Daily Telegraph: A team of scientists managed to ‘tie light in knots’
Wikipedia: Optical vortex
I thought light always went in straight lines (well, geodesics anyway). Is that wrong? Can anybody here explain this to a non-physicist? (Wiki was certainly no help.) Is it something to do with interfering waves?
Short explanation:
Light, left to itself, will travel in a straight line. When passing through an interface of two media (e.g., air and glass), it will bend. Media can be shaped to produce a pattern of interfaces that will create various optical effects, including vortices.
Sure, but does it continue to twirl after it exits the medium and is travelling through (say) vacuum?
The article makes things sound more impressive than I think it really is. “light travels in straight lines” is a good explanation for most everyday optics, and is pretty much true for propagation of plane and spherical 2waves. But a better explanation of light propagation is the Huygens-Fresnel principle, in which each point on a light wave acts as a source for the further propagation of light, and that you can tell what the lihght wabve will look like further along in time or space by summing up the contributions of different parts of the wave – taking into account variations with angle and intensity and coherence. This has been pretty successful, and is the basis of Physical Optics. One striking example of this is Poisson’s Spot (or Arago’s Spot), in which a light wave blocked by a spolid sphere will show a bright spot in the center of its shadow – which is directly opposed to the idea that “light travels in straight lines”
http://www.physics.montana.edu/demonstrations/apparatus/6_optics/demos/aragosspot.html
Holograms and micro-machined and nano-constructed materials give new capabilities in these areas, which is the kind of thing they’re talking about. (Although I note that there is a guy out there making holograms by hand, using nothing more than a compass) But the familiar Gaussian beam of a laser is itself a manifestation of the Huyh=gens’'Fresnel Principle, propagating in a wavefront that is neither spherical nor plane, and which can “reach around corners” to make spots inside the geometrical shadow.
Those spot phenomena are really cool. Am I right in understanding that the circular obstacle in that experiment is doing no more than clearing a space in which the phenomenon can be clearly manifest?
i.e. it’s not just the interaction of the light grazing the obstacle that’s causing it, but a general property of light?
In the case of Poisson’s spot, the solid object is essentially blocking parts of the planar light wave that would interfere with the rest of the beam and cause the center to be dark. Because it has done that, the central space is light. So yes, you are correct, it’s really a property of the light. It doesn’t matter what the blocking object is , or what it;'s made of, or if it’s a sphere or a flat disc – it just has to be circular.
And this is a phenomenon with serious importance – I once managed to burn a hole in an optical filter because the beam had passed through a circular aperture (rather than having a circular block in front of it), which lead to a small, intense point in thne middle. I got rid of the effect by switching to a square aperture (a Poisson’s Spot experiment with a square object won;'t work – it doesn’t block the beam portions properly).
You can do better by using a collection of concentrice regions that are alternately opaque and transparent, with the properly-sized radii. And still better if you replace the opaque portions with phase-shifting transparent materials. These are examples of Waveplates. Modern waveplates can be manufactured using holographic or micro-machining to produce all sorts of interesting effects, Optical Vortices among them.
I have to admit, I haven’t read the seminal 1974 article the reference in the OP cites, and I’m not really up on vortices. I’ll have to rectify that. But i do know that, while you can “bend” light and create wavefvronts that propagate in interesting ways, you can only do so much after the light has passed the last device you use to manipulate it. I don’t think you can set up a wavefront that will propagate so that, some distance after it has left your shapetr, a major part of it will reverse direction and come back at you. (i.e. – you can’t build a true optical Tractor Beam).
Ah - you accurately predicted my next question, which was whether there is any way to elicit this phenomenon without a physical object in the frame. If it were possible, proper free-floating 3D projection would be a possibility.
I’d never come across an optical vortex before, but I do work in electromagnetics, so I’ll try to explain what they seem to be.
The most basic EM wave is the plane wave. The phase of the wave progresses in the direction of propagation, and is constant in planes perpendicular to the direction of propagation. In a laser beam, like shown in the “0” case herein the optical vortex link, the portion near the axis of the beam is similar, with the phase progressing along the axis, and with the phase slowly varying in planes perpendicular to the beam axis. The phase will vary slowly from the beam axis outward, but in any circle centered on the beam axis, the phase is constant.
In the images labeled +1 and -1, in a circle centered on the beam axis, the phase varies 360 degrees around the circle, so at the center, the amplitude must be zero, but can vary linearly with distance from that point. For the images +2 and -2, the center is still zero, but the amplitude can only vary quadratically in radius, so the center hole is better defined. Similarly, for +3 and -3 the amplitude increases cubically, so the hole is even better defined.
The phase still progresses along the axis of the beam, and those circles are probably thousands of wavelengths around, so surfaces of constant phase corkscrew around very rapidly, but the directions perpendicular to these surfaces are almost parallel to the beam axis, and spiral very slowly around the axis. So the image of light corkscrewing around the beam isn’t really accurate. I’m not convinced that the Poynting vector actually spirals around the beam axis. The energy flow may be along the beam direction, with no corkscrewing at all.
For the knot of light, it appears that they used the hologram to adjust the phase of the light from a laser so that the phase varies 360 degrees (or some multiple) around the axis of the knot, so that there’s a knot of zero field. This doesn’t mean that the light is propagating along the axis of the knot, it’s still mostly propagating in one direction (e.g. into the screen). It’s still impressive, but not quite what you may be imagining.
Well, thanks for the answers. I think I understand at least partially now. The light energy still propagates in straight lines (setting aside things such as refraction and diffraction at the edges of objects), but there can be these eddies or “corkscrewing” in the phase of the waveform, and, through interference, this can lead to these dark vortices within the light beam. Is that more or less right? And it is one of these vortices, not the light itself, that they have somehow managed to get into the form of a knot.
Is this corkscrewing phase the same as, or related to, circular polarization, or is that something completely different?
Very different.
Yes, I think that’s right. Phase and polarization are two different things, although I wouldn’t be surprised if a certain polarization was required.
They are related in one way, though: both carry angular momentum. The difference between the optical vortices and circular polarization is essentially the difference between orbital angular momentum and spin angular momentum.
For an easier-to-understand type of paraxial mode that also carries orbital angular momentum, read all about Laguerre-Gaussian modes. (Link to PDF.)