Freely propagating light in the most general sense is governed by Maxwell’s equations as written in the strict absence of charge. These demand in particular that the electric and magnetic fields are divergenceless. The electromagnetic field lines must therefore extend indefinitely or else form closed loops. Solutions of the former kind, such as a single plane electromagnetic wave, are well-known. Various solutions of the second kind, such as an electromagnetic knot, are known as well, but the idea as a whole remains relatively unexplored. We will discuss these unusual electromagnetic disturbances, their creation, their dynamics and their potential applications.
Our approach is centred upon the fact that any electromagnetic field must be expressible as a superposition of plane waves. If the field is monochromatic, the tips of the wavevectors of these waves must lie on the surface of a sphere in reciprocal space. Stable closed field line configurations can then be built by distributing these wavevectors in a suitably symmetrical manner whilst choosing their polarisations appropriately. Finally, solutions of this kind but with different frequencies can be added together to yield the most general form of freely 'propagating' electromagnetic disturbance. To produce such fields in practice at long wavelengths might require little more than suitable arrangements of antennas. At shorter wavelengths one may more usefully regard the solutions as being superpositions of various vector modes.
Robert Cameron, "Unusual electromagnetic disturbances (Conference Presentation)," Proc. SPIE 10120, Complex Light and Optical Forces XI, 101200R (Presented at SPIE OPTO: February 01, 2017; Published: 28 April 2017); https://doi.org/10.1117/12.2251361.5397967367001.
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