[1] D. Thomson, A. Zilkie, J. E. Bowers, T. Komljenovic, G. T. Reed, L. Vivien,et al., “Roadmap on silicon photonics,”Journal of Optics, 2016, 18(7): 073003.

[2] J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,”Nature, 2013, 493: 195–199.

[3] Z. Wang, Z. Peng, Y. Zhang, Y. Wu, Y. Hu, J. Wu,et al., “93-THz ultra-broadband and ultra-low loss Y-junction photonic power splitter with phased inverse design,”Optics Express, 2023, 31(10): 15904−15916.

[4] H. Yuan, Z. Wang, Z. Peng, J. Wu, and J. Yang, “Ultra-compact and nonvolatile nanophotonic neural networks,”Advanced Optical Materials, 2023, 11(16): 2300215.

[5] J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de)multiplexer enabling simultaneous mode-and polarization-division-multiplexing,”Laser & Photonics Reviews, 2014, 8(2): L18–L22.

[6] D. Dai, C. Li, S. Wang, H. Wu, Y. Shi, Z. Wu,et al., “10-channel mode (de)multiplexer with dual polarizations,”Laser & Photonics Reviews, 2018, 12(1): 1700109.

[7] W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng,et al., “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,”Photonics Research, 2018, 6(7): 660−665.

[8] Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang,et al., “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,”Nature Communication, 2019, 10(1): 1−7.

[9] S. Howe, W. R. Headley, D. C. Cox, G. Z. Mashanovich, D. J. Thomson, and G. T. Reed, “Fabrication and tailoring of silicon photonic devices via focused ion beam,”Silicon Photonics IV, 2009, 7220(4): 220−228.

[10] M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,”Applied Physics Letters, 1970, 16: 523–525.

[11] R. Topley, G. Martinez-Jimenez, L. O’Faolain, N. Healy, S. Mailis, D. J. Thomson,et al., “Locally erasable couplers for optical device testing in silicon on insulator,”Journal of Lightwave Technology, 2014, 32(12): 2248−2253.

[12] S. Scheerlinck, D. Taillaert, D. Van Thourhout, and R. Baets, “Flexible metal grating based optical fiber probe for photonic integrated circuits,”Applied Physics Letters, 2008, 92(3): 031104.

[13] X. Chen, M. M. Milosevic, A. F. J. Runge, X. Yu, A. Z. Khokhar, S. Mailis,et al., “Silicon erasable waveguides and directional couplers by germanium ion implantation for configurable photonic circuits,”Optics Express, 2020, 28(12): 17630−17642.

[14] Y. Zhang, Q. Zhang, C. Ros, M. Y. Shalaginov, J. B. Chou, C. Roberts,et al., “Transient tap couplers for wafer-level photonic testing based on optical phase change materials,”ACS Photonics, 2021, 8(7), 1903–1908.

[15] H. Ma, X. He, G. Zhu, J. Wu, X. Jiang, T. Du,et al., “Different-mode power splitters based on a multi-dimension direct-binary-search algorithm,”Optics Express, 2023, 31(17): 27393−27406.

[16] L. Lu, M. Zhang, F. Zhou, W. Chang, J. Tang, D. Li,et al., “Inverse-designed ultra-compact star-crossings based on PhC-like subwavelength structures for optical intercross connect,”Optics Express, 2017, 25(15): 18355−18364.

[17] H. S. Ma, J. Huang, K. W. Zhang, and J. B. Yang, “Inverse-designed arbitrary-input and ultra-compact 1 ×Npower splitters based on high symmetric structure,”Scientific Reports, 2020, 10(1): 11757.

[18] L. Lu, D. Liu, F. Zhou, D. Li, M. Cheng, L. Deng,et al., “Inverse-designed single-step-etched colorless 3 dB couplers based on RIE-lag-insensitive PhC-like subwavelength structures,”Optics Letters, 2016, 41(21): 5051−5054.