Unidirectional sound transmission across a junction of two square sonic crystals with different orientations and lattice constants is numerically investigated. Re-scaling and rotating the wave vectors through refractions across the air-first sonic crystal interface and the junction, respectively, facilitate coupling into the spatial modes of the second crystal. Unidirectional transmission, demonstrated through finite element method simulations, is accomplished between 10.4 kHz and 12.8 kHz. Transmission values to the right and left are greater than 60% and less than 1.0%, respectively, between 11.0 kHz and 12.4 kHz, resulting in a contrast ratio greater than 0.9.

A system composed of air holes in a dielectric host to form two square photonic crystals, with the same orientation and lattice constant but different scatterer radii, making an interface along their body diagonals, is numerically demonstrated to facilitate unidirectional light transmission. Band structure computations are carried out via the plane wave expansion method, whereas finite-difference time-domain simulations are carried out to investigate the transient behavior. Unidirectional light transmission is achieved over two adjacent stop bands along the $\mathrm{\Gamma }\mathrm{X}$ direction, which are circumvented in the forward direction by scaling down the wave vector and rotating the surface normal. Contrast ratios as high as 0.9 are attained within the lower stop band.