Electromagnetic waves can have their momentum be defined by two independently varying factors, those being spin angular momentum and orbital angular momentum. Spin angular momentum is just a fancy way of saying polarisation, which is all about the direction the electric field oscillates, but the other, orbital angular momentum, is a bit harder to explain. Orbital angular momentum is about the distribution of the electric field over the beam, in a way the “shape” of the light beam. The most well defined orbital angular momentums are in helical beams as shown below:
The interesting thing is that it is has recently been shown to be possible to produce light beams that do not have an integer value for their orbital angular momentum. This is almost heretical to quantum physics as on the quantum scale, such as a single photon in this case, everything should come in integer numbers such as energy or momentum. Although the exact reason for the existence of these faction momentum beams will remain a mystery for a bit longer there have been many uses found for them. Optical communications can make use of them as well as material processing, imaging and experimental optical trapping.
The main method of producing these beams is conical refraction through a biaxial crystal (biaxial referring to the fact the crystal has two optical axis where light propagation is normal parallel to these and for any other angle the beam is split into two polarised parts). The problem comes from the fact that these crystals are only transparent for a range of 400 nm to 3000 nm and so cut out many possible uses of these fractional momentum beams. Researchers have luckily found a solution using a process called high-order harmonic generation. This is where an atom is ionised with a laser only to have the released electron be forced back towards it so that during recombination X-rays are produced. Due to the highly coherent nature of the driving laser with the X-rays produced it was shown that if the light that causes the ionisation is produced from the conical refraction method and therefore has partial momentum the produced X-ray also demonstrates a fractional orbital momentum. This opens up the application of fractional momentum beams as a much greater range of light frequencies can now be accessed through this method.
Paper links: Extreme Ultraviolet Fractional Orbital Angular Momentum Beams from High Harmonic Generation