Ultrafast Topological Transitions Driven by Permittivity Modulation in Non-Hermitian Multilayers

Ultrafast permittivity modulation in epsilon-near-zero (ENZ) media provides a pathway for real-time control of non-Hermitian photonic topology. We model ultrafast topological dynamics in an ITO/SiO$_2$/Ag multilayer supporting hybrid epsilon-near-zero (ENZ)-plasmon modes. Using a time-dependent Drude-Lorentz permittivity for ITO and rigorous coupled-wave analysis, it is found that carrier relaxation with a 10-ps time constant redshifts the ENZ resonance from 490 to 525~nm and shifts the reflection-phase singularities across the angle--wavelength plane. The motion of these singularities corresponds to the displacement of exceptional points and a discrete change in the cumulative winding number. The transient Floquet-like band structure exhibits avoided crossings and Dirac-type dispersions driven by ENZ modulation. The results directly link picosecond-scale permittivity dynamics to quantized topological transitions in non-Hermitian photonic systems.