  Unidirectional nonreciprocal transport is at the heart of many fundamental
problems and applications in both science and technology. Here we study the
novel design of wave diode devices by engineering asymmetric shapes of
nonlinear materials to realize the function of non-reciprocal wave
propagations. We first show analytical results revealing that both nonlinearity
and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave
propagations. Detailed numerical simulations are further performed for a more
realistic geometric wave diode model with typical asymmetric shape, where good
non-reciprocal wave diode effect is demonstrated. Finally, we discuss the
scalability of geometric wave diodes. The results open a flexible way for
designing wave diodes efficiently simply through shape engineering of nonlinear
materials, which may find broad implications in controlling energy, mass and
information transports.
