Bender, C. M. & Boettcher, S. Real spectra in non-hermitian hamiltonians having $$ {\mathcal{P}}{\mathcal{T}} $$ symmetry. Phys. Rev. Lett. 80 , 5243–5246 (1998)..

Guo, A. et al. Observation of $$ {\mathcal{P}}{\mathcal{T}} $$ -Symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103 , 093902 (2009)..

Chang, L. et al. Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators. Nat. Photonics 8 , 524–529 (2014)..

Peng, B. et al. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10 , 394–398 (2014)..

Feng, L. et al. Single-mode laser by parity-time symmetry breaking. Science 346 , 972–975 (2014)..

Lin, Z. et al. Unidirectional invisibility induced by $$ {\mathcal{P}}{\mathcal{T}} $$ -Symmetric periodic structures. Phys. Rev. Lett. 106 , 213901 (2011)..

Chen, W. J. et al. Exceptional poi nts enhance sensing in an optical microcavity. Nature 548 , 192–196 (2017)..

Lai, Y. H. et al. Observation of the exceptional-point-enhanced Sagnac effect. Nature 576 , 65–69 (2019)..

Kim, C. et al. Parity-time symmetry enabled ultra-efficient nonlinear optical signal processing. eLight 4 , 6 (2024)..

Chen, Y. et al. Exceptional points with memory in a microcavity Brillouin laser. Optica 9 , 971–979 (2022)..