## 2D Polygon Description

Each line describes a separate polygon. There is no limit to the number of polygons that can be entered. Each polygon descriptor starts with a flag (consisting of a few characters) followed by several numbers. The flag ends with x, y or z to account for anisotropic material properties. When x is specified, the polygon adds the incremental refractive index only to the x direction. When y is specified, the polygon adds the incremental refractive index only to the y direction. When z is specified, the same value is used for x and y (isotropic medium). Uniform Fill This function adds a uniform incremental value f to every point in space. b f Uniformly Filled Polygon This is the most generic polygon, which is described by its bounding (x,y) co-ordinates. All points inside that polygon will have an increemental value f. The syntax is: u f x1 y1 x2 y2 x3 y3 .... There is no limit to the number of bounding points to the polygon, which allows very complex shapes to be created. Note that only the points on the positive side of the x axis are considered when creating the shape. Any part of the shape that goes into the negative side will be ignored. The shape on the negative side is created as a mirror reflection of the positive side. All units are in microns. For example, the shape shown on the left would be specified by something like: u 1.0 0 1 3 2 5 -2 3 -4 0 -3 Uniformly Filled Circle / Ellipse This is similar to the uniformly filled polygon, except it outlines an ellipse (or circle) with a specified radii and center. The syntax is: c f rx ry xc yc theta1 theta2 where theta1 and theta2 are the beginning and ending angles of the circle/ellipse. These angles are measured clockwise from the positive x axis. For example, the shape shown on the left can be represented by: c 1 2 3 0 0 -90 90 The angles theta1 and theta2 can be used to construct partial ellipses, such as the one shows on the left: c 1 4 1 0 0 0 90 Parabolic Distribution This is similar to the ellipse except the values inside will be distributed parabolically as: The syntax is: p f rx ry xc yc theta1 theta2 rax ray where rx and ry are the radii along the x and y directions, xc and yc are the center coordinates of the parabola, theta1 and theta2 are the span angles as defined earlier. rax and ray are the radii of an aperture ellipse to clip off the parabolic equation. p 1 2 4 0 0 -90 90 2 4 would describe the shape shown on the left. The aperture function can be used to clip off the parabolic distribution. For example: p 1 2 4 0 0 -90 90 2 2 would describe the shape shown on the left. Additionally, the angles can be used to create partial traces of the parabolic distributions. For example: p 1 2 4 0 0 -45 90 2 2 would describe the shape shown on the left. Gaussian Distribution This will describe a gaussian distribution using the equation The syntax is g f rx ry xc yc theta1 theta2 rax ray The same aperture function is described by rax and ray. For example: g 1 3 4 0 0 -90 90 5 5 would describe the shape shown on the left.

## SUMMARY

 Distribution Syntax Uniform Fill b f Uniform Polygon u f x1 y1 x2 y2 x3 y3 .... Uniformly Filled Circle / Ellipse c f rx ry xc yc theta1 theta2 rax ray Parabolic Distribution p f rx ry xc yc theta1 theta2 rax ray Gaussian Distribution g f rx ry xc yc theta1 theta2 rax ray