Besides chiral edge states, the hallmark of quantum Hall insulators, antichiral edge states can exhibit unidirectional transport behavior but in topological semimetals. Although such edge states provide more flexibility for molding the flow of light, their realization usually suffers from time-reversal breaking. In this study, we propose the realization of antichiral surface states in a time-reversal-invariant manner and demonstrate our idea with a three-dimensional (3D) photonic metacrystal. Our system is a photonic semimetal possessing two asymmetrically dispersed Dirac nodal lines. Via dimension reduction, the nodal lines are rendered a pair of offset Dirac points. By introducing synthetic gauge flux, each two-dimensional (2D) subsystem with nonzero kz is analogous to a modified Haldane model, yielding a kz-dependent antichiral surface transport. Through microwave experiments, the bulk dispersion with asymmetric nodal lines and associated twisted ribbon surface states are demonstrated in our 3D time-reversal-invariant system. Although our idea is demonstrated in a photonic system, we propose a general approach to realize antichiral edge states in time-reversal-invariant systems. This approach can be easily extended to systems beyond photonics and may pave the way for further applications of antichiral transport.

In non-Hermitian systems, defective band degeneracies called exceptional points can form exceptional lines (ELs) in 3D momentum space in the absence of any symmetries. However, whether the presence of symmetries can affect the EL configurations had rarely been discussed. Here we show that a natural orientation can be assigned to every EL according to the eigenenergy braiding around it, and we establish the source-free principle of ELs stating that the number of ELs ingoing and outgoing from the junction must be conserved. Based on this principle, we discover that three crystalline-symmetry-based mechanisms can stabilize the junction of ELs, resulting in the formation of various types of exceptional chains (ECs). We further demonstrate that ECs can be observed in prototypical non-Hermitian photonic crystals. Our results combine the effect of non-Hermitian spatiotemporal symmetry and topology to pave the way for understanding and manipulating the morphology of ELs in non-Hermitian crystalline systems.