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Weyl points are the simplest topologically-protected degeneracy in athree-dimensional dispersion relation. The realization of Weyl semimetals inphotonic crystals has allowed these singularities and their consequences to beexplored with electromagnetic waves. However, it is difficult to achievenonlinearities in such systems. One promising approach is to use thestrong-coupling of photons and excitons, because the resulting polaritonsinteract through their exciton component. Yet topological polaritons have onlybeen realized in two dimensions. Here, we predict that the dispersion relationfor polaritons in three dimensions, in a bulk semiconductor with an appliedmagnetic field, contains Weyl points and Weyl line nodes. We show thatabsorption converts these Weyl points to Weyl exceptional rings. We concludethat bulk semiconductors are a promising system in which to investigatetopological photonics in three dimensions, and the effects of dissipation,gain, and nonlinearity.

Weyl points and exceptional rings with polaritons in bulk semiconductors