  The study of nonreciprocal wave propagation is of great interests for both
fundamental research and engineering applications. Here we demonstrate
theoretically and experimentally a bidirectional, nonreciprocal, and
high-quality diode that can rectify elastic waves in both forward and backward
directions in an elastic metamaterial designed to exhibit enhanced nonlinearity
of resonances. This diode can preserve or vary frequency, rectify low-frequency
long wave with small system size, offer high-quality insulation, can be
modulated by amplitude, and break reciprocity of both the total energy and
fundamental wave. We report three mechanisms to break reciprocity: the
amplitude-dependent bandgap combining interface reflection, chaotic response
combining linear bandgap, amplitude-dependent attenuation rate in damping
diode. The bidirectional diode paves ways for mutually controlling
information/energy transport between two sources, which can be used as new wave
insulators.
