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The purpose of this paper is to develop highly efficient decomposition finite difference methods for computing solutions of highly oscillatory beam propagation partial differential equations.

Highly oscillatory optical wave equations, such as the multidimensional paraxial Helmholtz equation, have been used extensively in modelling propagation of the light from lens to the focal region in various engineering applications. Numerical approximations of solutions of such equations contain crucial light information in focal regions even when the f-number is small. However, it has been difficult to acquire highly oscillatory numerical solutions efficiently. This paper proposes two correlated eikonal decomposition strategies for fast computations of the oscillatory solutions. Structures of the numerical methods are designed via an eikonal, or exponential, transformation. The approach converts successfully the oscillatory problems to non-oscillatory subproblems. Therefore, the underlying beam simulation equations can be solved readily with great accuracy and stability.

It is found that the two correlated eikonal transformation based decomposition methods effectively remove the highly oscillatory features of the wave equations. The coupled non-oscillatory subproblems resulted are easier to solve. Discretization steps in computations can be chosen to be relatively large and this ensures the efficiency of computations. The decomposed finite difference schemes are simple to use in different optical applications.

The computational approach provides a valuable tool to practical applications, such as those in the defence industry.

Although the eikonal transformation has been used in the theory of nonlinear optics, this is the first time it has been utilized for effective engineering computations.

The purpose of this paper is to present the method of lines (MOL) solution of the stimulated Brillouin scattering (SBS) equations (a system of three first-order hyperbolic partial differential equations (PDEs)), describing the three-wave interaction resulting from a coupling between light and acoustic waves. The system has complex numbers and boundary values.

System of three first-order hyperbolic PDEs are first transformed and then spatially discretized. Superbee flux limiter is proposed to offset numerical damping and dispersion, brought on by the low order approximation of spatial derivatives in the PDEs. In order to increase computational efficiency, the structured structure of the PDE Jacobian matrix is identified and a sparse integration algorithm option of the ordinary differential equation (ODE) solvers is used. The flux limiter based on higher order approximations eliminates numerical oscillation. Examples are presented, and the performance of the Matlab ODE solvers is evaluated by comparison.

This type of solution provides a rapid means of investigating SBS as a tool in fiber optic sensing.

To the best of the authors' knowledge, MOL solution is proposed for the first time for the modeling of three-wave interaction in a SBS-based fiber optic sensor.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme.

The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities.

The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients.

The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

Propagation of electromagnetic waves through InP‐based integrated optics structures is directly simulated by solving the full vectorial wave equation in parabolic approximation for the transversal components Hx and Hy of the magnetic intensity vector H. A novel scheme based on the alternating‐directions split‐step finite‐difference technique in combination with the Crank Nicolson scheme is introduced providing exact treatment of the field quantities at the dielectric interfaces between waveguide core and cladding. The method described is applied to the solution of the fundamental mode in a buried rectangular dielectric waveguide and to the numerical optimization of a tapered matching structure.

The purpose of this paper is to investigate the structural, electronic and optical properties of pure zinc oxide (ZnO) and transition metal (Tm)-doped ZnO using Tm elements from silver (Ag) and copper (Cu) by a first-principles study based on density functional theory (DFT) as implemented in the pseudo-potential plane wave in CASTEP computer code.

The calculations based on the generalized gradient approximation for Perdew-Burke-Ernzerhof for solids with Hubbard U (GGA-PBEsol+U) were performed by applying Hubbard corrections U_d = 5 eV for Zn 3d state, U_p = 9 eV for O 2p state, U_d = 6 eV for Ag 4d state and U_d = 9.5 eV for Cu 3d state. The crystal structure used in this calculation was hexagonal wurtzite ZnO with a space group of P63mc and supercell 2 × 2 × 2.

The total energy was calculated to determine the best position for Ag and Cu dopants. The band structures and density of states show that Tm-doped ZnO has a lower bandgaps value than pure ZnO because of impurity energy levels from Ag 4d and Cu 3d states. In addition, Ag-doped ZnO exhibits a remarkable enhancement in visible light absorption over pure ZnO and Cu-doped ZnO because of its lower energy region and extended wavelength spectrum.

The results of this paper are important for the basic understanding of the 3d and 4d Tm doping effect ZnO and have a wide range of applications in designing high-efficiency energy harvesting solar cells.

This paper sets out to give an overview about state‐of‐the‐art optical tomographic image reconstruction algorithms that are based on the equation of radiative transfer (ERT).

An objective function, which describes the discrepancy between measured and numerically predicted light intensity data on the tissue surface, is iteratively minimized to find the unknown spatial distribution of the optical parameters or sources. At each iteration step, the predicted partial current is calculated by a forward model for light propagation based on the ERT. The equation of radiative is solved with either finite difference or finite volume methods.

Tomographic reconstruction algorithms based on the ERT accurately recover the spatial distribution of optical tissue properties and light sources in biological tissue. These tissues either can have small geometries/large absorption coefficients, or can contain void‐like inclusions.

These image reconstruction methods can be employed in small animal imaging for monitoring blood oxygenation, in imaging of tumor growth, in molecular imaging of fluorescent and bioluminescent probes, in imaging of human finger joints for early diagnosis of rheumatoid arthritis, and in functional brain imaging.

Selective laser melting (SLM) is an advanced rapid prototyping or additive manufacturing technology that uses high power density laser to fabricate metal/alloy components with minimal geometric constraints. The SLM process is multi-physics in nature and its study requires development of complex simulation tools. The purpose of this paper is to study – for the first time, to the best of the authors’ knowledge – the electromagnetic wave interactions and thermal processes in SLM based dense powder beds under the full-wave formalism and identify prospective metal powder bed particle distributions that can substantially improve the absorption rate, SLM volumetric deposition rate and thereby the overall build time.

We present a self-consistent thermo-optical model of the laser-matter interactions pertaining to SLM. The complex electromagnetic interactions and thermal effects in the dense metal powder beds are investigated by means of full-wave finite difference simulations. The model allows for accurate simulations of the excitation of gap, bulk and surface electromagnetic resonance modes, the energy transport across the particles, time dependent local permittivity variations under the incident laser intensity, and the thermal effects (joule heating) due to electromagnetic energy dissipation.

Localized gap and surface plasmon polariton resonance effects are identified as possible mechanisms toward improved absorption in small and medium size titanium powder beds. Furthermore, the observed near homogeneous temperature distributions across the metal powders indicates fast thermalization processes and allows for development of simple analytical models to describe the dynamics of the SLM process.

To the best of the authors’ knowledge, for the first time the electromagnetic interactions and thermal processes with dense powder beds pertaining to SLM processes are investigated under full-wave formalism. Explicit description is provided for important SLM process parameters such as critical laser power density, saturation temperature and time to melt. Specific guidelines are presented for improved energy efficiency and optimization of the SLM process deposition rates.

The purpose of this paper is to discuss two‐dimensional electromagnetic diffraction by a finite set of parallel nonlinear rods (optical Kerr effect). To point out the versatility of this approach, a nonlinear (Kerr‐effect) finite crystal is considered.

In this paper, a new route for obtaining the scattered field by nonlinear obstacles is proposed. The basic idea consists in simulating the real incident field (e.g. plane waves) by a virtual field emitted by an appropriate antenna, located in a meshed domain, and encompassing or lying above the obstacles. This latest problem is then solved by a finite element method that is well suited to take into account the material inhomogeneities due to the nonlinearity of the permittivity.

The transmission through a finite Kerr crystal doped by a microcavity is given and a resonant wavelength is obtained. At this resonant wavelength, it is shown that the nonlinearity has a large influence on the behaviour of the electromagnetic wave.

Introducing the concept of virtual antenna, the paper proposes a rigorous treatment of the scattering of an electromagnetic wave by a bounded nonlinear obstacle of arbitrary shape.

The purpose of this paper is to carry out a comprehensive study of compressible flow over double wedge and biconvex airfoils using computational fluid dynamics (CFD) and three analytical models including shock and expansion wave theory, Busemann's second‐order linearized approximation and characteristic method (CHM).

Flow over double‐wedge and biconvex airfoils was investigated by the CFD technique using the Spalart‐Allmaras turbulence model for computation of the Reynolds stresses. Flow was considered compressible, two dimensional and steady. The no slip condition was applied at walls and the Sutherland law was used to calculate molecular viscosity as a function of static temperature. First‐order upwind discretization scheme was used for the convection terms. Finite‐volume method was used for the entire solution domain meshed by quadratic computational cells. Busemann's theory, shock and expansion wave technique and CHM were the analytical methods used in this work.

Static pressure, static temperature and aerodynamic coefficients of the airfoils were calculated at various angles of attack. In addition, aerodynamic coefficients of the double‐wedge airfoil were obtained at various free stream Mach numbers and thickness ratios of the airfoil. Static pressure and aerodynamic coefficients obtained from the analytical and numerical methods were in excellent agreement with average error of 1.62 percent. Variation of the static pressure normal to the walls was negligible in the numerical simulation as well as the analytical solutions. Analytical static temperature far from the walls was consistent with the numerical values with average error of 3.40 percent. However, it was not comparable to the numerical temperature at the solid walls. Therefore, analytical solutions give accurate prediction of the static pressure and the aerodynamic coefficients, however, for the static temperature; they are only reliable far from the solid surfaces. Accuracy of the analytical aerodynamic coefficients is because of accurate prediction of the static pressure which is not considerably influenced by the boundary layer. Discrepancies between analytical and numerical temperatures near the walls are because of dependency of temperature on the boundary layer and viscous heating. Low‐speed flow near walls causes transformation of the kinetic energy of the free stream into enthalpy that leads to high temperature on the solid walls; which is neglected in the analytical solutions.

This paper is useful for researchers in the area of external compressible flows. This work is original.