From structured light to structured waves

Introductory textbooks on quantum mechanics and electromagnetism typically use plane waves, standing waves formed from a superposition of two counter-propagating plane waves, or twin slit interference to illustrate concepts such as the role of boundary conditions, phase velocity, energy transport, interference, and so on. However, these special cases actually too simple to capture the full breadth of wave physics. A nice example of this is shown in Figure 1 of the review article "Singular Optics: Optical Vortices and Polarization Singularities", which was one of my first introductions to the field:

(a) Twin slit interference results in alternating bright and dark fringes, the latter corresponding to lines of vanishing intensity. (b) In three slit interference the intensity only vanishes at points, which correspond to singularities of the field's phase in (c). Panel (d) shows a close up of a pair of oppositely-charged phase singularities.

In the 2000s and early 2010s, studies of the peculiarities of these kinds of structured wave fields were focused on optics, where the availability of devices such as spatial light modulators made phenomena associated with structured waves conveniently accessible. There is now growing interest in structured waves in other wave systems including electron beams, acoustics, water waves, and condensed matter physics. Recent developments in this direction are summarised in a Journal of Optics article, "Roadmap on structured waves," that was just published today. Thanks to Konstantin Bliokh for the invitation to contribute to this article and the mammoth effort of collating and coordinating the work of the 49 coauthors!