  Impedance matching is one of the most important practice in wave engineering
as it enables to maximize the power transfer from the signal source to the load
in the wave system. Unfortunately, it is bounded by the Bode-Fano criterion
that states, for any passive, linear and time-invariant matching network, a
stringent tradeoff between the matching-bandwidth and efficiency; implying
severe constraints on various electromagnetic and acoustic wave systems. Here,
we propose a matching paradigm that overcome this issue by using a temporal
switching of the parameters of a metamaterial-based transmission-line, thus
revoking the time-invariance assumption underlying the Bode-Fano criterion.
Using this scheme we show theoretically that an efficient wideband matching,
beyond Bode-Fano bound, can be achieved for short-time pulses in challenging
cases of very high contrast between the load and the generator impedances, and
with significant load dispersion; situations common in e.g., small antennas
matching, cloaking, with applications for ultra-wideband communication, high
resolution imaging, and more.
