Reflection and transmission of electromagnetic waves at a temporal boundary

We consider propagation of an electromagnetic (EM) wave through a dynamic optical medium whose refractive index varies with time. Specifically, we focus on the reflection and transmission of EM waves from a temporal boundary and clarify the two different physical processes that contribute to them. One process is related to impedance mismatch, while the other results from temporal scaling related to a sudden change in the speed of light at the temporal boundary. Our results show that temporal scaling of the electric field must be considered for light propagation in dynamic media. Numerical solutions of Maxwell's equations are in full agreement with our theory.