http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

/pdf/exploring-complex-networks-2pdzihykyi.pdf

Exploring complex networks

Recurrence plots for the analysis of complex systems

The synchronization of chaotic systems

Chaos is good, if you are looking to send encrypted information across a broadband optical network. The idea that the transmission of light-based signals embedded in chaos can provide privacy in data transmission has been demonstrated over short distances in the laboratory. Now it has been shown to work for real, across a commercial fibre-optic channel in the metropolitan area network of Athens, Greece. The results show that the technology is robust to perturbations and channel disturbances unavoidable under real-world conditions. Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission1,2. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology3,4,5, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120 km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10-7. The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.

/pdf/chaos-based-communications-at-high-bit-rates-using-2z2lxtwks1.pdf

Chaos-based communications at high bit rates using commercial fibre-optic links

Recent experiments with chaotic electronic circuits have shown the possibility of communication with chaos The experimental demonstration of chaotic communication with an optical system is described An erbium-doped fiber ring laser (EDFRL) was used to produce chaotic light with a wavelength of 153 micrometers A small 10-megahertz message was embedded in the larger chaotic carrier and transmitted to a receiver system where the message was recovered from the chaos Chaotic optical waveforms can thus be used to communicate masked information at high bandwidths

https://science.sciencemag.org/content/sci/279/5354/1198.full.pdf

Communication with Chaotic Lasers

A chaotic carrier of information can be considered a generalization of the more traditional sinusoidal carrier. In communication systems which use chaotic waveforms, as in many more conventional methods, information can be recovered from the carrier using a receiver which is “tuned,” or synchronized, to the dynamics of the transmitter. Communication methods using chaotic carriers have been studied for the past few years, and several methods have been experimentally demonstrated in electronic circuits [1]. While chaotic electronic circuits typically have bandwidths of 100 kHz or less [2], the optical system presented here has a bandwidth of at least several GHz. In those electronic chaotic communication methods that have been demonstrated, the chaos usually has been low dimensional. For certain low-dimensional chaotic communication methods, it has been shown previously that the message can be extracted from the transmitted signal by reconstructing the system’s chaotic attractor [3]. A communication method utilizing higher dimensional chaos is likely to provide enhanced privacy. Numerical analysis of our experimental data indicates that the dynamics of our system are indeed high dimensional, of order 10 or greater. Previously, Goedgebuer and colleagues have demonstrated chaotic communication of a 2 kHz sine wave using a hybrid electro-optic system to generate highdimensional chaotic fluctuations in wavelength [4]. Also in earlier work, we injected a small 10 MHz square wave optical message into a ring laser producing highdimensional chaotic light. The square wave message was masked by the chaotic intensity fluctuations of the light from the ring laser as it propagated to a receiver, where the message was recovered [5]. Here we describe several qualitatively new developments, in both concept and technique, over previous work. Rather than using the chaotic light to mask a message, an intracavity intensity modulator is used to directly encode the message onto an optical chaotic carrier. Unlike our previous work, the message signal does not have to be small compared to the carrier or slow compared to the bandwidth of the laser fluctuations; they can have comparable bandwidths. The message modulation drives the chaotic dynamics of the laser. The laser dynamics, in turn, incorporate the digital message into the chaotic waveform. Both transmitter and receiver have configurations that involve two separate time delays, thereby enhancing the privacy of the transmission —successful recovery of the message depends on multiple parameter settings and a matched geometric configuration in the receiver. Finally, the receiver utilizes the polarization properties of the light to recover the digital information by dividing two signals, rather than taking a difference. These innovations enable us to demonstrate recovery of a pseudorandom sequence of bits at 126 Mbitsysec, limited by the bandwidth of our photodiodes. Placing a 1.5 km communication channel between the transmitter and receiver did not cause any obvious degradation of performance. The experimental setup of the fiber-optic system is shown in Fig. 1. The inner ring of the transmitter includes EDFA 1 (erbium-doped fiber amplifier) and a polarizing lithium niobate sLiNBO3d intensity modulator which encodes the message onto the chaotic light. The inner ring is approximately 40 m in length. The outer loop contains EDFA 2, to adjust the amplitude of the light field, and a polarization controller. The polarization controller consists of three wave plates (ly4, ly2, and ly4, respectively) which allow control over the relative phase and polarization of the light fields in the inner ring and outer loop. The outer loop itself is approximately 36 m long and provides a time delay between these light fields. Light coupled out of the transmitter propagates through a fiber-optic communication channel to the receiver. Ten percent of the transmitted light is sent through an attenuator to photodiode A (3-dB roll-off at 125 MHz). The length of the fiber in the outer loop of the receiver has been matched to the length of the transmitter’s outer loop. The time delay between reception of a signal at photodiode A and reception at photodiode B (also 3-dB roll-off at 125 MHz) has been matched to the round-trip time in the inner ring of the transmitter. The signals detected by the photodiodes are recorded by a digital sampling oscilloscope at a rate of 1 3 10 9 samplesysec.

Optical Communication with Chaotic Waveforms

Synchronization of the chaotic intensity fluctuations of three modulated Nd:YAG lasers oriented in a linear array with either a modulated pump or loss is investigated experimentally, numerically, and analytically. Experimentally, synchronization is only seen between the two outer lasers, with little synchrony between outer and inner lasers. Using a false nearest-neighbors method, we numerically estimate the experimental system dynamics to be five dimensional, which is in good agreement with analytical results. Numerically, synchronization is only seen between the two outer lasers, which matches the experimental data well. Lack of synchrony between outer and inner lasers, is explained analytically and then we numerically investigate loss of synchronization of the outer two lasers, observing the occurrence of a blowout bifurcation. Finally, the effects of noise and symmetry breaking are examined and discussed.

/pdf/synchronization-of-chaos-in-an-array-of-three-lasers-2otdur1uir.pdf

Synchronization of chaos in an array of three lasers

We discuss experimental demonstrations of chaotic communication in several optical systems. In each, an erbium-doped fiber ring laser (EDFRL) produces chaotic fluctuations of light intensity onto which is modulated a message consisting of a sequence of pseudorandom digital bits. This combination of chaos and message propagates at a wavelength of ~ 1.5 microns through standard single-mode optical fiber from the transmitter to a receiver, where the message is recovered from the chaos. We present evidence of the high-dimensional nature of the chaotic waveforms and demonstrate chaotic communications through 35 km of single-mode optical fiber at up to 250 Mbit/s, a rate that is, at present, limited only by the speed of our detector electronics.

Chaotic communication using time-delayed optical systems

We describe a novel interferometric method for characterizing optical components in the 1.5-/spl mu/m communications band. A complete polarization-resolved characterization of optical components is achieved with just one scan of a tunable laser. Measurements of three devices are presented, including a molecular gas cell, an arrayed waveguide grating, and a tunable dispersion compensator. A dynamic range of greater than 80 dB is demonstrated.

Gregory D. VanWiggeren

Papers

Communication with Chaotic Lasers

Optical Communication with Chaotic Waveforms

Synchronization of chaos in an array of three lasers

Chaotic communication using time-delayed optical systems

Single-scan interferometric component analyzer