Propagation of Vortex Hermite-Cosh-Gaussian Beams in a Gradient-Index Medium

Based on the Huygens–Fresnel integral, the propagation equation for a vortex Hermite-cosh-Gaussian beams (vHChGB) in gradient-index medium (GIM) is derived. From the obtained expression, the evolution of the intensity and the phase distributions of a vHChGB through a GIM are numerically demonstrated as a function of the gradient-index parameter β under the change of incident beam parameters. The results show that the characteristics of the output beam evolve periodically versus the propagation distance, and the period of evolution slows down when β is increased. Furthermore, it is demonstrated that the self-repeating properties of the intensity pattern and the phase distribution for the propagated vHChGB are altered by the incident beam parameters. The results obtained may be beneficial for applications in fiber communications and beam shaping.

The Behavior of Electromagnetic Wave Propagation in Photonic Crystals with or without a Defect

In this study, the electromagnetic wave propagation behavior of two-dimensional photonic crystal plates with a defect is investigated. For this purpose, the partial differential equation for the electromagnetic wave propagation in various photonic crystal plates containing a defect or not is obtained by using Maxwell’s equations. The defect is also defined in the electromagnetic wave propagation equation appropriately. In order to solve the electromagnetic wave propagation equation, the finite differences method is used. The material property parameters of the photonic crystal plates are determined with respect to the defects. Accordingly, the effects of material property parameters on electromagnetic wave propagation frequencies, phase velocities, and group velocities are examined. The effects of the size and position of the defects on the electromagnetic wave propagation frequencies are also discussed. The highest electromagnetic wave propagation fundamental frequency value obtained from the analyses performed is 1.198 Hz. This fundamental frequency value is obtained for the electromagnetic wave propagation in the t-shaped photonic crystal plate. Electromagnetic field distribution maps for the fundamental frequencies of the photonic crystal plates whose electromagnetic wave propagation behaviors are examined are obtained with the ANSYS package program based on the finite differences time-domain (FDTD) method.

Benchmarking of the Split-Step Fourier Method on Solving a Soliton Propagation Equation in a Nonlinear Optical Medium

Benchmarking of the numerical split-step Fourier method in solving a soliton propagation equation in a nonlinear optical medium is considered. This study is carried out by comparing the solutions calculated by numerics with those obtained by analytics. In particular, the soliton propagation equation used as the object of observation is the nonlinear Schrödinger (NLS) equation, which describes optical solitons in optical fiber. By using the split-step Fourier method, we show that the split-step Fourier method is accurate. We also confirm that the nonlinear and dispersion parameters of the optical fiber influence the soliton propagation.

Dental Amalgam Influence on the Amount of Absorbed Energy from Mobile Phone

The topic of the research presented in this paper is numerical calculation and analysis of the electric field and Specific Absorption Rate (SAR) distributions in the vicinity of dental amalgam exposed to the radiation of mobile phone at the frequencies corresponding to 3G and 4G mobile networks. This is carried out by numerical solving of the electromagnetic propagation equation. The results related to different tissues and organs placed in the vicinity of dental amalgam and exposed to radiation are presented and analysed. In order to obtain the most accurate results, the realistic 3D model of human jaw has been created. A comparative analysis of models with and without dental amalgam has been carried out, with aim to determine the impact of amalgam on biological tissues in its vicinity. According to the obtained results, the maximum values of electric field strength and SAR are higher in the presence of dental amalgam. In both cases, maximum values are out of bounds of safety limits.

Asynchronous computations for solving the acoustic wave propagation equation

The aim of this study is to design and implement an asynchronous computational scheme for solving the acoustic wave propagation equation with absorbing boundary conditions (ABCs) in the context of seismic imaging applications. While the convolutional perfectly matched layer (CPML) is typically used for ABCs in the oil and gas industry, its formulation further stresses memory accesses and decreases the arithmetic intensity at the physical domain boundaries. The challenges with CPML are twofold: (1) the strong, inherent data dependencies imposed on the explicit time-stepping scheme render asynchronous time integration cumbersome and (2) the idle time is further exacerbated by the load imbalance introduced among processing units. In fact, the CPML formulation of the ABCs requires expensive synchronization points, which may hinder the parallel performance of the overall asynchronous time integration. In particular, when deployed in conjunction with the multicore-optimized wavefront diamond temporal blocking (MWD-TB) approach for the inner domain points, it results in a major performance slow down. To relax CPML’s synchrony and mitigate the resulting load imbalance, we embed CPML’s calculation into MWD-TB’s inner loop and carry on the time integration with fine-grained computations in an asynchronous, holistic way. This comes at the price of storing transient results to alleviate dependencies from critical data hazards while maintaining the numerical accuracy of the original scheme. Performance and scalability results on various x86 architectures demonstrate the superiority of MWD-TB with CPML support against the standard spatial blocking on various grid sizes. To our knowledge, this is the first practical study that highlights the consolidation of CPML ABCs with asynchronous temporal blocking stencil computations.

Asymmetric hypergeometric laser beams

Here we study asymmetric Kummer beams (aK-beams) with their scalar complex amplitude being proportional to the Kummer function (a degenerate hypergeometric function). These beams are an exact solution of the paraxial propagation equation (Schrödinger-type equation) and obtained from the conventional symmetric hypergeometric beams by a complex shift of the transverse coordinates. On propagation, the aK-beams change their intensity weakly and rotate around the optical axis. These beams are an example of vortex laser beams with a fractional orbital angular momentum (OAM), which depends on four parameters: the vortex topological charge, the shift magnitude, the logarithmic axicon parameter and the degree of the radial factor. Changing these parameters, it is possible to control the beam OAM, either continuously increasing or decreasing it.

Pulse-Propagation Modeling and Experiment for Femtosecond-Laser Writing of Waveguide in Nd:YAG

In this work, unidirectional pulse propagation equation (UPPE) modeling is performed to study the nonlinear laser-mater interaction in silicon and Nd:Y3Al5O12 (Nd:YAG) crystals. The simulation results are validated with reported experimental results for silicon and applied to Nd:YAG crystals with experimental validation. Stress-induced waveguides are written in Nd:YAG crystals using 515 nm, 300 fs pulses at a 1 kHz repetition rate. Waveguides having a mean propagation loss of 0.21 ± 0.06 dB/cm are obtained, which is lower than the previous reported values for Type-II waveguides written in Nd:YAG crystals. The modeling and experimental results consistently show that the modification (waveguide track) depth increases with input energy. A detailed analysis is presented to control the modal properties of the waveguide in the context of UPPE simulation.