We demonstrate that reflectionless propagation of electromagnetic waves between two different materials can be achieved by designing an intermediate temporal medium, which can work in an ultra-wide frequency band. Such a temporal medium is designed with consideration of a multi-stage variation of the material’s permittivity in the time domain. The multi-stage temporal permittivity is formed by a cascaded quarter-wave temporal coating, which is an extension of the antireflection temporal coating by Pacheco-Peña et al [[1]...