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

Sunkyu Yu, Xianji Piao, Kyung Wan Yoo, Jonghwa Shin, Namkyoo Park

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish
Pages (from-to)24997-25008
Number of pages12
JournalOptics Express
Issue number19
StatePublished - 15 Sep 2015


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