Next-generation interferometry with gauge-invariant linear optical scatterers

Measurement technology employing optical interference phenomena such as a fringe pattern or frequency shift has been evolving for more than a century. The systems are being designed better, and their components are being built better. But the major components themselves hardly change. Most modern interferometers rely on the same conventional set of components to separate the electromagnetic field into multiple beams, such as plate optics and beam-splitters. This naturally limits the design scope and thus the potential applicability and performance. However, recent investigations suggest that incorporating novel, higher-dimensional linear-optical splitters in interferometer design can lead to several improvements. In this work, we review the underlying theory of these novel optical scatterers and some demonstrated configurations with enhanced resolution. The basic principles of optical interference and optical phase sensing are discussed in tandem. Emphasis is placed on both familiar and unfamiliar scatterers, such as the maximally-symmetric Grover multiport, whose actions are left unchanged by certain gauge transformations. These higher-dimensional, gauge-invariant multiports embody a new class of building blocks which can tailor optical interference for metrology in unconventional ways.