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We demonstrate the existence of exceptional points of degeneracy (EPD) ofperiodic eigenstates in non-Hermitian coupled chains of dipolar scatterers.Guided modes supported by these structures can exhibit an EPD in theirdispersion diagram at which two or more Bloch eigenstates coalesce, in boththeir eigenvectors and eigenvalues. We show a second-order modal EPD associatedwith the parity-time ($\cal{PT}$) symmetry condition, at which each particlepair in the double chain exhibits balanced gain and loss. Furthermore, we alsodemonstrate a fourth-order EPD occurring at the band edge. Such degeneracycondition was previously referred to as a degenerate band edge in losslessanisotropic photonic crystals. Here, we rigorously show it under the occurrenceof gain and loss balance for a discrete guiding system. We identify a moregeneral regime of gain and loss balance showing that $\cal{PT}$-symmetry is notnecessary to realize EPDs. Furthermore, we investigate the degree of detuningof the EPD when the geometrical symmetry or balanced condition is broken. Thesefindings open unprecedented avenues toward superior light localization andtransport with application to high-Q resonators utilized in sensors, filters,low-threshold switching and lasing.

Exceptional points of degeneracy and $\cal{PT}$-symmetry in photonic coupled chains of scatterers