## One-Way Optical Transition based on Causality in Momentum Space

Sunkyu Yu, Xianji Piao, KyungWan Yoo, Jonghwa Shin, Namkyoo Park

The concept of parity-time (PT) symmetry has been used to identify a novel route to nonreciprocal dynamics in optical momentum space, imposing the directionality on the flow of light. Whereas PT-symmetric potentials have been implemented under the requirement of $$V(x) = V*(-x)$$, this precondition has only been interpreted within the mathematical frame for the symmetry of Hamiltonians and has not been directly linked to nonreciprocity. Here, within the context of light-matter interactions, we develop an alternative route to nonreciprocity in momentum space by employing the concept of causality. We demonstrate that potentials with real and causal momentum spectra produce unidirectional transitions of optical states inside the k-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 enables the multi-dimensional manipulation of optical states, in contrast to one-dimensional control from the use of a Schrodinger-like equation in previous PT-symmetric optics.

http://arxiv.org/abs/1409.7031
Optics (physics.optics)