Parity–Time Symmetry and Exceptional Points in Wave Control, Sensing, and Energy Transfer

Studies of parity–time symmetry showed that non-Hermitian Hamiltonians can possess real spectra and provided a framework for controlling waves through gain, loss, and coupling. This review examines how the associated spectral and eigenstate properties connect wave generation, propagation, energy transfer, and sensing. A two-state Hamiltonian introduces symmetry breaking and exceptional points. Differences in modal growth rates enable laser-mode selection, while control of eigenvectors and their evolution extends this principle to directional emission and mode conversion. At finite intensity, the interplay between field localization and nonlinear response enables control of optical transport and adaptive energy transfer. The dependence of these states on system parameters also provides a basis for sensing, where the relation between response and fluctuations determines whether spectral enhancement improves measurement precision.