“…New methods supporting the crossing of multiple waveguides based on inverse-design [12] and the MFE lens [13] have been investigated. Multimode waveguides play an important role in PICs and variety of devices are proposed based on them such as optical filters [14][15][16], power splitters [17,18], polarization splitters [19,20], sensors [21,22], (de)multiplexers [23][24][25][26], switches [27][28][29], and wavelength converter [30]. Therefore, designing multimode waveguide crossings is vital in PICs and they have been introduced based on multimode-interference couplers [31,32], subwavelength asymmetric Y-junction [33], and the MFE lens [34].…”