“…Here, we define the LP 11a mode as the mode with two intensity peaks in the plane and the LP 11b mode as the mode with two intensity peaks in the vertical direction. To address this issue, various methods have been proposed and experimentally validated, such as mode rotators [ 18 , 19 , 20 , 21 , 22 , 23 , 24 ], vertical asymmetric directional couplers [ 25 , 26 , 27 ], horizontal directional couplers formed with waveguides of different heights [ 28 ], and degenerate-mode-selective couplers [ 29 ]. Polymer-based planar light-wave circuits (PLCs) offer a simple, low-cost, and flexible fabrication process [ 30 , 31 , 32 ] compared to silica and silicon.…”