Chaos, goes conventional wisdom, can only be a malign influence in telecommunications. But a technique that uses chaotically varying signals to transmit information more privately may help it shed that bad-boy image.
Synchronization leads to communication — even when the signals used are chaotic. That is the lesson of a study by Argyris and colleagues on page 343 of this issue1. It reports the successful transfer of digital information at gigabit rates by chaotically fluctuating laser light travelling through more than 100 kilometres of a commercial fibre-optic link around Athens, Greece (Fig. 1). The transmitter and receiver become harmonized in chaotic synchrony, allowing information to be reliably extracted at the other end — a result that brings us closer to exploiting the inherent advantages of chaos, rather than trying to eliminate it whenever it appears.
The phenomenon of synchronization in periodic systems has been known since at least 1665, when Christiaan Huygens observed that pendulum clocks become synchronized when placed close to each other on a common support. Asian fireflies flashing together, flocks of geese flying in remarkable formations and pedestrians in lock-step on London's Millennium Bridge are illustrations of synchronization when large numbers of living creatures get together2. But synchrony also arises in inert matter: lasers and masers both exploit the ability of large ensembles of atoms and molecules to harmonize their oscillations and emit light in coherence. The key to synchrony in such systems is that the individual elements are in some way coupled to each other, leading to the formation of — sometimes beautiful — patterns in space and time.
So can synchrony be observed in systems that behave chaotically? One of the hallmarks of chaotic systems that are isolated from one another is that their evolution diverges exponentially fast, even when their initial conditions are very similar. This is why predicting the weather more than a few days in advance is so hard. Therefore, the finding a couple of decades ago that suitably coupled chaotic systems could (under certain conditions) do exactly the opposite, and converge from distant initial conditions to synchronize their chaotic motions, came as a huge surprise3,4.
The subsequent discovery that lasers can emit light in patterns that are chaotic in time and space clearly implied that remote lasers should be able to synchronize if they receive light from one another, whether through space or through an optical fibre. Experiments soon confirmed this, and with the exchange of only small amounts of light, too5,6. The synchronization is sufficiently robust for information to be exchanged: if one of the chaotic laser systems, the transmitter, is perturbed by a message source, it can ‘fold’ that information into its own chaotic waveform, which it transmits to the input of the second laser system, the receiver. Meanwhile, the receiver's output is a synchronized replica of the transmitter's original, unperturbed chaotic waveform — so the receiver recovers the message as the difference between its input and output waveforms. (Analogously, a radio receiver that is tuned to a carrier frequency recovers information from perturbations of the amplitude or frequency of a periodic waveform.)
Argyris and colleagues1 take a large stride towards showing that the method of transmitting and receiving information using chaotic waveforms can also work in the real world, without the stable conditions of the laboratory. Applying chaotic systems in real-world communications is a beguiling prospect, because a third party intercepting the signal would have difficulty extracting the information sent. Such security aspects of chaos-based communications admittedly need much further analysis. But as the authors point out, chaotic carrier waveforms offer privacy in a manner that could be complementary to and compatible with conventional software-based and quantum-cryptographic systems.
The remarkable features of the authors' work are the simplicity of their set-up — they use chaotic diode laser systems and instrumentation that are widely available off the peg — and their demonstration that information can be recovered with quite reasonable bit-error rates over a commercial fibre-optic link. The optical fibre used for the experiments in Athens was temporarily free of network traffic, but was still installed and connected to the switches of the network nodes. The authors measured the characteristics of the fibre, such as its attenuation and chromatic dispersion, before the experiment. This allowed them, for example, to exactly counter the effects of dispersion by inserting an appropriate length of dispersion-compensating fibre at the beginning of the link. Three amplifiers were used, one at the transmitter, one 50 kilometres from the transmitter, and one at the receiver, followed by optical filters with bandwidths of around 1 nanometre — this respectively compensated for optical losses and removed spontaneous noise.
The scheme used by Argyris et al. exploited time-delayed feedback to generate high-dimensional, high-capacity chaotic waveforms at high bandwidths. This has turned out to be a most fruitful approach: the bit-rate limit of several gigabits in these experiments is set by the electronic and optical components used, and could become much higher with suitably designed systems. For instance, the authors' strategy is compatible with a technique known as wavelength multiplexing; this allows much higher bit rates to pass through a single fibre by transmitting light of many different wavelengths simultaneously.
The exciting possibilities revealed by these experiments1 may be pursued in other directions that more fully exploit the possibilities available for communication using electromagnetic waves. The vector properties of light waves (their polarization) could be used to encode data7. Optical patterns that are chaotic in time and space might also be used to communicate holographic information8 by generalized synchronization. Here, transmitter and receiver do not share identical synchronized dynamics; instead, the relationship between the two is given by a mathematical function, supplying an additional element of privacy.
The success of such developments will ultimately depend on our willingness to implement new ways of transporting optical signals, as well as on novel transmitters and receivers. The rewards could be considerable, not only in understanding the communication of information using chaotic physical systems. Such work could in the long term also help us to elucidate the workings of that most private of communication networks — the human brain.
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Roy, R. Chaos down the line. Nature 438, 298 (2005). https://doi.org/10.1038/438298b
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