[1] Armstrong, J. A. et al. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962). doi: 10.1103/PhysRev.127.1918
[2] Berger, V. Nonlinear photonic crystals. Phys. Rev. Lett. 81, 4136–4139 (1998). doi: 10.1103/PhysRevLett.81.4136
[3] Chen, B. Q. et al. High-efficiency broadband high-harmonic generation from a single quasi-phase-matching nonlinear crystal. Phys. Rev. Lett. 115, 083902 (2015). doi: 10.1103/PhysRevLett.115.083902
[4] Zhu, S. N., Zhu, Y. Y. & Ming, N. B. Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. Science 278, 843–846 (1997). doi: 10.1126/science.278.5339.843
[5] Zhang, Y. et al. Nonlinear Talbot effect. Phys. Rev. Lett. 104, 183901 (2010). doi: 10.1103/PhysRevLett.104.183901
[6] Jin, H. et al. Compact engineering of path-entangled sources from a monolithic quadratic nonlinear photonic crystal. Phys. Rev. Lett. 111, 023603 (2013). doi: 10.1103/PhysRevLett.111.023603
[7] Leng, H. Y. et al. On-chip steering of entangled photons in nonlinear photonic crystals. Nat. Commun. 2, 429 (2011). doi: 10.1038/ncomms1439
[8] Yamada, M. et al. First‐order quasi‐phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second‐harmonic generation. Appl. Phys. Lett. 62, 435–436 (1993). doi: 10.1063/1.108925
[9] Magel, G. A., Fejer, M. M. & Byer, R. L. Quasi‐phase‐matched second‐harmonic generation of blue light in periodically poled LiNbO3. Appl. Phys. Lett. 56, 108–110 (1990). doi: 10.1063/1.103276
[10] Li, G. X., Zhang, S. & Zentgraf, T. Nonlinear photonic metasurfaces. Nat. Rev. Mater. 2, 17010 (2017). doi: 10.1038/natrevmats.2017.10
[11] Segal, N. et al. Controlling light with metamaterial-based nonlinear photonic crystals. Nat. Photonics 9, 180–184 (2015). doi: 10.1038/nphoton.2015.17
[12] Wei, D. Z. et al. Experimental demonstration of a three-dimensional lithium niobate nonlinear photonic crystal. Nat. Photonics 12, 596–600 (2018). doi: 10.1038/s41566-018-0240-2
[13] Xu, T. X. et al. Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate. Nat. Photonics 12, 591–595 (2018). doi: 10.1038/s41566-018-0225-1
[14] Wei, D. Z. et al. Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals. Nat. Commun. 10, 4193 (2019). doi: 10.1038/s41467-019-12251-0
[15] Liu, S. et al. Nonlinear wavefront shaping with optically induced three-dimensional nonlinear photonic crystals. Nat. Commun. 10, 3208 (2019). doi: 10.1038/s41467-019-11114-y
[16] Makey, G. et al. Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors. Nat. Photonics 13, 251–256 (2019). doi: 10.1038/s41566-019-0393-7
[17] Blanche, P. A. et al. Holographic three-dimensional telepresence using large-area photorefractive polymer. Nature 468, 80–83 (2010). doi: 10.1038/nature09521
[18] Curtis, K. R. Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
[19] Heanue, J. F., Bashaw, M. C. & Hesselink, L. Volume holographic storage and retrieval of digital data. Science 265, 749–752 (1994). doi: 10.1126/science.265.5173.749
[20] Fang, X. Y., Ren, H. R. & Gu, M. Orbital angular momentum holography for high-security encryption. Nat. Photonics 14, 102–108 (2020). doi: 10.1038/s41566-019-0560-x
[21] Alexandrov, S. A. et al. Synthetic aperture fourier holographic optical microscopy. Phys. Rev. Lett. 97, 168102 (2006). doi: 10.1103/PhysRevLett.97.168102
[22] Ye, W. M. et al. Spin and wavelength multiplexed nonlinear metasurface holography. Nat. Commun. 7, 11930 (2016). doi: 10.1038/ncomms11930
[23] Almeida, E., Bitton, O. & Prior, Y. Nonlinear metamaterials for holography. Nat. Commun. 7, 12533 (2016). doi: 10.1038/ncomms12533
[24] Shapira, A., Juwiler, I. & Arie, A. Nonlinear computer-generated holograms. Opt. Lett. 36, 3015–3017 (2011). doi: 10.1364/OL.36.003015
[25] Shapira, A. et al. Two-dimensional nonlinear beam shaping. Opt. Lett. 37, 2136–2138 (2012). doi: 10.1364/OL.37.002136
[26] Bloch, N. V. et al. Twisting light by nonlinear photonic crystals. Phys. Rev. Lett. 108, 233902 (2012). doi: 10.1103/PhysRevLett.108.233902
[27] Liu, H. G. et al. Dynamic computer-generated nonlinear optical holograms in a non-collinear second-harmonic generation process. Opt. Lett. 43, 3236–3239 (2018). doi: 10.1364/OL.43.003236
[28] Mao, N. B. et al. Nonlinear diatomic metasurface for real and fourier space image encoding. Nano Lett. 20, 7463–7468 (2020). doi: 10.1021/acs.nanolett.0c02910
[29] Gao, Y. S. et al. Nonlinear holographic all-dielectric metasurfaces. Nano Lett. 18, 8054–8061 (2018). doi: 10.1021/acs.nanolett.8b04311
[30] Hong, X. H. et al. Nonlinear volume holography for wave-front engineering. Phys. Rev. Lett. 113, 163902 (2014). doi: 10.1103/PhysRevLett.113.163902
[31] Yang, B. et al. 2D wave-front shaping in optical superlattices using nonlinear volume holography. Opt. Lett. 41, 2927–2929 (2016). doi: 10.1364/OL.41.002927
[32] Saltiel, S. M. et al. Multiorder nonlinear diffraction in frequency doubling processes. Opt. Lett. 34, 848–850 (2009). doi: 10.1364/OL.34.000848
[33] Krasnok, A., Tymchenko, M. & Alù, A. Nonlinear metasurfaces: a paradigm shift in nonlinear optics. Mater. Today 21, 8–21 (2018). doi: 10.1016/j.mattod.2017.06.007
[34] Reineke, B. et al. Silicon metasurfaces for third harmonic geometric phase manipulation and multiplexed holography. Nano Lett. 19, 6585–6591 (2019). doi: 10.1021/acs.nanolett.9b02844
[35] Hu, X. P., Zhang, Y. & Zhu, S. N. Nonlinear beam shaping in domain engineered ferroelectric crystals. Adv. Mater. 32, 1903775 (2020).
[36] Arie, A., Habshoosh, N. & Bahabad, A. Quasi phase matching in two-dimensional nonlinear photonic crystals. Optical Quantum Electron. 39, 361–375 (2007). doi: 10.1007/s11082-007-9102-8
[37] Chang, C. L. et al. Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg-Saxton algorithm. Appl. Opt. 54, 6994–7001 (2015). doi: 10.1364/AO.54.006994
[38] Gerke, T. D. & Piestun, R. Aperiodic volume optics. Nat. Photonics 4, 188–193 (2010). doi: 10.1038/nphoton.2009.290
[39] Lohmann, A. W. & Paris, D. P. Binary fraunhofer holograms, generated by computer. Appl. Opt. 6, 1739–1748 (1967). doi: 10.1364/AO.6.001739
[40] Zhang, Y. et al. Nonlinear photonic crystals: from 2D to 3D. Optica 8, 372–381 (2021). doi: 10.1364/OPTICA.416619
[41] Keren-Zur, S. & Ellenbogen, T. A new dimension for nonlinear photonic crystals. Nat. Photonics 12, 575–577 (2018). doi: 10.1038/s41566-018-0262-9