Nie, J. W.et al. Adaptive beam shaping for enhanced underwater wireless optical communication. Opt. Express 29 , 26404–26417 (2021)..

Lu, Z. H. et al. Tunable Bessel beam shaping for robust atmospheric optical communication. J. Light. Technol. 40 , 5097–5106 (2022)..

Ren, W. B. et al. Free-space beam shaping and steering based on a silicon optical phased array. Photonics Res. 11 , 2093–2099 (2023)..

Duocastella, M. & Arnold, C. B. Bessel and annular beams for materials processing. Laser Photonics Rev. 6 , 607–621 (2012)..

Zupancic, P. et al. Ultra-precise holographic beam shaping for microscopic quantum control. Opt. Express 24 , 13881–13893 (2016)..

Shealy, D. L. & Hoffnagle, J. A. Laser beam shaping profiles and propagation. Appl. Opt. 45 , 5118–5131 (2006)..

Koyama, F. & Gu, X. D. Beam steering, beam shaping, and intensity modulation based on VCSEL photonics. IEEE J. Sel. Top. Quantum Electron. 19 , 1701510 (2013)..

Xue, Z. W. et al. Actively compensation of low order aberrations by refractive shaping system for high power slab lasers. Opt. Laser Technol. 75 , 71–75 (2015)..

Kalyoncu, S. K. et al. Analytical study on arbitrary waveform generation by MEMS micro mirror arrays. Opt. Express 20 , 27542–27553 (2012)..

Tan, L. Y. et al. Approach to improve beam quality of inter-satellite optical communication system based on diffractive optical elements. Opt. Express 17 , 6311–6319 (2009)..

Lee, S. et al. Geometric-phase intraocular lenses with multifocality. Light Sci. Appl. 11 , 320 (2022)..

Katz, S., Kaplan, N. & Grossinger, I. Using diffractive optical elements: DOEs for beam shaping–fundamentals and applications. Opt. Photonik 13 , 83–86 (2018)..

Qu, W. D. et al. Precise design of two-dimensional diffractive optical elements for beam shaping. Appl. Opt. 54 , 6521–6525 (2015)..

Johansson, M. & Bengtsson, J. Robust design method for highly efficient beam-shapingdiffractive optical elements using an iterative-Fourier-transform algorithm with soft operations. J. Mod. Opt. 47 , 1385–1398 (2000)..

Li, S. S. et al. High-quality near-field beam achieved in a high-power laser based on SLM adaptive beam-shaping system. Opt. Express 23 , 681–689 (2015)..

Ackermann, L., Roider, C. & Schmidt, M. Uniform and ef ficient beam shaping for high-energy lasers. Opt. Express 29 , 17997–18009 (2021)..

Salter, P. S. et al. Adaptive slit beam shaping for direct laser written waveguides. Opt. Lett. 37 , 470–472 (2012)..

Hasan, M. Z. & Kane, C. L. Colloquium : topological insulators. Rev. Mod. Phys. 82 , 3045–3067 (2010)..

Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83 , 1057–1110 (2011)..

Ando, Y. Topological insulator materials. J. Phys. Soc. Jpn. 82 , 102001 (2013)..

Hasan, M. Z. & Moore, J. E. Three-dimensional topological insulators. Annu. Rev. Condens. Matter Phys. 2 , 55–78 (2011)..

Jackiw, R. & Rebbi, C. Solitons with fermion number. Phys. Rev. D. 13 , 3398–3409 (1976)..

Shen, S. Q. Topological Insulators: Dirac Equation in Condensed Matters (Springer, 2012).

Asbóth, J. K., Oroszlány, L. & Pályi, A. A Short Course on Topological Insulators (Springer, 2016).

Lee, K. Y. et al. Topological guided-mode resonances at non-Hermitian nanophotonic interfaces. Nanophotonics 10 , 1853–1860 (2021)..

An, S. C. et al. Topological exciton polaritons in compact perovskite junction metasurfaces. Adv. Funct. Mater. 34 , 2313840 (2024)..

Choi, Y. S., Lee, K. Y. & Yoon, J. W. Topological surface Plasmon resonance in deep subwavelength structure. Curr. Appl. Phys. 45 , 72–75 (2023)..

Gorlach, A. A. et al. Photonic Jackiw-Rebbi states in all-dielectric structures controlled by bianisotropy. Phys. Rev. B 99 , 205122 (2019)..

Gupta, N. K. et al. Realization of Jackiw–Rebbi zero-energy modes at photonic crystal domain walls: emergence of polarization-indiscriminate surface states. Appl. Phys. Lett. 124 , 091104 (2024)..

Kim, M. & Rho, J. Quantum Hall phase and chiral edge states simulated by a coupled dipole method. Phys. Rev. B 101 , 195105 (2020)..

Li, F. F. et al. Topological light-trapping on a dislocation. Nat. Commun. 9 , 2462 (2018)..

Slobozhanyuk, A. et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photonics 11 , 130–136 (2017)..

Tran, T. X. & Biancalana, F. Linear and nonlinear photonic Jackiw-Rebbi states in interfaced binary waveguide arrays. Phys. Rev. A 96 , 013831 (2017)..

Chen, K. et al. Photonic Dirac cavities with spatially varying mass term. Sci. Adv. 9 , eabq4243 (2023)..

Lee, K. Y. et al. Topological beaming of light. Sci. Adv. 8 , eadd8349 (2022)..

Kane, C. L. Topological band theory and the $$ {{\mathbb{Z}}_{2}}$$ invariant. Contemp. Concepts Condens. Matter Sci. 6 , 3–34 (2013)..

Schindler, F. Dirac equation perspective on higher-order topological insulators. J. Appl. Phys. 128 , 221102 (2020)..

Lee, S. G. & Magnusson, R. Band flips and bound-state transitions in leaky-mode photonic lattices. Phys. Rev. B 99 , 045304 (2019)..

Kazarinov, R. & Henry, C. Second-order distributed feedback lasers with mode selection provided by first-order radiation losses. IEEE J. Quantum Electron. 21 , 144–150 (1985)..

Rosenblatt, D., Sharon, A. & Friesem, A. A. Resonant grating waveguide structures. IEEE J. Quantum Electron. 33 , 2038–2059 (1997)..

Ding, Y. & Magnusson, R. Band gaps and leaky-wave effects in resonant photonic-crystal waveguides. Opt. Express 15 , 680–694 (2007)..

Yoshida, M. et al. High-brightness scalable continuous-wave single-mode photonic-crystal laser. Nature 618 , 727–732 (2023)..

Contractor, R. et al. Scalable single-mode surface-emitting laser via open-Dirac singularities. Nature 608 , 692–698 (2022)..

Shao, Z. K. et al. A high-performance topological bulk laser based on band-inversion-induced reflection. Nat. Nanotechnol. 15 , 67–72 (2020)..

Vakulenko, A. et al. Adiabatic topological photonic interfaces. Nat. Commun. 14 , 4629 (2023)..

Park, C. Y. et al. Compact coherent perfect absorbers using topological guided-mode resonances. Sci. Rep. 14 , 14144 (2024)..