[1] C. Li, D. Liu, D. Dai. Multimode silicon photonics. Nanophotonics, 8, 227(2018).

[2] D. Dai, J. Wang, Y. Shi. Silicon mode (de)multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light. Opt. Lett., 38, 1422(2013).

[3] X. Wang, H. Yu, Q. Zhang et al. Ultra-compact silicon mode (de)multiplexer based on directional couplers with subwavelength sidewall corrugations. Opt. Lett., 47, 2198(2022).

[4] Q. Wang, Y. He, H. Wang et al. On-chip mode division (de)multiplexer for multi-band operation. Opt. Express, 30, 22779(2022).

[5] J. You, G. You, S. Li et al. Ultra-compact and low loss on chip higher order mode pass filter based on topology optimization. Appl. Phys. Express, 13, 022005(2020).

[6] C. Sun, W. Wu, Y. Yu et al. Integrated tunable mode filter for a mode-division multiplexing system. Opt. Lett., 43, 3658(2018).

[7] T. Dou, S. Yue, R. Wang et al. Ultra-compact and ultra-broadband arbitrary-order silicon photonic multi-mode converter designed by an intelligent algorithm. Opt. Express, 31, 9481(2023).

[8] J. Li, M. Wang, H. Ye. Heuristic inverse design of integrated mode converter by directly reshaping silicon waveguide. Opt. Laser Technol., 165, 109573(2023).

[9] S. Sun, Z. Yang, J. Wang et al. Ultra-sharp silicon multimode waveguide bends based on double free-form curves. Photonics Res., 10, 1484(2022).

[10] S. Gao, H. Wang, X. Yi et al. Ultra-compact multimode waveguide bend with shallowly etched grooves. Opt. Express, 29, 38683(2021).

[11] X. Guan, Y. Ding, L. H. Frandsen. Ultra-compact broadband higher order-mode pass filter fabricated in a silicon waveguide for multimode photonics. Opt. Lett., 40, 3893(2015).

[12] W. Jiang, J. Miao, T. Li et al. Low-loss and broadband silicon mode filter using cascaded plasmonic BSWGs for on-chip mode division multiplexing. Opt. Express, 27, 30429(2019).

[13] J. Liao, L. Zhang, M. Liu et al. Mode splitter without changing the mode order in SOI waveguide. IEEE Photonics Technol. Lett., 28, 2597(2016).

[14] S. Hada, B. Rahman. Design of compact mode splitters using identical coupled waveguides with slots. OSA Contin., 2, 848(2019).

[15] W. Jiang, S. Xu. Experimental realization of broadband mode-splitting using bridged subwavelength grating. J. Lightwave Technol., 39, 6239(2021).

[16] S. Molesky, Z. Lin, A. Y. Piggott et al. Inverse design in nanophotonics. Nat. Photonics, 12, 659(2018).

[17] S. Mao, J. Hu, H. Zhang et al. Optimal design and experimental demonstration of a silicon-based ultra-compact mode splitter. Opt. Lett., 47, 4167(2022).

[18] C. M. Lalau-Keraly, S. Bhargava, O. D. Miller et al. Adjoint shape optimization applied to electromagnetic design. Opt. Express, 21, 21693(2013).

[19] O. D. Miller. Photonic Design: From Fundamental Solar Cell Physics to Computational Inverse Design(2012).

[20] J. Wang, Y. Xuan, M. Qi et al. Ultra-broadband integrated four-channel mode-division-multiplexing based on tapered mode-evolution couplers. European Conference on Optical Communication (ECOC)(2016).