Convex and concave lenses form the basis of Ray optics. Convex lens converges the light rays and concave lenses diverge the light rays. But how does the wave picture of light rays look? This post is dedicated to design your own lens of different radii and shape and study its property in MEEP FDTD.
(note: I'm assuming you have basic knowledge about MEEP FDTD. If not, you can first see some of my previous posts about MEEP(http://blog.vikramank.com/tag/meep/). In any case if you are stuck, feel free to contact me!)
The shape of convex lens is the common region of two intersecting circles. But it is impossible to create the shape directly. The only option is to follow this method (http://blog.vikramank.com/2014/12/creating-structures-meep-fdtd/) . Convex lenses are characterized by radius of both sides, and refractive index. The trick here is, chose the center of respective circles, and define the points in the intersection. You can select the points with the help of polar coordinates. After defining them convert them to Cartesian coordinates in terms of radius, sine and cosine. Now that you have your points, go ahead and create your structure and run your simulation. In your simulation units, its better to chose your unit as centimeters.
Concave lens is relatively very easy. Describe 3 structures. Two non intersecting circles and a rectangular block in between. Define the refractive index of the lens in the block and air for the circles. (Note: Define the block first, followed by the circles). You have your desired lens. In my simulation, I have changed the property of the source, so that maximum amount of light travels along the axis of the lens, in order to observe a good diverging effect.