenmodes with different quantum numbers are orthogonal in a Hilbert sense and therefore correspond to mutually and reciprocally independent quantum states for the radio beam. For this reason, the different OAM eigenmodes in a radio beam that carries OAM of any kind, do not interact during the propagation of the radio beam in a homogeneous unbounded medium, in particular in free space.

The exploiting of OAM modes for wireless communication offers a number of relevant advantages, since several orthogonal and independent communication channels become available for any given carrier frequency.
In a propagating EM wave having a given carrier frequency, the phase of OAM modes having a state of vorticity I<> 0 is not constant along a plane but it has a well-defined spatial periodic structure, which may be properly exploited for the transmission of information.

The idea of exploiting the superimposition of OAM modes for performing a multi-modal transmission of information is already used in optics, mostly in the visible region.

However, this concept of physics is basically valid for any wavelength, since Maxwell's equations are linearly scalable in wavelength. Telecommunication apparatuses exploiting OAM modes are at present very crude and apparently addressed towards only a point-to-point transmission/reception of EM waves that is mainly designed for optical applications. Apparently, the extension of the proposed solution to radio telecommunication is inherently not suitable for radio signal broadcasting.

At present no radio telecommunication systems exploiting OAM modes are commercially available.

However some papers have envisaged to use antennas having a particular kind of geometry shape for OAM transmission and reception. Radiation lobes of the transmitting antennas, which are designed for point-to-point transmission/reception, may be directed only towards predefined directions, basically towards a single receiving antenna and are not suitable for broadcasting. Also the receiving antennas are designed for preferable direction reception. Further, such telecommunication systems are apparently difficult and expensive to realize at industrial level, at radio frequencies.

Finally, they do not allow properly identifying/ recognizing the transmitted/received OAM states...


Further advantages of the invention will appear more evident in the following detailed description, with reference to the accompanying drawings, in which:

figure 1 schematically shows an embodiment of the telecommunication apparatus, according to the invention;

figure 2, 3, 4A, 4B schematically show possible embodiments of the transmitting devices of the telecommunication apparatus of figure 1 ;


figure 5 schematically shows a portion of a further embodiment of the telecommunication apparatus, according to the invention...

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