On the propagation of vector ultra-short pulses

A two component vector generalization of the Schäfer-Wayne short pulse equation which describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization is presented. As a special case, the integrable two-component short pulse equations are constructed which represent the counterpart of the Manakov system in the case of ultra-short pulses

Effect of higher-order dispersion on modulation instability, soliton propagation and pulse splitting

By solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in highly nonlinear fibers. In the anomalous dispersion regime third-order dispersion can, in general, induce soliton fission and yields asymmetric spectra, whereas modulation instability can be slightly suppressed. In the normal dispersion regime we demonstrate pulse splitting by third-order dispersion, as well as its later suppression by fourth-order dispersion

3D Polarized Light Imaging Portrayed: Visualization of Fiber Architecture Derived from 3D-PLI

3D polarized light imaging (3D-PLI) is a neuroimaging technique that has recently opened up new avenues to study the complex architecture of nerve fibers in postmortem brains at microscopic scales. In a specific voxel-based analysis, each voxel is assigned a single 3D fiber orientation vector. This leads to comprehensive 3D vector fields. In order to inspect and analyze such high-resolution fiber orientation vector field, also in combination with complementary microscopy measurements, appropriate visualization techniques are essential to overcome several challenges, such as the massive data sizes, the large amount of both unique and redundant information at different scales, or the occlusion issues of inner structures by outer layers. Here, we introduce a comprehensive software tool that is able to visualize all information of a typical 3D-PLI dataset in an adequate and sophisticated manner. This includes the visualization of (i) anatomic structural and fiber architectonic data in one representation, (ii) a large-scale fiber orientation vector field, and (iii) a clustered version of the field. Alignment of a 3D-PLI dataset to an appropriate brain atlas provides expert-based delineation, segmentation, and, ultimately, visualization of selected anatomical structures. By means of these techniques, a detailed analysis of the complex fiber architecture in 3D is feasible

Towards Ultra-High Resolution Fibre Tract Mapping of the Human Brain – Registration of Polarised Light Images and Reorientation of Fibre Vectors

Polarised light imaging (PLI) utilises the birefringence of the myelin sheaths in order to visualise the orientation of nerve fibres in microtome sections of adult human post-mortem brains at ultra-high spatial resolution. The preparation of post-mortem brains for PLI involves fixation, freezing and cutting into 100-μm-thick sections. Hence, geometrical distortions of histological sections are inevitable and have to be removed for 3D reconstruction and subsequent fibre tracking. We here present a processing pipeline for 3D reconstruction of these sections using PLI derived multimodal images of post-mortem brains. Blockface images of the brains were obtained during cutting; they serve as reference data for alignment and elimination of distortion artefacts. In addition to the spatial image transformation, fibre orientation vectors were reoriented using the transformation fields, which consider both affine and subsequent non-linear registration. The application of this registration and reorientation approach results in a smooth fibre vector field, which reflects brain morphology. PLI combined with 3D reconstruction and fibre tracking is a powerful tool for human brain mapping. It can also serve as an independent method for evaluating in vivo fibre tractography

On the propagation of vector ultra short pulses,

Abstract A two component vector generalization of the Schäfer-Wayne short pulse equation is derived. It describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization. We show that in a special case this system gives rise to three different integrable two-component short pulse equations which represent the counterpart of the Manakov system in the case of ultra-short pulses

A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI

Structural connectivity of the brain can be conceptionalized as a multiscale organization. The present study is built on 3D-Polarized Light Imaging (3D-PLI), a neuroimaging technique targeting the reconstruction of nerve fiber orientations and therefore contributing to the analysis of brain connectivity. Spatial orientations of the fibers are derived from birefringence measurements of unstained histological sections that are interpreted by means of a voxel-based analysis. This implies that a single fiber orientation vector is obtained for each voxel, which reflects the net effect of all comprised fibers. We have utilized two polarimetric setups providing an object space resolution of 1.3 μm/px (microscopic setup) and 64 μm/px (macroscopic setup) to carry out 3D-PLI and retrieve fiber orientations of the same tissue samples, but at complementary voxel sizes (i.e., scales). The present study identifies the main sources which cause a discrepancy of the measured fiber orientations observed when measuring the same sample with the two polarimetric systems. As such sources the differing optical resolutions and diverging retardances of the implemented waveplates were identified. A methodology was implemented that enables the compensation of measured different systems' responses to the same birefringent sample. This opens up new ways to conduct multiscale analysis in brains by means of 3D-PLI and to provide a reliable basis for the transition between different scales of the nerve fiber architecture

On the propagation of vector ultra-short pulses

A two component vector generalization of the Schäfer-Wayne short pulse equation which describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization is presented. As a special case, the integrable two-component short pulse equations are constructed which represent the counterpart of the Manakov system in the case of ultra-short pulses

Effect of higher-order dispersion on modulation instability, soliton propagation and pulse splitting

By solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in highly nonlinear fibers. In the anomalous dispersion regime third-order dispersion can, in general, induce soliton fission and yields asymmetric spectra, whereas modulation instability can be slightly suppressed. In the normal dispersion regime we demonstrate pulse splitting by third-order dispersion, as well as its later suppression by fourth-order dispersion

Effects of higher-order dispersion on pulse splitting in the normal dispersion regime

By solving numerically the extended nonlinear Schrödinger equation we investigate the influence of higher-order dispersion effects on the propagation of optical pulses in the normal dispersion regime in a highly nonlinear fiber. Already a small amount of third-order dispersion can lead to a pulse-breakup above a certain pulse power. The splitting is followed by an expansion of the spectrum towards longer wavelengths without any impact of Raman scattering. The transfer of energy to longer wavelengths strongly depends on the dispersion profile of the fiber