Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.

Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

Depth propagation and surface construction in 3-D vision

Motion discontinuities can signal object boundaries where few or no other cues, such as luminance, colour, or texture, are available. Hence, motion-defined contours are an ecologically important counterpart to luminance contours. We developed a novel motion-defined Gabor stimulus to investigate the nature of neural operators analysing visual motion fields in order to draw parallels with known luminance operators. Luminance-defined Gabors have been successfully used to discern the spatial-extent and spatial-frequency specificity of possible visual contour detectors. We now extend these studies into the motion domain. We define a stimulus using limited-lifetime moving dots whose velocity is described over 2-D space by a Gabor pattern surrounded by randomly moving dots. Participants were asked to determine whether the orientation of the Gabor pattern (and hence of the motion contours) was vertical or horizontal in a 2AFC task, and the proportion of correct responses was recorded. We found that with practice participants became highly proficient at this task, able in certain cases to reach 90% accuracy with only 12 limited-lifetime dots. However, for both practised and novice participants we found that the ability to detect a single boundary saturates with the size of the Gaussian envelope of the Gabor at approximately 5 deg full-width at half-height. At this optimal size we then varied spatial frequency and found the optimum was at the lowest measured spatial frequency (0.1 cycle deg-1 ) and then steadily decreased with higher spatial frequencies, suggesting that motion contour detectors may be specifically tuned to a single, isolated edge.

Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications

All-optical data processing is expected to play a major role in future optical communications. The fiber nonlinear optical loop mirror (NOLM) is a valuable tool in optical signal processing applications. This paper presents an overview of our recent advances in developing NOLM-based all-optical processing techniques for application in fiber-optic communications. The use of in-line NOLMs as a general technique for all-optical passive 2R (reamplification, reshaping) regeneration of return-to-zero (RZ) on-off keyed signals in both high-speed, ultralong-distance transmission systems and terrestrial photonic networks is reviewed. In this context, a theoretical model enabling the description of the stable propagation of carrier pulses with periodic all-optical self-regeneration in fiber systems with in-line deployment of nonlinear optical devices is presented. A novel, simple pulse processing scheme using nonlinear broadening in normal dispersion fiber and loop mirror intensity filtering is described, and its employment is demonstrated as an optical decision element at a RZ receiver as well as an in-line device to realize a transmission technique of periodic all-optical RZ-nonreturn-to-zero-like format conversion. The important issue of phase-preserving regeneration of phase-encoded signals is also addressed by presenting a new design of NOLM based on distributed Raman amplification in the loop fiber. © 2008 Elsevier Inc. All rights reserved.

Optical frequency conversion, pulse compression and signal copying using triangular pulses

We propose techniques of optical frequency conversion, pulse compression and signal copying based on a combination of cross-phase modulation using triangular pump pulses and subsequent propagation in a dispersive medium.

Signal processing techniques for ultrasonic inspection

This thesis discusses the need for nondestructive testing and highlights some of the limitations in present day techniques. Special interest has been given to ultrasonic examination techniques and the problems encountered when they are applied to thick welded plates. Some suggestions are given using signal processing methods. Chapter 2 treats the need for nondestructive testing as seen in the light of economy and safety. A short review of present day techniques in nondestructive testing is also given. The special problems using ultrasonic techniques for welded structures is discussed in Chapter 3 with some examples of elastic wave propagation in welded steel. The limitations in applying sophisticated signal processing techniques to ultrasonic NDT~ mainly found in the transducers generating or receiving the ultrasound. Chapter 4 deals with the different transducers used. One of the difficulties with ultrasonic testing is the interpretation of the signals encountered. Similar problems might be found with SONAR/RADAR techniques and Chapter 5 draws some analogies between SONAR/RADAR and ultrasonic nondestructive testing. This chapter also includes a discussion on some on the techniques used in signal processing in general. A special signal processing technique found useful is cross-correlation detection and this technique is treated in Chapter 6. Electronic digital compute.rs have made signal processing techniques easier to implement -Chapter 7 discusses the use of digital computers in ultrasonic NDT. Experimental equipment used to test cross-correlation detection of ultrasonic signals is described in Chapter 8. Chapter 9 summarises the conclusions drawn during this investigation.

All-optical nonlinear fibre signal processing

All-optical technologies for data processing and signal manipulation are expected to play a major role in future optical communications. Nonlinear phenomena occurring in optical fibre have many attractive features and great, but not yet fully exploited potential in optical signal processing. Here, we overview our recent results and advances in developing novel photonic techniques and approaches to all-optical processing based on fibre nonlinearities. Amongst other topics, we will discuss phase-preserving optical 2R regeneration, the possibility of using parabolic/flat-top pulses for optical signal processing and regeneration, and nonlinear optical pulse shaping. A method for passive nonlinear pulse shaping based on pulse pre-chirping and propagation in a normally dispersive fibre will be presented. The approach provides a simple way of generating various temporal waveforms of fundamental and practical interest. Particular emphasis will be given to the formation and characterization of pulses with a triangular intensity profile. A new technique of doubling/copying optical pulses in both the frequency and time domains using triangular-shaped pulses will be also introduced.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Nonlinear and ROADM induced penalties in 28 Gbaud dynamic optical mesh networks employing electronic signal processing

We report the impact of cascaded reconfigurable optical add-drop multiplexer induced penalties on coherently-detected 28 Gbaud polarization multiplexed m-ary quadrature amplitude modulation (PM m-ary QAM) WDM channels. We investigate the interplay between different higher-order modulation channels and the effect of filter shapes and bandwidth of (de)multiplexers on the transmission performance, in a segment of pan-European optical network with a maximum optical path of 4,560 km (80km x 57 spans). We verify that if the link capacities are assigned assuming that digital back propagation is available, 25% of the network connections fail using electronic dispersion compensation alone. However, majority of such links can indeed be restored by employing single-channel digital back-propagation employing less than 15 steps for the whole link, facilitating practical application of DBP. We report that higher-order channels are most sensitive to nonlinear fiber impairments and filtering effects, however these formats are less prone to ROADM induced penalties due to the reduced maximum number of hops. Furthermore, it has been demonstrated that a minimum filter Gaussian order of 3 and bandwidth of 35 GHz enable negligible excess penalty for any modulation order.

Optical frequency conversion, pulse compression and signal copying using triangular pulses

We propose techniques of optical frequency conversion, pulse compression and signal copying based on a combination of cross-phase modulation using triangular pump pulses and subsequent propagation in a dispersive medium.

All-optical nonlinear fibre signal processing

All-optical technologies for data processing and signal manipulation are expected to play a major role in future optical communications. Nonlinear phenomena occurring in optical fibre have many attractive features and great, but not yet fully exploited potential in optical signal processing. Here, we overview our recent results and advances in developing novel photonic techniques and approaches to all-optical processing based on fibre nonlinearities. Amongst other topics, we will discuss phase-preserving optical 2R regeneration, the possibility of using parabolic/flat-top pulses for optical signal processing and regeneration, and nonlinear optical pulse shaping. A method for passive nonlinear pulse shaping based on pulse pre-chirping and propagation in a normally dispersive fibre will be presented. The approach provides a simple way of generating various temporal waveforms of fundamental and practical interest. Particular emphasis will be given to the formation and characterization of pulses with a triangular intensity profile. A new technique of doubling/copying optical pulses in both the frequency and time domains using triangular-shaped pulses will be also introduced.

Digital signal processing based on inverse scattering transform

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal. © 2013 Optical Society of America.

Impact of longitudinal power budget in coherent transmission systems employing digital back-propagation

We report the impact of longitudinal signal power profile on the transmission performance of coherently-detected 112 Gb/s m-ary polarization multiplexed quadrature amplitude modulation system after compensation of deterministic nonlinear fibre impairments. Performance improvements up to 0.6 dB (Q(eff)) are reported for a non-uniform transmission link power profile. Further investigation reveals that the evolution of the transmission performance with power profile management is fully consistent with the parametric amplification of the amplified spontaneous emission by the signal through four-wave mixing. In particular, for a non-dispersion managed system, a single-step increment of 4 dB in the amplifier gain, with respect to a uniform gain profile, at similar to 2/3(rd) of the total reach considerably improves the transmission performance for all the formats studied. In contrary a negative-step profile, emulating a failure (gain decrease or loss increase), significantly degrades the bit-error rate.

Ultra-long range distributed fibre sensing using virtually transparent propagation

Distributed fibre sensors provide unique capabilities for monitoring large infrastructures with high resolution. Practically, all these sensors are based on some kind of backscattering interaction. A pulsed activating signal is launched on one side of the sensing fibre and the backscattered signal is read as a function of the time of flight of the pulse along the fibre. A key limitation in the measurement range of all these sensors is introduced by fibre attenuation. As the pulse travels along the fibre, the losses in the fibre cause a drop of signal contrast and consequently a growth in the measurement uncertainty. In typical single-mode fibres, attenuation imposes a range limit of less than 30km, for resolutions in the order of 1-2 meters. An interesting improvement in this performance can be considered by using distributed amplification along the fibre [1]. Distributed amplification allows having a more homogeneous signal power along the sensing fibre, which also enables reducing the signal power at the input and therefore avoiding nonlinearities. However, in long structures (≥ 50 km), plain distributed amplification does not perfectly compensate the losses and significant power variations along the fibre are to be expected, leading to inevitable limitations in the measurements. From this perspective, it is simple to understand intuitively that the best possible solution for distributed sensors would be offered by a virtually transparent fibre, i.e. a fibre exhibiting effectively zero attenuation in the spectral region of the pulse. In addition, it can be shown that lossless transmission is the working point that allows the minimization of the amplified spontaneous emission (ASE) noise build-up. © 2011 IEEE.

Optical communication based on the periodic nonlinear Fourier transform signal processing

In this work we introduce the periodic nonlinear Fourier transform (PNFT) and propose a proof-of-concept communication system based on it by using a simple waveform with known nonlinear spectrum (NS). We study the performance (addressing the bit-error-rate (BER), as a function of the propagation distance) of the transmission system based on the use of the PNFT processing method and show the benefits of the latter approach. By analysing our simulation results for the system with lumped amplification, we demonstrate the decent potential of the new processing method.