Multidimensional optical singularities and their applications

Optical singularities are positions in an electromagnetic field in which a parameter such as phase or polarization becomes undefined. These singularities confine light tightly and surround it with steep field gradients, properties now exploited in super-resolution microscopy, sensing and communication. The features themselves have been catalogued for decades under an expanding and partially inconsistent nomenclature. This proliferation of names obscures how few field parameters can be singular and can make it hard to design a singularity. This Review presents an application-driven and mathematically accessible framework in which any singular field reduces to a finite set of fundamental, generic singularities. The robustness of these singularities against small perturbations follows from a topology set by the dimensions of the spaces in which they are defined. We examine forward and inverse methods for designing both stable and unstable singularities, survey their uses across disciplines and consider how higher-dimensional singularities might be reached.