Nonlinear communication channels with capacity above the linear Shannon limit

We prove that, under certain conditions, the capacity of an optical communication channel with in-line, nonlinear filtering (regeneration) elements can be higher than the Shannon capacity for the corresponding linear Gaussian white noise channel. © 2012 Optical Society of America.

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.

Binocular combination at threshold: temporal filtering and summation of signals in separate ON and OFF channels

How does the brain combine spatio-temporal signals from the two eyes? We quantified binocular summation as the improvement in 2AFC contrast sensitivity for flickering gratings seen by two eyes compared with one. Binocular gratings in-phase showed sensitivity up to 1.8 times higher, suggesting nearly linear summation of contrasts. The binocular advantage decreased to 1.4 at lower spatial and higher temporal frequencies (0.25 cycle deg-1, 30 Hz). Dichoptic, antiphase gratings showed only a small binocular advantage, by a factor of 1.1 to 1.2, but no evidence of cancellation. We present a signal-processing model to account for the contrast-sensitivity functions and the pattern of binocular summation. It has linear sustained and transient temporal filters, nonlinear transduction, and half-wave rectification that creates ON and OFF channels. Binocular summation occurs separately within ON and OFF channels, thus explaining the phase-specific binocular advantage. The model also accounts for earlier findings on detection of brief antiphase flashes and the surprising finding that dichoptic antiphase flicker is seen as frequency-doubled (Cavonius et al, 1992 Ophthalmic and Physiological Optics 12 153 - 156). [Supported by EPSRC project GR/S74515/01].

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.

Picosecond soliton transmission using concatenated nonlinear optical loop mirror intensity filters

We investigate the use of nonlinear optical loop mirrors as saturable absorbers in picosecond soliton transmission systems. It is found that they allow short (1–5-ps) pulses to be propagated through chains of optical amplifiers spaced at intervals of typically 10 km. The loop mirror removes dispersive waves and stabilizes the peak amplitude of the soliton. An additional advantage is that the self-frequency shift of the soliton may be suppressed by bandwidth filtering without causing growth of dispersive waves at the center of the passband. The timing jitter and soliton interactions present in the scheme are also described.

Assessing interactions of linear and nonlinear neuronal sources using MEG beamformers:a proof of concept

Objective: This study aimed to explore methods of assessing interactions between neuronal sources using MEG beamformers. However, beamformer methodology is based on the assumption of no linear long-term source interdependencies [VanVeen BD, vanDrongelen W, Yuchtman M, Suzuki A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 1997;44:867-80; Robinson SE, Vrba J. Functional neuroimaging by synthetic aperture magnetometry (SAM). In: Recent advances in Biomagnetism. Sendai: Tohoku University Press; 1999. p. 302-5]. Although such long-term correlations are not efficient and should not be anticipated in a healthy brain [Friston KJ. The labile brain. I. Neuronal transients and nonlinear coupling. Philos Trans R Soc Lond B Biol Sci 2000;355:215-36], transient correlations seem to underlie functional cortical coordination [Singer W. Neuronal synchrony: a versatile code for the definition of relations? Neuron 1999;49-65; Rodriguez E, George N, Lachaux J, Martinerie J, Renault B, Varela F. Perception's shadow: long-distance synchronization of human brain activity. Nature 1999;397:430-3; Bressler SL, Kelso J. Cortical coordination dynamics and cognition. Trends Cogn Sci 2001;5:26-36]. Methods: Two periodic sources were simulated and the effects of transient source correlation on the spatial and temporal performance of the MEG beamformer were examined. Subsequently, the interdependencies of the reconstructed sources were investigated using coherence and phase synchronization analysis based on Mutual Information. Finally, two interacting nonlinear systems served as neuronal sources and their phase interdependencies were studied under realistic measurement conditions. Results: Both the spatial and the temporal beamformer source reconstructions were accurate as long as the transient source correlation did not exceed 30-40 percent of the duration of beamformer analysis. In addition, the interdependencies of periodic sources were preserved by the beamformer and phase synchronization of interacting nonlinear sources could be detected. Conclusions: MEG beamformer methods in conjunction with analysis of source interdependencies could provide accurate spatial and temporal descriptions of interactions between linear and nonlinear neuronal sources. Significance: The proposed methods can be used for the study of interactions between neuronal sources. © 2005 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

All-optical nonlinear signal processing at a RZ receiver

We propose a novel all-optical signal processor for use at a return-to-zero receiver utilising loop mirror intensity filtering and nonlinear pulse broadening in normal dispersion fibre. The device offers reamplification and cleaning up of the optical signals, and phase margin improvement. The efficiency of the technique is demonstrated by application to 40 Gbit/s data transmission.

New fiber laser architecture with transform-limited nonlinear spectral compression

We numerically demonstrate a new fiber laser architecture supporting spectral compression of negatively chirped pulses in passive normally dispersive fiber. Such a process is beneficial for improving the energy efficiency of the cavity as it prevents narrow spectral filtering from being highly dissipative. The proposed laser design provides an elegant way of generating transform-limited picosecond pulses. © 2012 IEEE.

Amplifier similariton fiber laser with nonlinear spectral compression

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser’s power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.

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.

Design of Raman-based nonlinear loop mirror for all-optical 2R regeneration of differential phase-shift-keying transmission

We present a concept for all-optical regeneration of signals modulated in phase-sensitive modulation formats, which is based on a new design of Raman amplified nonlinear optical loop mirror (RA-NOLM). We demonstrate simultaneous amplitude-shape regeneration and phase-noise reduction in high-speed differential phase-shift-keying transmission systems by use of the RA-NOLM combined with spectral filtering.

All-optical nonlinear pulse processing based on normal dispersion fiber-enhanced nonlinear optical loop mirror

A novel simple all-optical nonlinear pulse processing technique using loop mirror intensity filtering and nonlinear broadening in normal dispersion fiber is described. The pulse processor offers reamplification and cleaning up of the optical signals and phase margin improvement. The efficiency of the technique is demonstrated by application to 40-Gb/s return-to-zero optical data streams.

All-optical passive 2R regeneration for N×40 Gbit/s WDM transmission using NOLM and novel filtering technique

We propose an all-optical passive 2R regeneration method for WDM (N×40 Gbit/s) dispersion-managed RZ transmission based on specially designed WDM guiding filters and in-line nonlinear optical loop mirrors. By system optimisation, the feasibility of 150 GHz-spaced × l6 channel transmission over 25,000 km of standard fibre is numerically demonstrated.

All-optical passive 2R regeneration for N × 40 Gbit/s WDM transmission using NOLM and novel filtering technique

We propose a passive all-optical 2R regeneration method for WDM (N×40 Gbit/s) dispersion-managed RZ transmission based on specially designed WDM guiding filters and in-line nonlinear optical loop mirrors. By system optimisation, the feasibility of 150 GHz-spaced × 16 channel 25000 km transmission over standard fibre is numerically demonstrated.