The electric and magnetic fields of a plane electromagnetic wave are orthogonal to each other and the direction of propagation. This suggests that the maximum number of waves with the same frequency that can be superposed without any interference is three. This can be done by choosing three waves travelling in mutually orthogonal directions and choosing all three polarisations orthogonal to each other.
If one is content with only the mean square of the electric field being homogeneous without requiring that the mean square of the magnetic field also be homogeneous, larger superpositions are allowed. For many practical purposes, such superpositions can still be considered noninterfering, as it is the electric field that interacts most with matter, including fluorescent dyes, CCDs and the light-sensitive pigments in the human eye. The inhomogeneity in the magnetic field is relatively difficult to detect.
The helicity density, a quantity that indicates the handedness of the light, is in general inhomogeneous for our noninterfering superpositions. It will vary in space in a pattern that is quite often, although not necessarily, periodic and resembles the intensity variations in optical lattices. There is enough freedom left in our superpositions to allow for a large variety of helicity
Fully-structured light, light with non-uniform intensity, phase and polarization, lies at the heart of an extremely promising field of research, with applications in high-resolution imaging and optical trapping and manipulation of nanoparticles. Such fields are readily constructed from superpositions of two orthogonally polarized Laguerre-Gaussian modes carrying different orbital angular momentum (OAM). This opens new possibilities in engineering complex light distributions for specific applications.
We simulate the propagation of fully-structured light in a self-focusing nonlinear medium using a coupled two-dimensional nonlinear Schrödinger equation with saturable self-focusing nonlinearity and show that the spatial structure of the polarization can be used to control both the collapse dynamics of the beams  and the amount of polarisation rotation. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Complex light can also have non-uniform helicity density and the resultant gradients in helicity density will generate a force that will interact differently with opposite enantiomers of chiral molecules . Here we demonstrate how the energy and helicity gradients in the fields, and the corresponding dipole and chiral forces, can be engineered for specific applications. We also investigate the use of nonlinearity to control and manipulate the spatially-varying chiral force.
 F. Bouchard et al., Phys. Rev. Lett 117, 233903 (2016)
 R. Cameron et al., New J. Phys. 16, 013020 (2014)
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.
We present details on how the newly introduced technique of chiral rotational spectroscopy can be used to extract orientated information from otherwise freely rotating molecules in the gas phase. In this technique circularly polarized light is used to illuminate chiral molecules and shift their rotational levels to yield orientated chiroptical information via their rotational spectrum. This enables in particular the determination of the individual, physically relevant components of the orientated optical activity pseudotensor. Using the explicit example of (S)-propylene glycol we show how measuring the rotational spectrum of molecules in the microwave domain allows for the recording of a small set of rotational transitions from which the individual polarizability components can be determined.