What is/are Singular Optics?

This maybe should have been the first post, but I thought if this were the first post it would set a rather more serious tone than I would like for this blog.

I mentioned in my first post that I'm doing theoretical physics, specifically singular optics, but I didn't really say what that was. Partly because it didn't seem needed, and partially because I don't like trying to explain what I research since I don't fully understand what my field encompasses. Somewhat tautologically, the field of singular optics studies optical fields that display singularities. Since pretty much everytime I say I am studying optics people ask, "So, eyeglasses...?" I think its safe to say each of those terms could use some defining.  

The general study of optics covers a section of the electromagnetic spectrum that is centered around the visible range. These days it also covers light a little above and below the visible portion, namely ultraviolet (UV) and infrared (IR) radiation. In a sense, optics is very, very old. There is evidence to suggest that the Ancient Egyptians and Mesopotamians used lenses. The oldest known 'lens'  is the Nimrud lens from ancient Assyria, which may have been used as a magnifying glass or to light fires. The contemporary study of optics in some part can be traced to Newton who did a great deal of work with prisms, but optics really could not take off beyond what is now known as geometrical optics until James Clark Maxwell codified existing theories of electromagnetism into Maxwell's equations. This so called 'classical electromagnetism' describes the behavior of light even into the realm of relativity (it is in fact inherently relativistic), but not on the quantum level (you need quantum optics for that). While Maxwell's equations cover the whole of the electromagnetic spectrum, from gamma rays to x-rays to microwaves to radiowaves, 'optics' is considered to only cover a tiny section of that spectrum--the light we can see and the 'colors' just beyond what we can see.

From xkcd.com

The concept of singularities is essentially mathematical, though it has an obvious physical representation. If something is 'singular', that usually means that it is either a) going to plus/minus infinity b) some part of it has gone to zero, making another part undefined.  From the omniscient Wikipedia, "In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability." Singularity is the point where the mathematical equivalent of "Monty Python's" The Colonel declares that everything is getting too silly and to get on with it. There is always something weird, and to certain deranged minds like mine, cool about ill behaved math/physics. The obvious and most well known example of a singularity is a black hole. Everything breaks down  inside a black hole--no one really knows what goes on inside those things other than seemingly infinite gravity and time dilation. 

Singular optics is not quite as dramatic as a black hole. I doubt anyone will be making computer skins depicting singular optical phenomena who isn't directly involved in it in some way. Dr Skull over at "Skulls in the Stars" explains it far better than I can, with really cool pictures. Basically, it boils down to this. Light is made up of waves (try to forget about photons for a moment). Waves have an amplitude and a phase. Think of an ocean wave. Amplitude would describe how high above the surface the wave gets, while phase would describe a point along the wave. We tend to think of this as nice, well behaved math and physics. Sines and cosines are easy. The weirdness comes in if you have two waves that are interfering with each other. Sometimes they cancel each other out and sometimes they double up. When they double up, they are still well behaved, which is to say that they have a well defined amplitude and phase. When they cancel each other out though, you have no amplitude, and the phase is undefined. This is the singularity with which this branch of optics deals. Where the phase is undefined, it takes on all possible phase values at once. Which seems like utter nonsense, but it turns out to be very, very useful. 

How on earth is this useful? Well, one of the nice things about these singularities is that they create what are known as optical vortices. The light goes around in circles in some sense. Two things are nice about this. One, is that the vortices carry angular momentum, which can be used to rotate things, say microscopic objects held by optical tweezers. Another is that these vortices remain stable under perturbation. They will still go clockwise or counterclockwise, for example, when you send them through a lens or some sort of perturbing medium. In theory, you could use this property to send data optically (i.e., a right-handed vortex = 0, a left handed vortex = 1 for computer bits), perhaps even through free space. There are probably many other applications we just haven't thought of yet because this subfield is only about 40 years old, and lasers are only now becoming relatively cheap. 

I am only just starting my research in this field and really only just starting to understand what it all means. I'm sure in a year I am going to reread this blog post and cringe at my pathetic understanding of my own chosen field, but you have to start somewhere. So here it is, my first baby steps of understanding. 

Cheers!