Fig. 4: PS directional coupler.

a Microscope top image of the fabricated PS directional coupler after selective etching. The purple color depicts the designed pattern. b Simulated cross-section of the propagation inside the NLPC for an idler input, showing the propagation of both signal and idler. After the scattered eigenstate is scattered from the lower PS waveguide, the guided eigenstate tunnels to the upper waveguide. Then, it tunnels back to the first lower waveguide. The white dashed line marks the experimentally measured crystal length. c Near field image of signal field at the output facet showing the guided eigenstate, |\({\psi }_{+}\)〉 port 2, after tunneling from port 1. Similar to the single waveguide case, the eigenstate is guided along the ‘X’ axis and freely propagates along the ‘Y’ axis. The light at the edges corresponds to the scattered eigenstate |\({\psi }_{-}\) 〉. d Same as panel c, but now the input beams enter from port 2, obtaining tunneling from port 2 to port 1. e, f Simulation results for (c, d). Similarly, to the experiment, due to tunneling of the guided PS between the two ports, a small portion of the signal power can be seen at the input port (either port 1 in panel e or port 2 in panel (f)).