  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-Pe\~na et al [[1]
Optica 7, 323 (2020)]. The strategy to render ultra-wideband antireflection
temporal medium is discussed analytically and verified numerically. In-depth
analysis shows that the multi-stage design of the temporal media implies a
continuously temporal variation of the material' s constitutive parameters,
thus an ultra-wideband antireflection temporal medium is reasonably obtained.
As an illustrative example for application, the proposed temporal medium is
adopted to realize impedance matching between a dielectric slab and free space,
which validates our new findings.
