A novel and general formulation for wave propagation in time-varying media is presented. Unlike previous reports, our formalism is able to solve propagation in media with arbitrary time variations of permittivity or permeability, for both transient and steady-state periodic variations. The formulation is approximate yet strikingly accurate in most practical cases. The provided closed-form expressions show that the normalized average power after the transition of the permittivity does not depend on the details of the transition, while the energy density does. Some important discussions are made about time-periodic media, and it is shown that there is an accumulation of energy when the temporal equivalent of the Bragg condition is met. All results are validated through comparison against analytical or numerical solutions.
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