Fig. 2

Numerical simulation for asymmetric and symmetric configurations of SUSY transformation optics. a, c The optical potentials and the corresponding mode profiles of three eigenstates (blue, red, green) at five different \(z\) coordinates at \(z=0, 0.25L, 0.5L, 0.75L,\) and \(L\), for asymmetric a and symmetric c designs. The offsets of the mode profiles indicate their effective mode indices from high, middle to low: \({n}_{blue}=1.868\), \({n}_{red}=1.755\), and \({n}_{green}=1.656\). b, d Simulated electric field intensity in the GRIN metamaterials with prescribed gap distributions for asymmetric b and symmetric d designs. From the top, center, to bottom, different optical states are excited at \(z=0\), as denoted by the colors of the arrows, corresponding to the blue, red, and green eigenstates, respectively, in a and c. It is evident that fundamental mode excitations from different input ports transform to the fundamental, first-order, and second-order modes from \(z=0\) to \(z=0.5L\), consistent with the design in a and c