New light on eigenmodes and scattering. And on chirality and reciprocity, while we’re at it.

Eigenmodes are powerful things in physics – there’s a reason we learn so much about them early on in BSc studies. They tell us how a system likes to behave if it’s left alone, decoupled from the outside world. But physical systems are never decoupled fully from their surroundings. Optical systems (i.e., structured polarizable matter), for example, can be driven by light waves coming in from afar, and in turn radiate waves into the space surrounding them – a response that is captured in the scattering matrix of a system. That scattering matrix is a powerful thing too: For any given incoming field, it tells us what waves we could expect to come out of the system. For example, it can tell us how a chiral optical system can change the polarization of light transmitted through it.

It was in trying to understand the chiral response of a complex photonic crystal slab that we stumbled on a very general problem. We wondered if we could predict the full scattering matrix of a system, if we happened to know all of its eigenmodes? Even though in recent years it has become clear how we can talk about eigenmodes in systems that are not decoupled from the rest of the world (by talking about complex ‘quasi-normal modes’ instead), the answer to that question was not known, except for very special cases.

In a publication in Physical Review X, we now present the solution to that general problem, showing that one can accurately predict and understand the response of any optical system from the fields of its eigenmodes at some distance away from the structure. We think it’s a hugely powerful method, that can actually be much faster than brute-force alternatives to calculate scattering matrices of practically any nanophotonic system one can think of. And it allowed us to solve the problem that started it all: to understand just how ‘chiral’ a thin photonic crystal slab can be. In a paper in ACS Photonics, we show that such systems can show large asymmetric transmission of polarized light, that is connected to the polarization of its eigenmodes. And we reveal that there is a fundamental limit on asymmetric transmission, that is linked to the principle of reciprocity. Using our theory, we show how one can design chiral photonic crystals that have nearly ideal asymmetry: blocking light of a certain polarization in one direction, while allowing it through in the other.

Congratulations to Nikhil Parappurath and Filippo Alpeggiani for shedding so much new light!