Boyd, R. W. Nonlinear Optics (Academic, 2008).
Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nat. Photonics 6, 84–92 (2012).
Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, eaay3676 (2020).
Gaeta, A. L., Lipson, M. & Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photonics 13, 158–169 (2019).
Dudley, J. M., Genty, G. & Coen, S. Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135 (2006).
Dutt, A., Mohanty, A., Gaeta, A. L. & Lipson, M. Nonlinear and quantum photonics using integrated optical materials. Nat. Rev. Mater. 9, 321–346 (2024).
Ansari, V., Donohue, J. M., Brecht, B. & Silberhorn, C. Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings. Optica 5, 534–550 (2018).
Caspani, L. et al. Integrated sources of photon quantum states based on nonlinear optics. Light Sci. Appl. 6, e17100 (2017).
Koenderink, A. F., Alù, A. & Polman, A. Nanophotonics: shrinking light-based technology. Science 348, 516–521 (2015).
Timurdogan, E., Poulton, C. V., Byrd, M. J. & Watts, M. R. Electric field-induced second-order nonlinear optical effects in silicon waveguides. Nat. Photonics 11, 200–206 (2017).
Heydari, D. et al. Degenerate optical parametric amplification in CMOS silicon. Optica 10, 430–437 (2023).
Nitiss, E., Hu, J., Stroganov, A. & Brès, C.-S. Optically reconfigurable quasi-phase-matching in silicon nitride microresonators. Nat. Photonics 16, 134–141 (2022).
Lu, X., Moille, G., Rao, A., Westly, D. A. & Srinivasan, K. Efficient photoinduced second-harmonic generation in silicon nitride photonics. Nat. Photonics 15, 131–136 (2020).
Billat, A. et al. Large second harmonic generation enhancement in Si3N4 waveguides by all-optically induced quasi-phase-matching. Nat. Commun. 8, 1016 (2017).
Hickstein, D. D. et al. Self-organized nonlinear gratings for ultrafast nanophotonics. Nat. Photonics 13, 494–499 (2019).
Li, B. et al. Down-converted photon pairs in a high-Q silicon nitride microresonator. Nature 639, 922–927 (2025).
Serino, L. et al. Realization of a multi-output quantum pulse gate for decoding high-dimensional temporal modes of single-photon states. PRX Quantum 4, 020306 (2023).
Lu, H.-H., Liscidini, M., Gaeta, A. L., Weiner, A. M. & Lukens, J. M. Frequency-bin photonic quantum information. Optica 10, 1655–1671 (2023).
Oliver, R. et al. N-way parametric frequency beamsplitter for quantum photonics. Phys. Rev. Res. 7, 023108 (2025).
Willner, A. E., Khaleghi, S., Chitgarha, M. R. & Yilmaz, O. F. All-optical signal processing. J. Light. Technol. 32, 660–680 (2013).
McMahon, P. L. The physics of optical computing. Nat. Rev. Phys. 5, 717–734 (2023).
Saxena, M., Eluru, G. & Gorthi, S. S. Structured illumination microscopy. Adv. Opt. Photonics 7, 241–275 (2015).
Heist, S. et al. 5D hyperspectral imaging: fast and accurate measurement of surface shape and spectral characteristics using structured light. Opt. Express 26, 23366–23379 (2018).
Wang, Z. et al. Metasurface-empowered five-dimensional imaging with structured light. ACS Photonics 11, 3898–3906 (2024).
Hum, D. S. & Fejer, M. M. Quasi-phasematching. C. R. Phys. 8, 180–198 (2006).
Hu, X., Xu, P. & Zhu, S. Engineered quasi-phase-matching for laser techniques. Photonics Res. 1, 171–185 (2013).
Chen, B.-Q., Zhang, C., Hu, C.-Y., Liu, R.-J. & Li, Z.-Y. High-efficiency broadband high-harmonic generation from a single quasi-phase-matching nonlinear crystal. Phys. Rev. Lett. 115, 083902 (2015).
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).
Imeshev, G. et al. Engineerable femtosecond pulse shaping by second-harmonic generation with Fourier synthetic quasi-phase-matching gratings. Opt. Lett. 23, 864–866 (1998).
Ellenbogen, T., Voloch-Bloch, N., Ganany-Padowicz, A. & Arie, A. Nonlinear generation and manipulation of Airy beams. Nat. Photonics 3, 395–398 (2009).
Dolev, I., Ellenbogen, T. & Arie, A. Switching the acceleration direction of Airy beams by a nonlinear optical process. Opt. Lett. 35, 1581–1583 (2010).
Fang, B., Li, H., Zhu, S. & Li, T. Second-harmonic generation and manipulation in lithium niobate slab waveguides by grating metasurfaces. Photonics Res. 8, 1296–1300 (2020).
Yoo, S. J. B. et al. Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding. Appl. Phys. Lett. 68, 2609–2611 (1996).
Boes, A. et al. Efficient second harmonic generation in lithium niobate on insulator waveguides and its pitfalls. J. Phys. Photonics 3, 012008 (2021).
Chen, P.-K. et al. Adapted poling to break the nonlinear efficiency limit in nanophotonic lithium niobate waveguides. Nat. Nanotechnol. 19, 44–50 (2023).
Maker, P. D. & Terhune, R. W. Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. 137, A801 (1965).
Oudar, J. L. & Le Person, H. Second-order polarizabilities of some aromatic molecules. Opt. Commun. 15, 258–262 (1975).
Lüpke, G. Characterization of semiconductor interfaces by second-harmonic generation. Surf. Sci. Rep. 35, 75–161 (1999).
Zhao, X. et al. Nontrivial phase matching in helielectric polarization helices: universal phase matching theory, validation, and electric switching. Proc. Natl Acad. Sci. 119, e2205636119 (2022).
Sultanov, V. et al. Tunable entangled photon-pair generation in a liquid crystal. Nature 631, 294–299 (2024).
Onodera, T. et al. Scaling on-chip photonic neural processors using arbitrarily programmable wave propagation. Preprint at https://arxiv.org/abs/2402.17750 (2024).
Wu, T., Menarini, M., Gao, Z. & Feng, L. Lithography-free reconfigurable integrated photonic processor. Nat. Photonics 17, 710–716 (2023).
Margules, P., Moses, J., Suchowski, H. & Porat, G. Ultrafast adiabatic frequency conversion. J. Phys. Photonics 3, 022011 (2021).
Shiloh, R. & Arie, A. Spectral and temporal holograms with nonlinear optics. Opt. Lett. 37, 3591–3593 (2012).
Leshem, A., Shiloh, R. & Arie, A. Experimental realization of spectral shaping using nonlinear optical holograms. Opt. Lett. 39, 5370–5373 (2014).
Buono, W. T. & Forbes, A. Nonlinear optics with structured light. Opto-Electron. Adv. 5, 210174 (2022).
Efremidis, N. K., Chen, Z., Segev, M. & Christodoulides, D. N. Airy beams and accelerating waves: an overview of recent advances. Optica 6, 686–701 (2019).
Ji, X. et al. Ultra-low-loss silicon nitride photonics based on deposited films compatible with foundries. Laser Photonics Rev. 17, 2200544 (2023).
Ji, X., Roberts, S., Corato-Zanarella, M. & Lipson, M. Methods to achieve ultra-high quality factor silicon nitride resonators. APL Photonics 6, 071101 (2021).
Liu, J. et al. High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits. Nat. Commun. 12, 2236 (2021).
Yanagimoto, R. et al. Data repository for “Programmable on-chip nonlinear photonics”. Zenodo https://doi.org/10.5281/zenodo.17074707 (2025).
Bolla, L. EMpy – Electromagnetic Python. GitHub https://github.com/lbolla/EMpy (2017).