Temporal and spectral nonlinear pulse shaping methods in optical fibers

The combination of the third-order optical nonlinearity with chromatic dispersion in optical fibers offers an extremely rich variety of possibilities for tailoring the temporal and spectral content of a light signal, depending on the regime of dispersion that is used. Here, we review recent progress on the use of third-order nonlinear processes in optical fibers for pulse shaping in the temporal and spectral domains. Various examples of practical significance will be discussed, spanning fields from the generation of specialized temporal waveforms to the generation of ultrashort pulses, and to stable continuum generation.

Interhemispheric differences of spectral power in expressive language:a MEG study with clinical applications

In the last decade we have seen an exponential growth of functional imaging studies investigating multiple aspects of language processing. These studies have sparked an interest in applying some of the paradigms to various clinically relevant questions, such as the identification of the cortical regions mediating language function in surgical candidates for refractory epilepsy. Here we present data from a group of adult control participants in order to investigate the potential of using frequency specific spectral power changes in MEG activation patterns to establish lateralisation of language function using expressive language tasks. In addition, we report on a paediatric patient whose language function was assessed before and after a left hemisphere amygdalo-hippocampectomy. Our verb generation task produced left hemisphere decreases in beta-band power accompanied by right hemisphere increases in low beta-band power in the majority of the control group, a previously unreported phenomenon. This pattern of spectral power was also found in the patient's post-surgery data, though not her pre-surgery data. Comparison of pre and post-operative results also provided some evidence of reorganisation in language related cortex both inter- and intra-hemispherically following surgery. The differences were not limited to changes in localisation of language specific cortex but also changes in the spectral and temporal profile of frontal brain regions during verb generation. While further investigation is required to establish concordance with invasive measures, our data suggest that the methods described may serve as a reliable lateralisation marker for clinical assessment. Furthermore, our findings highlight the potential utility of MEG for the investigation of cortical language functioning in both healthy development and pathology.

The (n+1)/2 rule for dealiasing in the split-step Fourier methods for n-wave interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (n+1)/2, where n is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(n+1) fraction of each spectral dimension.

Analysis of β-amyloid (Aβ) deposition in the temporal lobe in Alzheimer's disease using Fourier (spectral) analysis

To determine the spatial pattern of ß-amyloid (Aß) deposition throughout the temporal lobe in Alzheimer's disease (AD). Methods: Sections of the complete temporal lobe from six cases of sporadic AD were immunolabelled with antibody against Aß. Fourier (spectral) analysis was used to identify sinusoidal patterns in the fluctuation of Aß deposition in a direction parallel to the pia mater or alveus. Results: Significant sinusoidal fluctuations in density were evident in 81/99 (82%) analyses. In 64% of analyses, two frequency components were present with density peaks of Aß deposits repeating every 500–1000 µm and at distances greater than 1000 µm. In 25% of analyses, three or more frequency components were present. The estimated period or wavelength (number of sample units to complete one full cycle) of the first and second frequency components did not vary significantly between gyri of the temporal lobe, but there was evidence that the fluctuations of the classic deposits had longer periods than the diffuse and primitive deposits. Conclusions: (i) Aß deposits exhibit complex sinusoidal fluctuations in density in the temporal lobe in AD; (ii) fluctuations in Aß deposition may reflect the formation of Aß deposits in relation to the modular and vascular structure of the cortex; and (iii) Fourier analysis may be a useful statistical method for studying the patterns of Aß deposition both in AD and in transgenic models of disease.

The effect of spectral filters on reading speed and accuracy following stroke

Purpose - The aim of the study was to determine the effect of optimal spectral filters on reading performance following stroke. Methods - Seventeen stroke subjects, aged 43-85, were considered with an age-matched Control Group (n = 17). Subjects undertook the Wilkins Rate of Reading Test on three occasions: (i) using an optimally selected spectral filter; (ii) subjects were randomly assigned to two groups: Group 1 used an optimal filter, whereas Group 2 used a grey filter, for two-weeks. The grey filter had similar photopic reflectance to the optimal filters, intended as a surrogate for a placebo; (iii) the groups were crossed over with Group 1 using a grey filter and Group 2 given an optimal filter, for two weeks, before undertaking the task once more. An increase in reading speed of >5% was considered clinically relevant. Results - Initial use of a spectral filter in the stroke cohort, increased reading speed by ~8%, almost halving error scores, findings not replicated in controls. Prolonged use of an optimal spectral filter increased reading speed by >9% for stroke subjects; errors more than halved. When the same subjects switched to using a grey filter, reading speed reduced by ~4%. A second group of stroke subjects used a grey filter first; reading speed decreased by ~3% but increased by ~4% with an optimal filter, with error scores almost halving. Conclusions - The present study has shown that spectral filters can immediately improve reading speed and accuracy following stroke, whereas prolonged use does not increase these benefits significantly. © 2013 Spanish General Council of Optometry.

A near real-time water surface detection method based on HSV transformation of MODIS multi-Spectral time series data

In the face of global population growth and the uneven distribution of water supply, a better knowledge of the spatial and temporal distribution of surface water resources is critical. Remote sensing provides a synoptic view of ongoing processes, which addresses the intricate nature of water surfaces and allows an assessment of the pressures placed on aquatic ecosystems. However, the main challenge in identifying water surfaces from remotely sensed data is the high variability of spectral signatures, both in space and time. In the last 10 years only a few operational methods have been proposed to map or monitor surface water at continental or global scale, and each of them show limitations. The objective of this study is to develop and demonstrate the adequacy of a generic multi-temporal and multi-spectral image analysis method to detect water surfaces automatically, and to monitor them in near-real-time. The proposed approach, based on a transformation of the RGB color space into HSV, provides dynamic information at the continental scale. The validation of the algorithm showed very few omission errors and no commission errors. It demonstrates the ability of the proposed algorithm to perform as effectively as human interpretation of the images. The validation of the permanent water surface product with an independent dataset derived from high resolution imagery, showed an accuracy of 91.5% and few commission errors. Potential applications of the proposed method have been identified and discussed. The methodology that has been developed 27 is generic: it can be applied to sensors with similar bands with good reliability, and minimal effort. Moreover, this experiment at continental scale showed that the methodology is efficient for a large range of environmental conditions. Additional preliminary tests over other continents indicate that the proposed methodology could also be applied at the global scale without too many difficulties

Spectral modification of type IA fibre Bragg gratings by high-power near-infrared lasers

We report the first experimental measurements on the spectral modification of type IA fibre Bragg gratings, incorporated in an optical network, which result from the use of high-power, near-infrared lasers. The fibre grating properties are modified in a controlled manner by exploiting the characteristics of the inherent 1400 nm absorption band of the optical fibre, which grows in strength during the type IA grating inscription. If the fibre network is illuminated with a high-power laser, having an emission wavelength coincident with the absorption band, the type IA centre wavelength and chirp can be modified. Furthermore, partial grating erasure is demonstrated. This has serious implications when using type IA gratings in an optical network, as their spectrum can be modified using purely optical methods (no external heating source acts on the fibre), and to their long-term stability as the grating is shown to decay. Conversely, suitably stabilized gratings can be spectrally tailored, for tuning fibre lasers or edge filter modification in sensing applications, by purely optical means. © 2006 IOP Publishing Ltd.

Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers

In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.