A Coordinate Transformation Method based on the Random Variable for Showing the Optical Properties

Authors

  • Jiang Xing-fang School of Mathematics and Physics, Changzhou University, China State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou, China
  • Li Xin-lu School of Mathematics and Physics, Changzhou University, China
  • Kong Xiang-min School of Mathematics and Physics, Changzhou University, China
  • Huang Shuang School of Mathematics and Physics, Changzhou University, China State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou, China

DOI:

https://doi.org/10.14738/tmlai.42.1811

Keywords:

Cloaking material, Coordinate transformation, Projection

Abstract

A coordinate transformation method of square projection circular with random various has been proposed for the optical properties of the cloaking material. The square produced randomly is projected to the circle and all the points in the perfectly matched layer are transformed. The perfectly matched layer is between the produced square and the border of the square. The first kind transformation has three steps. The first step is that the square grids are produced. The second step is the lattice grids are transformed. The third step is that the lattice grids and those transformed lattice grids are shown. The second kind transformation has four steps. The first step is that the ray came through the center point is assumed. The second step is that the 10 points each ray in the perfectly matched layer are produced randomly. The third step is the 10 points each ray are transformed. The fourth step is that the 10 points each ray and those transformed points are shown. The results show that the transformed results are nothing to do with the position of the randomly produced square. The transformation method is suit for the research of the optical properties in cloaking material.

References

(1) J. B. Pendry, D. Schurig, D. R. Smith. Controlling electromagnetic fields [J]. Science. 2006, 312:1780-1782

(2) Ulf Leonhardt. Optical conformal mapping and dielectric invisibility devices [J]. Science. 2006, 312: 1777-1780

(3) Adrian Cho. High-tech materials could render objects invisible [J]. Science. 2006, 312: 1120

(4) Raimond Grimberg. Electromagnetic metamaterials [J]. Materials Science and Engineering B. 2013, 178: 1285-1295

(5) Jaeyub Hyun, Junghwan Kook, Semyung Wang. Efficient and stable model reduction scheme for the numerical simulation of broadband axoustic metamaterials [J]. Computers and Mathematics with Application. 2015, 69: 876-892

(6) D. Schurig, J. J. Mock, B. J. Justice, et al. Metamaterial electromagnetic cloak at microwave frequencies [J]. Science. 2006, 314: 977-980

(7) Ozlem Ozgun, Mustafa Kuzuoglu. Monte Carlo simulations of Helmholtz scattering from randomly positioned array of scatters by utilizing coordinate transformations in finite element method [J]. Wave Motion.2015, 56: 165-182

(8) Archana Rajput, Kumar vaibhav Srivastava. Dispersion study on scattering cross section of metamaterial cloak due to various cloaking parameters [J]. Optik. 2015, 126: 2362-2367

(9) ZiyuWang, WeiWei, NiHu, et al. Manipulation of elastic waves by zero index metamaterials [J]. Journal of Application Physics. 2014, 116; 204501,1-5

(10) Ozlem Ozgun, Mustafa Kuzuoglu. Electromagnetic metamorphosis: reshaping scatters via conformal anisotropic metamaterial coatings [J]. Microwave and Optical Technology Letters. 2007, 49: 2386-2392

Downloads

Published

2016-05-01

How to Cite

Xing-fang, J., Xin-lu, L., Xiang-min, K., & Shuang, H. (2016). A Coordinate Transformation Method based on the Random Variable for Showing the Optical Properties. Transactions on Machine Learning and Artificial Intelligence, 4(2), 01. https://doi.org/10.14738/tmlai.42.1811