One-way optical modal transition based on causality in momentum space

The concept of parity-time (PT) symmetry has been used to identify a route toward unidirectional dynamics in optical κ-space: imposing asymmetry on the flow of light. Although PT-symmetric potentials have been implemented under the requirement of V(x) = V∗(-x), this precondition has only been interpreted within the mathematical framework for the symmetry of Hamiltonians and has not been directly linked to unidirectionality induced by PT symmetry. In this paper, within the context of light-matter interactions, we develop an alternative route toward unidirectionality in κ-space by employing the concept of causality. We demonstrate that potentials with real and causal momentum spectra produce unidirectional transitions of optical modes inside the κ-continuum, which corresponds to an exceptional point on the degree of PT symmetry. Our analysis reveals a critical link between non-Hermitian problems and spectral theory and also enables multi-dimensional designer manipulation of optical modes, in contrast to the one-dimensional approach that used a Schrödinger-like equation in previous PT-symmetric optics.