Non-Coincident Topological, Exceptional Point, and Optical Lifshitz Transitions in Optical Materials

Harnessing the exotic functionalities of optical materials, such as subwavelength imaging and topologically protected transport, requires a predictive understanding of their emergent phase transitions. However, current research largely relies on case-specific analyses. Here, we develop an effective-medium Hamiltonian framework that provides general, analytic criteria for three fundamental transitions: the topological transition, the exceptional point (EP) transition, and the optical Lifshitz transition. Contrary to prevailing intuition, we show that these transitions are generically non-coincident, with their separation governed by factors such as anisotropic chirality, nonreciprocity, and principal-axis mismatch. This separation reveals markedly richer phase diagrams than previously recognized. Our framework offers a broadly applicable theoretical toolkit for the systematic discovery and design of optical materials with tailored electromagnetic properties.