Comparison of numerical methods for light propagating in fibers with high steps of refractive index

2012 ◽  
Vol 20 (1) ◽  
Author(s):  
K. Zegadło ◽  
M. Karpierz
Keyword(s):  
Refractive Index ◽  
Numerical Methods ◽  
Light Propagation ◽  
Chromatic Dispersion ◽  
Three Dimensional ◽  
Complex Structures ◽  
Two Dimensional ◽  
Approximate Methods ◽  
Fast Development ◽  
Numerical Tools

AbstractFast development of complex structures like microstructural fibers, photonic nanowires or slot waveguides requires numerical tools to predict a light propagation. There are many works concerning weakly guided case, but the microstructural fibers need algorithm for a high step of the refractive index. In this paper, three approximate methods are compared. The comparison concerns a structure consisting of circular cores surrounded by cladding for different values of the refractive index steps. Application of these methods in chromatic dispersion case is also presented. It is shown that certain conditions prefer two dimensional scalar algorithms (based on approximated methods) than three dimensional ones. This allows us to implement more efficient and less complicated methods.

Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
W. Wayne Chen ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Fourier Transform ◽  
Numerical Methods ◽  
Fast Fourier Transform ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Response Functions ◽  
Strain Fields ◽  
Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

scholarly journals DIMENSION REDUCTION USING THE INVERSE STAMPING METHOD

2021 ◽  
Vol 2021 (4) ◽  
pp. 4810-4817
Author(s):  
JAROMIR KASPAR ◽  
◽  
MARCEL SVAGR ◽  
PETR BERNARDIN ◽  
VACLAVA LASOVA ◽  
...  
Keyword(s):  
Graph Theory ◽  
Dimension Reduction ◽  
Automotive Industry ◽  
Three Dimensional ◽  
Stochastic Methods ◽  
Complex Structures ◽  
Two Dimensional ◽  
Crucial Step ◽  
Development Tool ◽  
Wide Range

The aim of this work is to improve the inverse stamping method and increase its robustness. The first, crucial step of inverse stamping is the reduction of the three-dimensional part into a two-dimensional flat plane. There are several methods for reducing the dimension. These are geometrical methods, methods based on graph theory and stochastic methods. We examine the last two methods because of their reliability. These methods can even be used for geometrically complex structures which include holes, hooks and walls perpendicular to the flat plane. An algorithm which combines several methods for dimension reduction is proposed for use for a wide range of parts. Deep drawing is a widely used technology in the automotive industry and inverse stamping is a useful development tool.

scholarly journals Design of highly-efficient acoustic waveguide couplers using impedance-tunable transformation acoustics

2020 ◽  
Vol 34 (32) ◽  
pp. 2050250
Author(s):  
Jun Cao ◽  
Fenghua Qi ◽  
Senlin Yan ◽  
Lifa Zhang
Keyword(s):  
Refractive Index ◽  
Impedance Matching ◽  
Coupling Efficiency ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Low Frequencies ◽  
Acoustic Waveguide ◽  
Acoustic Coupling ◽  
Transformation Medium ◽  
Transformation Acoustics

In this paper, the theory of impedance-tunable transformation acoustics in the geometric-acoustics limit is proposed to design efficient two-dimensional acoustic waveguide couplers. By choosing suitable impedance functions in the original space, impedance matching between the transformation medium and the background medium becomes possible, and the reflection at the boundary is reduced. The theory can be used to enable efficient acoustic coupling between waveguides of different sizes and different embedded media. By selecting an appropriate impedance function and a tunable acoustic refractive index, the transformed medium in the coupler can become a simplified parameter medium, for which the bulk modulus is a constant. This makes the experiment substantially easier. The problem of a reduced coupling-efficiency at low frequencies (a deviation from the geometric acoustic approximation) can be mitigated by selecting a large acoustic refractive index. Our two-dimensional numerical simulations indicate that this theoretical design works very well. The method can be extended to other transformation acoustic designs including three-dimensional cases.

scholarly journals Femtosecond Laser Micromachining of Fabry-Pérot Interferometers for Magnetic Field Sensing

2019 ◽  
Vol 215 ◽  
pp. 13001 ◽  
Author(s):  
João M. Maia ◽  
Vítor A. Amorim ◽  
Duarte Viveiros ◽  
P. V. S. Marques
Keyword(s):  
Magnetic Field ◽  
Refractive Index ◽  
Optical Waveguides ◽  
Light Propagation ◽  
Three Dimensional ◽  
Laser Micromachining ◽  
Fused Silica ◽  
Microfluidic Channels ◽  
Focal Volume ◽  
Fabry Perot

Fs-laser micromachining is a high precision fabrication technique that can be used to write novel three-dimensional structures, depending on the nature of light-matter interaction. In fused silica, the material modification can lead to (i) an increase of the refractive index around the focal volume, resulting in the formation of optical circuits, or (ii) an enhancement of the etch rate of the laser-affected zones relative to the pristine material, leading to a selective and anisotropic etching reaction that enables fabrication of microfluidic systems. Here, both effects are combined to fabricate a Fabry-Pérot interferometer, where optical waveguides and microfluidic channels are integrated monolithically in a fused silica chip. By filling the channel with a magnetic fluid whose refractive index changes with an external magnetic field, the device can be used as a magnetic field sensor. A linear sensitivity of -0.12 nm/mT is obtained in the 5.0±0.5 to 33.0±0.5 mT range, with the field being applied parallel to the light propagation direction.

Two- and three-Dimensional Refractive Index Lattices Formed by Laterally Patterned Porous Silicon Layers

1999 ◽  
Vol 597 ◽  
Author(s):  
S. Uehara ◽  
H. Sasabu ◽  
K Taira ◽  
T. Hashimoto ◽  
T. Matsubara
Keyword(s):  
Refractive Index ◽  
Porous Silicon ◽  
Three Dimensional ◽  
Index Structure ◽  
Two Dimensional ◽  
Cladding Layer ◽  
Anodization Process ◽  
N Doping ◽  
Index Contrast ◽  
P Type

AbstractPorous silicon was used to fabricate refractive index lattices. Patterned n-doping and/ or substrate etching were used to introduce lateral periodicity. By anodizing p-type substrate with an n-doped area, we realized large refractive index contrast two-dimensional lattices with underlying cladding layer. The anodization process showed an effect specific to the small dimensional patterning and this effect has significant influence on the formed refractive index structure.

Particle Transport via Three-Dimensional Chaotic Advection to Produce Electrically Conducting Plastics With Powder Additives

1999 ◽  
Author(s):  
R. I. Danescu ◽  
D. A. Zumbrunnen
Keyword(s):  
Carbon Black ◽  
Three Dimensional ◽  
Chaotic Advection ◽  
Chaotic Mixing ◽  
Complex Structures ◽  
Two Dimensional ◽  
Electrical Measurements ◽  
Electrically Conducting ◽  
Scale Structures ◽  
Large Clusters

Abstract Extended micron-scale structures were produced in thermoplastic melts from initially large clusters of conducting carbon black particles transported by three-dimensional chaotic mixing. The structures formed networks that were captured by solidification and rendered the composite materials electrically conducting. A systematic study was carried out to assess the influence of key parameters and relate the electrical properties to the microstructures. Micrographs showed complex structures exhibiting patterns characteristic of chaos. Electrical measurements indicated that conductivity was achieved at carbon black concentrations significantly lower than achievable by common mixing methods, and lower than reported recently for two-dimensional chaotic mixing.

scholarly journals Equatorial spread F studies using SAMI3 with two-dimensional and three-dimensional electrostatics

2013 ◽  
Vol 31 (12) ◽  
pp. 2157-2162 ◽  
Author(s):  
H. C. Aveiro ◽  
J. D. Huba
Keyword(s):  
Three Dimensional ◽  
Complex Structures ◽  
Two Dimensional ◽  
Plasma Velocity ◽  
Potential Solution ◽  
Parallel Electric Field ◽  
F Region ◽  
Spread F ◽  
Rayleigh Taylor Instability ◽  
D Model

Abstract. This letter presents a study of equatorial F region irregularities using the NRL SAMI3/ESF model, comparing results using a two-dimensional (2-D) and a three-dimensional (3-D) electrostatic potential solution. For the 3-D potential solution, two cases are considered for parallel plasma transport: (1) transport based on the parallel ambipolar field, and (2) transport based on the parallel electric field. The results show that the growth rate of the generalized Rayleigh–Taylor instability is not affected by the choice of the potential solution. However, differences are observed in the structures of the irregularities between the 2-D and 3-D solutions. Additionally, the plasma velocity along the geomagnetic field computed using the full 3-D solution shows complex structures that are not captured by the simplified model. This points out that only the full 3-D model is able to fully capture the complex physics of the equatorial F region.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

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