Analysis of laser radiation using the Nonlinear Fourier transform

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions

Applicability of ground penetration radar (GPR) technique to optimize soil Nail Wall designs

Soil nailing is used to stabilize existing natural slopes or excavations using soil reinforcement technique. Due to lack of information on ground profiles and thickness of soil layers, the required soil nail lengths cannot be determined in advance, for most of the steep slopes. Furthermore, the cost of drilling in fresh rock is much higher than the cost of drilling in soft soil and weathered rock. Without proper information on the depth at which the fresh rock is found, a cost-effective soil nail wall design cannot be finalized. This research was focused on studying the methods that can be used for soil nail wall design optimization by applying Ground Penetration Radar (GPR). The study was carried out on an unstable slope near Nursing Training School located in Kandy in the central part of Sri Lanka.The physical properties of soil were determined by direct shear tests, and stability analysis was done by means of “Slope-W” software. GPR techniques were also used in this study. The investigation results showed that the existing slope is unstable, and necessary to be protected. Further, it was identified that the basement rock cannot be encountered at already designed depths of the soil nails, which was subcequently proven as correctbased on data from ongoing drilling for soil nail installations. With the precise knowledge about the underground geological structure using GPR technique, the drilling cost, nail transporting cost, nail off cutting time to complete the total work can be reduced