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

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.