In a previous post (http://wp.me/p2IwTC-5Q) I discussed the possibility of a cloaking device in the context of Klingon space ships, etc, but since that post there has been some activity on the scientific front, not so much with ships, but somewhat smaller “cloaks”. Perhaps one of the more spectacular, at least from the publicity status, was from Choi and Howell ( http://arxiv.org/abs/1409.4705 ) who demonstrated paraxial (small-angle) ray optical cloaking. They start by defining an ideal cloaking device, thus it should have sufficient volume in which to hide the object, and it should act the same way if it were not there. The device should behave as if its space were replaced by the surrounding medium and the ray angles exiting the device should be the same as it would be if the space were empty. These conditions permit the image of whatever is behind the object to be exactly the same as if the object were not there. If we accept that as the definition of a “cloak”, then the science of optics apparently allows some progress, and what I find surprising is they have already been demonstrated for some time, but we don’t think of them that way.
What Choi and Howell then do is to take the relationships of lenses that were defined by Newton and represent these conditions for a series of lenses in matrix form, replace the terms with physical conditions defined by the lenses, and then solve to determine whether the appropriate matrix is possible. This is an excellent simple example of deductive reasoning. We know the conditions required for the matrices and so we can work out the exact requirements of the simplest device, which in this case is four lenses appropriately placed. What that means is that light from an object has to pass through all four lenses for a coherent image to eventuate. Anything less, and no image is obtained. Accordingly, anything inserted in this cloaking device is invisible because light from it cannot go through the required number of lenses hence it is dissipated. The important point is not that light from the object ceases to exist, but rather that it cannot form an image. The paper has a photo of a demonstration, in which a hand is inserted into the device, and no image of it can be seen through the lens, while the background is represented uninterrupted. Check the images now by following the link, and see if you notice something before reading further on this post.
To understand this better, it might be worth recalling another example of invisibility: the Newtonian reflecting telescope. How this works is there is a long tube and a suitable (spherical or parabolic) mirror that reflects the light back to a mirror held in the centre of the tube at an appropriate distance, which reflects the light to a lens located outside the tube. The invisibility lies in the fact that the mirror assembly inside and near the top of the tube is not seen. The reason lies in the fact that any part of the primary mirror sends information of the whole image, and hence there is no “shadow” of the second mirror. The primary mirror does not have to be one mirror, although it is usually much easier to focus if it is, and the Cassegrainian telescope reflects the light back through a hole in the centre of the primary mirror. (For diagrams that show the light paths, see http://en.wikipedia.org/wiki/Reflecting_telescope#The_Cassegrain_design_and_its_variations )
If we think about this, the trick for the “four-lens” cloaking is that it is important that enough light from the background get through the four lenses. If the intervening object were the size of the lenses, you would see nothing that was coherent because no light can get through the cylinder defined by the layout of the lenses. In this context, in the images in the paper, you will notice that the continuations of the fingers (that which is cloaked) are near the edges of the cylinder of the device. This no doubt assists getting the most light from the background image through the device. There have been similar tricks with mirrors and lighting carried out by stage magicians, with varying degrees of effectiveness. The stage magician has the advantage that nobody looks too closely, the effect is a oncer, and the audience is some distance away, nevertheless they also have difficulties because they have to deal with wider angles than those resulting from parallel rays through four lenses. If you see something like this, though, you can be sure the background will be well-lit, to ensure plenty of the light you want seen is available.
It takes little imagination, though, to see that the four-lens trick is not exactly suitable as it stands for cloaking a space ship. Nevertheless, the demonstration is impressive, as can be seen by clicking on the link and scrolling down to the examples.