Vol. 184
Latest Volume
All Volumes
PIER 184 [2025] PIER 183 [2025] PIER 182 [2025] PIER 181 [2024] PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2025-12-31 Fellow Article
Progress in Structured Light with Nonlinear Optics
By
, Vol. 184, 109-124, 2025
Abstract
The control of all of light's degrees of freedom and its harnessing for applications is captured by the emergent field of structured light. The modern toolkit includes external modulation of light with devices such as metasurfaces and spatial light modulators, their intra-cavity insertion for structured light directly at the source, and their deployment to engineer quantum structured light at the single photon and entangled state regimes. Historically, this control has involved linear optical elements, with nonlinear optics only recently coming to the fore. This has opened unprecedented functionality while revealing new paradigms for nonlinear optics beyond plane waves. In this review we look at the recent progress in structured light with nonlinear optics, covering the fundamentals and the powerful applications they are facilitating in both the classical and quantum domains.
Citation
Sachleen Singh, and Andrew Forbes, "Progress in Structured Light with Nonlinear Optics," , Vol. 184, 109-124, 2025.
doi:10.2528/PIER25110804
References

1. Forbes, Andrew, Michael de Oliveira, and Mark R. Dennis, "Structured light," Nature Photonics, Vol. 15, No. 4, 253-262, 2021.
doi:10.1038/s41566-021-00780-4        Google Scholar

2. Zhan, Qiwen, "Spatiotemporal sculpturing of light: A tutorial," Advances in Optics and Photonics, Vol. 16, No. 2, 163-228, 2024.
doi:10.1364/aop.507558        Google Scholar

3. Yang, Yiqian, Andrew Forbes, and Liangcai Cao, "A review of liquid crystal spatial light modulators: Devices and applications," Opto-Electronic Science, Vol. 2, No. 8, 230026, 2023.
doi:10.29026/oes.2023.230026        Google Scholar

4. Dorrah, Ahmed H. and Federico Capasso, "Tunable structured light with flat optics," Science, Vol. 376, No. 6591, eabi6860, 2022.
doi:10.1126/science.abi6860        Google Scholar

5. Forbes, Andrew and Isaac Nape, "Quantum mechanics with patterns of light: Progress in high dimensional and multidimensional entanglement with structured light," AVS Quantum Science, Vol. 1, No. 1, 011701, 2019.
doi:10.1116/1.5112027        Google Scholar

6. Nape, Isaac, Bereneice Sephton, Pedro Ornelas, Chane Moodley, and Andrew Forbes, "Quantum structured light in high dimensions," APL Photonics, Vol. 8, No. 5, 051101, 2023.
doi:10.1063/5.0138224        Google Scholar

7. Paúr, Martin, Bohumil Stoklasa, Zdenek Hradil, Luis L. Sánchez-Soto, and Jaroslav Rehacek, "Achieving the ultimate optical resolution," Optica, Vol. 3, No. 10, 1144-1147, 2016.
doi:10.1364/optica.3.001144        Google Scholar

8. Dorn, R., S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Physical Review Letters, Vol. 91, No. 23, 233901, Dec. 2003.
doi:10.1103/physrevlett.91.233901        Google Scholar

9. Willner, Alan E., Kai Pang, Hao Song, Kaiheng Zou, and Huibin Zhou, "Orbital angular momentum of light for communications," Applied Physics Reviews, Vol. 8, No. 4, 041312, 2021.
doi:10.1063/5.0054885        Google Scholar

10. Angelsky, Oleg V., Aleksandr Y. Bekshaev, Steen G. Hanson, Claudia Yu Zenkova, Igor I. Mokhun, and Jun Zheng, "Structured light: Ideas and concepts," Frontiers in Physics, Vol. 8, 114, 2020.
doi:10.3389/fphy.2020.00114        Google Scholar

11. Wang, Jian and Yize Liang, "Generation and detection of structured light: A review," Frontiers in Physics, Vol. 9, 688284, 2021.
doi:10.3389/fphy.2021.688284        Google Scholar

12. Cheng, Mingjian, Wenjie Jiang, Lixin Guo, Jiangting Li, and Andrew Forbes, "Metrology with a twist: Probing and sensing with vortex light," Light: Science & Applications, Vol. 14, No. 1, 4, 2025.
doi:10.1038/s41377-024-01665-1        Google Scholar

13. Forbes, Andrew, "Structured light from lasers," Laser & Photonics Reviews, Vol. 13, No. 11, 1900140, 2019.
doi:10.1002/lpor.201900140        Google Scholar

14. Forbes, Andrew, Light Mkhumbuza, and Liang Feng, "Orbital angular momentum lasers," Nature Reviews Physics, Vol. 6, No. 6, 352-364, 2024.
doi:10.1038/s42254-024-00715-2        Google Scholar

15. Buono, Wagner Tavares and Andrew Forbes, "Nonlinear optics with structured light," Opto-Electronic Advances, Vol. 5, No. 6, 210174, 2022.
doi:10.29026/oea.2022.210174        Google Scholar

16. Fang, Yiqi, Zijian Lyu, and Yunquan Liu, "Ultrafast physics with structured light," Nature Reviews Physics, Vol. 7, 713-727, 2025.
doi:10.1038/s42254-025-00887-5        Google Scholar

17. Martín-Hernández, Rodrigo, Guan Gui, Luis Plaja, Henry C. Kapteyn, Margaret M. Murnane, Chen-Ting Liao, Miguel A. Porras, and Carlos Hernández-García, "Extreme-ultraviolet spatiotemporal vortices via high harmonic generation," Nature Photonics, Vol. 19, 817-824, 2025.
doi:10.1038/s41566-025-01699-w        Google Scholar

18. Harrison, Justin, Darryl Naidoo, Andrew Forbes, and Angela Dudley, "Progress in high-power and high-intensity structured light," Advances in Physics: X, Vol. 9, No. 1, 2327453, 2024.
doi:10.1080/23746149.2024.2327453        Google Scholar

19. Carbajo, Sergio, Seung-Whan Bahk, Justin Baker, Andrea Bertozzi, Abhimanyu Borthakur, Antonino Di Piazza, Andrew Forbes, Spencer Gessner, Jack Hirschman, et al. "Structured light at the extreme: Harnessing spatiotemporal control for high-field laser-matter interactions," arXiv preprint arXiv:2512.05042, 2025.
doi:10.48550/arXiv.2512.05042        Google Scholar

20. Forbes, Andrew, Fazilah Nothlawala, and Adam Vallés, "Progress in quantum structured light," Nature Photonics, Vol. 19, 1291-1300, 2025.
doi:10.1038/s41566-025-01795-x        Google Scholar

21. Boyd, R. W., Nonlinear Optics, 3rd Ed., 253-275, Academic Press, Burlington, 2008.

22. Kovacic, Ivana and Michael J. Brennan, The Duffing Equation: Nonlinear Oscillators and Their Behaviour, John Wiley & Sons, 2011.

23. New, Geoffrey, Introduction to Nonlinear Optics, Cambridge University Press, 2011.
doi:10.1017/cbo9780511975851

24. Barh, Ajanta, Peter John Rodrigo, Lichun Meng, Christian Pedersen, and Peter Tidemand-Lichtenberg, "Parametric upconversion imaging and its applications," Advances in Optics and Photonics, Vol. 11, No. 4, 952-1019, 2019.
doi:10.1364/aop.11.000952        Google Scholar

25. Emanueli, Shai and Ady Arie, "Temperature-dependent dispersion equations for KTiOPO4 and KTiOAsO4," Applied Optics, Vol. 42, No. 33, 6661-6665, 2003.
doi:10.1364/ao.42.006661        Google Scholar

26. Ma, Jianan, Xiaoyan Cheng, Ningchong Zheng, Pengcheng Chen, Xiaoyi Xu, Tianxin Wang, Dunzhao Wei, Yuefeng Nie, Shining Zhu, Min Xiao, and Yong Zhang, "Fabrication of 100-nm-period domain structure in lithium niobate on insulator," Optics Express, Vol. 31, No. 23, 37464-37471, 2023.
doi:10.1364/oe.501804        Google Scholar

27. Singh, Sachleen, Isaac Nape, and Andrew Forbes, "Enhanced fidelity in nonlinear structured light by virtual light-based apertures," Optics Express, Vol. 33, No. 13, 27615-27625, 2025.
doi:10.1364/oe.562028        Google Scholar

28. De Oliveira, A. G., G. Santos, N. Rubiano da Silva, L. J. Pereira, G. B. Alves, A. Z. Khoury, and P. H. Souto Ribeiro, "Beyond conservation of orbital angular momentum in stimulated parametric down-conversion," Physical Review Applied, Vol. 16, No. 4, 044019, 2021.
doi:10.1103/physrevapplied.16.044019        Google Scholar

29. Yao, Alison M. and Miles J. Padgett, "Orbital angular momentum: Origins, behavior and applications," Advances in Optics and Photonics, Vol. 3, No. 2, 161-204, 2011.
doi:10.1364/aop.3.000161        Google Scholar

30. Chaitanya, N. Apurv, M. V. Jabir, J. Banerji, and G. K. Samanta, "Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum," Scientific Reports, Vol. 6, No. 1, 32464, 2016.
doi:10.1038/srep32464        Google Scholar

31. Weiss, Tim F. and Alberto Peruzzo, "Nonlinear domain engineering for quantum technologies," Applied Physics Reviews, Vol. 12, No. 1, 011318, 2025.
doi:10.1063/5.0223013        Google Scholar

32. Pertsch, Thomas and Yuri Kivshar, "Nonlinear optics with resonant metasurfaces," MRS Bulletin, Vol. 45, No. 3, 210-220, 2020.
doi:10.1557/mrs.2020.65        Google Scholar

33. Litchinitser, Natalia M., "Structured light meets structured matter," Science, Vol. 337, No. 6098, 1054-1055, 2012.
doi:10.1126/science.1226204        Google Scholar

34. Trajtenebrg-Mills, Sivan and Ady Arie, "Shaping light beams in nonlinear processes using structured light and patterned crystals," Optical Materials Express, Vol. 7, No. 8, 2928-2942, 2017.
doi:10.1364/ome.7.002928        Google Scholar

35. Liu, Haigang and Xianfeng Chen, "The manipulation of second-order nonlinear harmonic wave by structured material and structured light," Journal of Nonlinear Optical Physics & Materials, Vol. 27, No. 4, 1850047, 2018.
doi:10.1142/s0218863518500479        Google Scholar

36. Disa, Ankit S., Tobia F. Nova, and Andrea Cavalleri, "Engineering crystal structures with light," Nature Physics, Vol. 17, No. 10, 1087-1092, 2021.
doi:10.1038/s41567-021-01366-1        Google Scholar

37. Yanagimoto, Ryotatsu, Benjamin A. Ash, Mandar M. Sohoni, Martin M. Stein, Yiqi Zhao, Federico Presutti, Marc Jankowski, Logan G. Wright, Tatsuhiro Onodera, and Peter L. McMahon, "Programmable on-chip nonlinear photonics," Nature, 1-8, 2025.
doi:10.1038/s41586-025-09620-9        Google Scholar

38. Qiu, Xiaodong, Fangshu Li, Wuhong Zhang, Zhihan Zhu, and Lixiang Chen, "Spiral phase contrast imaging in nonlinear optics: Seeing phase objects using invisible illumination," Optica, Vol. 5, No. 2, 208-212, 2018.
doi:10.1364/optica.5.000208        Google Scholar

39. Hong, Ling, Fei Lin, Xiaodong Qiu, and Lixiang Chen, "Second harmonic generation based joint transform correlator for human face and QR code recognitions," Applied Physics Letters, Vol. 116, No. 23, 231101, 2020.
doi:10.1063/5.0001301        Google Scholar

40. De Oliveira, André G., Marcelo F. Z. Arruda, Willamys C. Soares, Stephen P. Walborn, Rafael M. Gomes, Renné Medeiros de Araújo, and Paulo H. Souto Ribeiro, "Real-time phase conjugation of vector vortex beams," ACS Photonics, Vol. 7, No. 1, 249-255, 2020.
doi:10.1021/acsphotonics.9b01524        Google Scholar

41. Zhu, Zhanghang, Di Zhang, Fei Xie, Junjun Ma, Jiaxin Chen, Shengchao Gong, Wei Wu, Wei Cai, Xinzheng Zhang, Mengxin Ren, and Jingjun Xu, "Nonlinear polarization imaging by parametric upconversion," Optica, Vol. 9, No. 11, 1297-1302, 2022.
doi:10.1364/optica.471177        Google Scholar

42. Jhajj, N., I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, "Spatiotemporal optical vortices," Physical Review X, Vol. 6, No. 3, 031037, 2016.
doi:10.1103/physrevx.6.031037        Google Scholar

43. Yusufu, Taximaiti, Sujian Niu, Paerhatijiang Tuersun, Yusufu Tulake, Katsuhiko Miyamoto, and Takashige Omatsu, "Tunable 3 µm optical vortex parametric oscillator," Japanese Journal of Applied Physics, Vol. 57, No. 12, 122701, 2018.
doi:10.7567/jjap.57.122701        Google Scholar

44. Gibbs, Hyatt, Optical Bistability: Controlling Light With Light, Elsevier, 2012.
doi:10.1063/1.2820150

45. Desyatnikov, A. S. and A. I. Maimistov, "Interaction of two spatially separated light beams in a nonlinear Kerr medium," Journal of Experimental and Theoretical Physics, Vol. 86, No. 6, 1101-1106, 1998.
doi:10.1134/1.558578        Google Scholar

46. Pura, B., J. Petykiewicz, L. Adamowicz, W. Jeda, M. Wierzbicki, and K. Brudzewski, "Polarisation control of light by light in a nonlinear polymer," Applied Physics B, Vol. 67, No. 2, 211-215, 1998.
doi:10.1007/s003400050495        Google Scholar

47. Zhang, Jianfa, Kevin F. MacDonald, and Nikolay I. Zheludev, "Controlling light-with-light without nonlinearity," Light: Science & Applications, Vol. 1, No. 7, e18, 2012.
doi:10.1038/lsa.2012.18        Google Scholar

48. Dholakia, K., N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Physical Review A, Vol. 54, No. 5, R3742, 1996.
doi:10.1103/physreva.54.r3742        Google Scholar

49. Wu, Hai-Jun, Hao-Ran Yang, Carmelo Rosales-Guzmán, Wei Gao, Bao-Sen Shi, and Zhi-Han Zhu, "Vectorial nonlinear optics: Type-II second-harmonic generation driven by spin-orbit-coupled fields," Physical Review A, Vol. 100, No. 5, 053840, 2019.
doi:10.1103/physreva.100.053840        Google Scholar

50. Wang, Jinwen, Francesco Castellucci, and Sonja Franke-Arnold, "Vectorial light-matter interaction: Exploring spatially structured complex light fields," AVS Quantum Science, Vol. 2, No. 3, 031702, 2020.
doi:10.1116/5.0016007        Google Scholar

51. Wright, Logan G., William H. Renninger, Demetri N. Christodoulides, and Frank W. Wise, "Nonlinear multimode photonics: Nonlinear optics with many degrees of freedom," Optica, Vol. 9, No. 7, 824-841, 2022.
doi:10.1364/optica.461981        Google Scholar

52. Buono, W. T., A. Santos, M. R. Maia, L. J. Pereira, D. S. Tasca, K. Dechoum, T. Ruchon, and A. Z. Khoury, "Chiral relations and radial-angular coupling in nonlinear interactions of optical vortices," Physical Review A, Vol. 101, No. 4, 043821, 2020.
doi:10.1103/physreva.101.043821        Google Scholar

53. Wu, Hai-Jun, Li-Wei Mao, Yuan-Jie Yang, Carmelo Rosales-Guzmán, Wei Gao, Bao-Sen Shi, and Zhi-Han Zhu, "Radial modal transitions of Laguerre-Gauss modes during parametric up-conversion: Towards the full-field selection rule of spatial modes," Physical Review A, Vol. 101, No. 6, 063805, 2020.
doi:10.1103/physreva.101.063805        Google Scholar

54. Yang, Hao-Ran, Hai-Jun Wu, Wei Gao, Carmelo Rosales-Guzmán, and Zhi-Han Zhu, "Parametric upconversion of Ince-Gaussian modes," Optics Letters, Vol. 45, No. 11, 3034-3037, 2020.
doi:10.1364/ol.393146        Google Scholar

55. Steinlechner, Fabian, Nathaniel Hermosa, Valerio Pruneri, and Juan P. Torres, "Frequency conversion of structured light," Scientific Reports, Vol. 6, No. 1, 21390, 2016.
doi:10.1038/srep21390        Google Scholar

56. Zdagkas, Apostolos, Cormac McDonnell, Junhong Deng, Yijie Shen, Guixin Li, Tal Ellenbogen, Nikitas Papasimakis, and Nikolay I. Zheludev, "Observation of toroidal pulses of light," Nature Photonics, Vol. 16, No. 7, 523-528, 2022.
doi:10.1038/s41566-022-01028-5        Google Scholar

57. Abrahao, Raphael A., Henri P. N. Morin, Jordan T. R. Pagé, Akbar Safari, Robert W. Boyd, and Jeff S. Lundeen, "Shadow of a laser beam," Optica, Vol. 11, No. 11, 1549-1555, 2024.
doi:10.1364/optica.534596        Google Scholar

58. Fickler, R., L. Kopf, and M. Ornigotti, "Higher-order Poincaré spheres and spatiospectral Poincaré beams," Physical Review Research, Vol. 6, No. 3, 033298, 2024.
doi:10.1103/physrevresearch.6.033298        Google Scholar

59. Gariepy, G., Conservation of orbital angular momentum in high-harmonic generation, University of Ottawa, Ottawa, Canada, 2013.

60. Rego, Laura, Kevin M. Dorney, Nathan J. Brooks, Quynh L. Nguyen, Chen-Ting Liao, Julio San Román, David E. Couch, Allison Liu, Emilio Pisanty, Maciej Lewenstein, et al. "Generation of extreme-ultraviolet beams with time-varying orbital angular momentum," Science, Vol. 364, No. 6447, eaaw9486, 2019.
doi:10.1126/science.aaw9486        Google Scholar

61. Li, X. F., A. L'Huillier, M. Ferray, L. A. Lompré, and G. Mainfray, "Multiple-harmonic generation in rare gases at high laser intensity," Physical Review A, Vol. 39, No. 11, 5751, 1989.
doi:10.1103/physreva.39.5751        Google Scholar

62. Gao, Jingsong, Xiang Zhang, Yang Wang, Yiqi Fang, Qi Lu, Zheng Li, Yi Liu, Chengyin Wu, Qihuang Gong, Yunquan Liu, and Hongbing Jiang, "Structured air lasing of N2+," Communications Physics, Vol. 6, No. 1, 97, 2023.
doi:10.1038/s42005-023-01226-9        Google Scholar

63. Srinivasa Rao, A., Katsuhiko Miamoto, and Takashige Omatsu, "Ultraviolet intracavity frequency-doubled Pr3+:LiYF4 orbital Poincaré laser," Optics Express, Vol. 28, No. 25, 37397-37405, 2020.
doi:10.1364/OE.411624        Google Scholar

64. Alam, Sabir Ul, A. Srinivasa Rao, Anirban Ghosh, Pravin Vaity, and G. K. Samanta, "Nonlinear frequency doubling characteristics of asymmetric vortices of tunable, broad orbital angular momentum spectrum," Applied Physics Letters, Vol. 112, No. 17, 171102, 2018.
doi:10.1063/1.5024445        Google Scholar

65. Pan, Jin-Tao, Bo-Han Zhu, Ling-Ling Ma, Wei Chen, Guang-Yang Zhang, Jie Tang, Yuan Liu, Yang Wei, Chao Zhang, Zhi-Han Zhu, et al. "Nonlinear geometric phase coded ferroelectric nematic fluids for nonlinear soft-matter photonics," Nature Communications, Vol. 15, No. 1, 8732, 2024.
doi:10.1038/s41467-024-53040-8        Google Scholar

66. De Ceglia, Domenico, Laure Coudrat, Iännis Roland, Maria Antonietta Vincenti, Michael Scalora, Rana Tanos, Julien Claudon, Jean-Michel Gérard, Aloyse Degiron, Giuseppe Leo, and Costantino De Angelis, "Nonlinear spin-orbit coupling in optical thin films," Nature Communications, Vol. 15, No. 1, 1625, 2024.
doi:10.1038/s41467-024-45607-2        Google Scholar

67. Ren, Zhi-Cheng, Yan-Chao Lou, Zi-Mo Cheng, Li Fan, Jianping Ding, Xi-Lin Wang, and Hui-Tian Wang, "Optical frequency conversion of light with maintaining polarization and orbital angular momentum," Optics Letters, Vol. 46, No. 10, 2300-2303, 2021.
doi:10.1364/ol.419753        Google Scholar

68. Pinheiro da Silva, Braian, Wagner T. Buono, Leonardo J. Pereira, Daniel S. Tasca, Kaled Dechoum, and Antonio Z. Khoury, "Spin to orbital angular momentum transfer in frequency up-conversion," Nanophotonics, Vol. 11, No. 4, 771-778, 2022.
doi:10.1515/nanoph-2021-0493        Google Scholar

69. Samim, Masood, Serguei Krouglov, and Virginijus Barzda, "Nonlinear stokes-mueller polarimetry," Physical Review A, Vol. 93, No. 1, 013847, 2016.
doi:10.1103/physreva.93.013847        Google Scholar

70. Chen, Huifeng, Guanyu Liu, Shuang Zhang, Yongchun Zhong, Jianhui Yu, Zhe Chen, and Wenguo Zhu, "Spin Hall effect of nonlinear photons," Laser & Photonics Reviews, Vol. 17, No. 5, 2200681, 2023.
doi:10.1002/lpor.202200681        Google Scholar

71. Tang, Yutao, Zixian Hu, Junhong Deng, Kingfai Li, and Guixin Li, "Sequential harmonic spin-orbit angular momentum generation in nonlinear optical crystals," Opto-Electronic Advances, Vol. 7, No. 12, 240138, 2025.
doi:10.29026/oea.2024.240138        Google Scholar

72. Tang, Y., K. Li, X. Zhang, J. Deng, G. Li, and E. Brasselet, "Harmonic spin-orbit angular momentum cascade in nonlinear optical crystals," Nature Photonics, Vol. 14, No. 11, 658-662, 2020.
doi:10.1038/s41566-020-0691-0        Google Scholar

73. Li, Yan, Zhi-Yuan Zhou, Dong-Sheng Ding, and Bao-Sen Shi, "Sum frequency generation with two orbital angular momentum carrying laser beams," Journal of the Optical Society of America B, Vol. 32, No. 3, 407-411, 2015.
doi:10.1364/josab.32.000407        Google Scholar

74. Aguilar-Cardoso, A. A., C. Li, T. J. B. Luck, M. F. Ferrer-Garcia, J. Upham, J. S. Lundeen, and R. W. Boyd, "Tailoring spatial modes produced by stimulated parametric down-conversion," Physical Review A, Vol. 112, No. 4, 043541, 2025.
doi:10.1103/g22l-cgr1        Google Scholar

75. Wu, H.-J., B.-S. Yu, J.-Q. Jiang, C.-Y. Li, C. Rosales-Guzmán, S.-L. Liu, Z.-H. Zhu, and B.-S. Shi, "Observation of anomalous orbital angular momentum transfer in parametric nonlinearity," Physical Review Letters, Vol. 130, No. 15, 153803, 2023.
doi:10.1103/physrevlett.130.153803        Google Scholar

76. Kumar, Subith, Ravi K. Saripalli, Anirban Ghosh, Wagner T. Buono, Andrew Forbes, and G. K. Samanta, "Controlling the coverage of full Poincaré beams through second-harmonic generation," Physical Review Applied, Vol. 19, No. 3, 034082, 2023.
doi:10.1103/physrevapplied.19.034082        Google Scholar

77. Liu, Haigang, Hui Li, Yuanlin Zheng, and Xianfeng Chen, "Nonlinear frequency conversion and manipulation of vector beams," Optics Letters, Vol. 43, No. 24, 5981-5984, 2018.
doi:10.1364/ol.43.005981        Google Scholar

78. Luttmann, M., M. Vimal, M. Guer, J.-F. Hergott, A. Z. Khoury, C. Hernández-García, E. Pisanty, and T. Ruchon, "Nonlinear up-conversion of a polarization möbius strip with half-integer optical angular momentum," Science Advances, Vol. 9, No. 12, eadf3486, 2023.
doi:10.1126/sciadv.adf3486        Google Scholar

79. Da Motta, M. R. L., G. B. Alves, A. Z. Khoury, and S. S. Vianna, "Poincaré-sphere symmetries in four-wave mixing with orbital angular momentum," Physical Review A, Vol. 109, No. 1, 013506, 2024.
doi:10.1103/physreva.109.013506        Google Scholar

80. Pan, Churong, Huangjie Li, Hao Pang, Ruibo Ru, Sannv Zhang, Dong Wei, Haixia Chen, Hong Gao, and Fuli Li, "Generation and manipulation of spin-orbit coupling mode via four-wave mixing with quantum interference," Laser & Photonics Reviews, Vol. 18, No. 2, 2300625, 2024.
doi:10.1002/lpor.202300625        Google Scholar

81. Pan, Churong, Huangjie Li, Xuzhe Zhang, Yanzhe Liu, Lianglong Wu, Hao Pang, Haixia Chen, Dong Wei, Hong Gao, and Fuli Li, "All-optical controlled multichannel nonlinear holography for switchable beam shaping in an atomic vapor," Optica, Vol. 12, No. 7, 1054-1060, 2025.
doi:10.1364/optica.559378        Google Scholar

82. Yuan, Jinpeng, Xuewen Wang, Gang Chen, Lirong Wang, Liantuan Xiao, and Suotang Jia, "High-fidelity frequency converter in high-dimensional spaces," Laser & Photonics Reviews, Vol. 18, No. 11, 2400368, 2024.
doi:10.1002/lpor.202400368        Google Scholar

83. Gao, Wei, Sandan Wang, Jinpeng Yuan, Lirong Wang, Liantuan Xiao, and Suotang Jia, "High-contrast nonlinear spiral phase contrast imaging via four-wave mixing in atomic medium," Optics Express, Vol. 33, No. 18, 38382-38391, 2025.
doi:10.1364/oe.572157        Google Scholar

84. Bornman, Nicholas, Wagner Tavares Buono, Michael Lovemore, and Andrew Forbes, "Optimal pump shaping for entanglement control in any countable basis," Advanced Quantum Technologies, Vol. 4, No. 10, 2100066, 2021.
doi:10.1002/qute.202100066        Google Scholar

85. Jabir, M. V., N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, "Generation of ``perfect'' vortex of variable size and its effect in angular spectrum of the down-converted photons," Scientific Reports, Vol. 6, No. 1, 21877, 2016.
doi:10.1038/srep21877        Google Scholar

86. Nirala, Gaurav, Siva T. Pradyumna, Ashok Kumar, and Alberto M. Marino, "Information encoding in the spatial correlations of entangled twin beams," Science Advances, Vol. 9, No. 22, eadf9161, 2023.
doi:10.1126/sciadv.adf9161        Google Scholar

87. Rozenberg, E., A. Karnieli, O. Yesharim, J. Foley-Comer, S. Trajtenberg-Mills, D. Freedman, A. M. Bronstein, and A. Arie, "Inverse design of spontaneous parametric downconversion for generation of high-dimensional qudits," Optica, Vol. 9, No. 6, 602-615, 2022.
doi:10.1364/optica.451115        Google Scholar

88. Kysela, J., M. Erhard, A. Hochrainer, M. Krenn, and A. Zeilinger, "Path identity as a source of high-dimensional entanglement," Proceedings of the National Academy of Sciences, Vol. 117, No. 42, 26 118-26 122, 2020.
doi:10.1073/pnas.2011405117        Google Scholar

89. Trovatello, Chiara, Andrea Marini, Michele Cotrufo, Andrea Alù, P. James Schuck, and Giulio Cerullo, "Tunable optical nonlinearities in layered materials," ACS Photonics, Vol. 11, No. 8, 2860-2873, 2024.
doi:10.1021/acsphotonics.4c00521        Google Scholar

90. Yesharim, O., I. Hurvitz, J. Foley-Comer, and A. Arie, "Bulk nonlinear metamaterials for generation of quantum light," Applied Physics Reviews, Vol. 12, No. 1, 011323, 2025.
doi:10.1063/5.0216714        Google Scholar

91. Huang, Jianming Huang and Prem Kumar, "Observation of quantum frequency conversion," Physical Review Letters, Vol. 68, 2153, 1992.
doi:10.1103/PhysRevLett.68.2153        Google Scholar

92. Vandevender, Aaron P. and Paul G. Kwiat, "High efficiency single photon detection via frequency up-conversion," Journal of Modern Optics, Vol. 51, No. 9-10, 1433-1445, 2004.
doi:10.1080/09500340408235283        Google Scholar

93. Zaske, Sebastian, Andreas Lenhard, Christian A. Keßler, Jan Kettler, Christian Hepp, Carsten Arend, Roland Albrecht, Wolfgang-Michael Schulz, Michael Jetter, Peter Michler, and Christoph Becher, "Visible-to-telecom quantum frequency conversion of light from a single quantum emitter," Physical Review Letters, Vol. 109, No. 14, 147404, 2012.
doi:10.1103/physrevlett.109.147404        Google Scholar

94. Ansari, Vahid, John M. Donohue, Benjamin Brecht, and Christine Silberhorn, "Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings," Optica, Vol. 5, No. 5, 534-550, 2018.
doi:10.1364/optica.5.000534        Google Scholar

95. Eckstein, Andreas, Benjamin Brecht, and Christine Silberhorn, "A quantum pulse gate based on spectrally engineered sum frequency generation," Optics Express, Vol. 19, No. 15, 13770-13778, 2011.
doi:10.1364/oe.19.013770        Google Scholar

96. Ansari, V., J. M. Donohue, M. Allgaier, L. Sansoni, B. Brecht, J. Roslund, N. Treps, G. Harder, and C. Silberhorn, "Tomography and purification of the temporal-mode structure of quantum light," Physical Review Letters, Vol. 120, No. 21, 213601, 2018.
doi:10.1103/physrevlett.120.213601        Google Scholar

97. Serino, L., J. Gil-Lopez, M. Stefszky, R. Ricken, C. Eigner, B. Brecht, and C. Silberhorn, "Realization of a multi-output quantum pulse gate for decoding high-dimensional temporal modes of single-photon states," PRX Quantum, Vol. 4, No. 2, 020306, 2023.
doi:10.1103/prxquantum.4.020306        Google Scholar

98. Serino, L., C. Eigner, B. Brecht, and C. Silberhorn, "Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate," Optics Express, Vol. 33, No. 3, 5577-5586, 2025.
doi:10.1364/oe.544206        Google Scholar

99. Donohue, John M., Megan Agnew, Jonathan Lavoie, and Kevin J. Resch, "Coherent ultrafast measurement of time-bin encoded photons," Physical Review Letters, Vol. 111, 153602, 2013.
doi:10.1103/physrevlett.111.153602        Google Scholar

100. Allgaier, M., V. Ansari, J. M. Donohue, C. Eigner, V. Quiring, R. Ricken, B. Brecht, and C. Silberhorn, "Pulse shaping using dispersion-engineered difference frequency generation," Physical Review A, Vol. 101, No. 4, 043819, 2020.
doi:10.1103/physreva.101.043819        Google Scholar

101. Sephton, B., A. Vallés, I. Nape, M. A. Cox, F. Steinlechner, T. Konrad, J. P. Torres, F. S. Roux, and A. Forbes, "Quantum transport of high-dimensional spatial information with a nonlinear detector," Nature Communications, Vol. 14, No. 1, 8243, 2023.
doi:10.1038/s41467-023-43949-x        Google Scholar

102. Qiu, Xiaodong, Haoxu Guo, and Lixiang Chen, "Remote transport of high-dimensional orbital angular momentum states and ghost images via spatial-mode-engineered frequency conversion," Nature Communications, Vol. 14, No. 1, 8244, 2023.
doi:10.1038/s41467-023-43950-4        Google Scholar

103. Tsujimoto, Yoshiaki, Kentaro Wakui, Tadashi Kishimoto, Shigehito Miki, Masahiro Yabuno, Hirotaka Terai, Mikio Fujiwara, and Go Kato, "Experimental entanglement swapping through single-photon χ(2) nonlinearity," Nature Communications, Vol. 16, No. 1, 8720, 2025.
doi:10.1038/s41467-025-63785-5        Google Scholar

104. Akin, J., Y. Zhao, P. G. Kwiat, E. A. Goldschmidt, and K. Fang, "Faithful quantum teleportation via a nanophotonic nonlinear bell state analyzer," Physical Review Letters, Vol. 134, No. 16, 160802, 2025.
doi:10.1103/physrevlett.134.160802        Google Scholar

105. Ackermann, Lisa, Clemens Roider, Kristian Cvecek, Nicolas Barré, Christian Aigner, and Michael Schmidt, "Polarization-controlled nonlinear computer-generated holography," Scientific Reports, Vol. 13, No. 1, 10338, 2023.
doi:10.1038/s41598-023-37443-z        Google Scholar

106. Tamura, Rihito, Praveen Kumar, A. Srinivasa Rao, Kazuki Tsuda, Fanny Getzlaff, Katsuhiko Miyamoto, Natalia M. Litchinitser, and Takashige Omatsu, "Direct imprint of optical skyrmions in azopolymers as photoinduced relief structures," APL Photonics, Vol. 9, No. 4, 046104, 2024.
doi:10.1063/5.0192239        Google Scholar

107. Trajtenberg-Mills, Sivan, Irit Juwiler, and Ady Arie, "On-axis shaping of second-harmonic beams," Laser & Photonics Reviews, Vol. 9, No. 6, L40-L44, 2015.
doi:10.1002/lpor.201500154        Google Scholar

108. Wang, Mingjie, Yang Li, Yutao Tang, Jiafei Chen, Rong Rong, Guixin Li, Tun Cao, and Shumei Chen, "Nonlinear chiroptical holography with Pancharatnam-Berry phase controlled plasmonic metasurface," Laser & Photonics Reviews, Vol. 16, No. 12, 2200350, 2022.
doi:10.1002/lpor.202200350        Google Scholar

109. Coudrat, Laure, Guillaume Boulliard, Jean-Michel Gérard, Aristide Lemaître, Aloyse Degiron, and Giuseppe Leo, "Unravelling the nonlinear generation of designer vortices with dielectric metasurfaces," Light: Science & Applications, Vol. 14, No. 1, 51, 2025.
doi:10.1038/s41377-025-01741-0        Google Scholar

110. Rong, Rong, Yang Li, Mingjie Wang, Yutao Tang, Hongjie Xu, Kingfai Li, Guixin Li, Tun Cao, and Shumei Chen, "Beam steering of nonlinear optical vortices with phase gradient plasmonic metasurfaces," ACS Photonics, Vol. 10, No. 9, 3248-3254, 2023.
doi:10.1021/acsphotonics.3c00677        Google Scholar

111. Park, Seongjin, Jaeyeon Yu, Gerhard Boehm, Mikhail A. Belkin, and Jongwon Lee, "Electrically tunable third-harmonic generation using intersubband polaritonic metasurfaces," Light: Science & Applications, Vol. 13, No. 1, 169, 2024.
doi:10.1038/s41377-024-01517-y        Google Scholar

112. Zhang, X., H. Li, S. Liu, Y. Chen, Z. Zhu, H. Liu, S. Zhu, and X. Hu, "Tailoring beam profile and oam spectrum in domain-engineered nonlinear photonic crystals," APL Photonics, Vol. 10, No. 1, 2025.
doi:10.1063/5.0245407        Google Scholar

113. Yang, Jia-Chen, Wei Chen, Ling-Ling Ma, An-Zhuo Yu, Jin-Tao Pan, Jin-Tao Fan, Ming-Lie Hu, and Yan-Qing Lu, "Nonlinear photon sieves for high-fidelity wavefront engineering," Laser & Photonics Reviews, Vol. 19, No. 22, e01117, 2025.
doi:10.1002/lpor.202501117        Google Scholar

114. Yesharim, O., S. Pearl, J. Foley-Comer, I. Juwiler, and A. Arie, "Direct generation of spatially entangled qudits using quantum nonlinear optical holography," Science Advances, Vol. 9, No. 8, eade7968, 2023.
doi:10.1126/sciadv.ade7968        Google Scholar

115. Ye, Zhiyuan, Wanting Hou, Chen-Xin Ding, Xue-Jiao Men, Run-Jie He, Jilun Zhao, Hai-Bo Wang, Jun Xiong, and Kaige Wang, "Random holography: Generating EPR-like correlation with thermal photons," Laser & Photonics Reviews, Vol. 19, No. 6, 2401610, 2025.
doi:10.1002/lpor.202401610        Google Scholar

116. Hou, Wanting, Run-Jie He, Zhiyuan Ye, Xue-Jiao Men, Chen-Xin Ding, Hong-Chao Liu, Hai-Bo Wang, and Jun Xiong, "Manipulating classical triple correlations for optical information processing and metrology," Photonics Research, Vol. 13, No. 8, 2073-2087, 2025.
doi:10.1364/prj.559681        Google Scholar

117. Lukens, Joseph M., Amir Dezfooliyan, Carsten Langrock, Martin M. Fejer, Daniel E. Leaird, and Andrew M. Weiner, "Orthogonal spectral coding of entangled photons," Physical Review Letters, Vol. 112, No. 13, 133602, 2014.
doi:10.1103/physrevlett.112.133602        Google Scholar

118. Xu, Y., S. Tang, A. Nicholas Black, and R. W. Boyd, "Orthogonal spatial coding with stimulated parametric down-conversion," Optics Express, Vol. 31, No. 25, 42 723-42 729, 2023.
doi:10.1364/oe.506383        Google Scholar

119. Qi, Tong, Yi-Zhe Chen, Ding Yan, and Wei Gao, "Wavefront-reversal, low-threshold, and enhanced stimulated brillouin scattering for arbitrary structured light," Laser & Photonics Reviews, Vol. 18, No. 6, 2301080, 2024.
doi:10.1002/lpor.202301080        Google Scholar

120. Singh, S., B. Sephton, W. Tavares Buono, V. D'Ambrosio, T. Konrad, and A. Forbes, "Light correcting light with nonlinear optics," Advanced Photonics, Vol. 6, No. 2, 026 003, 2024.
doi:10.1117/1.ap.6.2.026003        Google Scholar

121. Zhou, Huibin, Xinzhou Su, Yuxiang Duan, Yue Zuo, Zile Jiang, Muralekrishnan Ramakrishnan, Jan Tepper, Volker Ziegler, Robert W. Boyd, Moshe Tur, and Alan E. Willner, "Automatic mitigation of dynamic atmospheric turbulence using optical phase conjugation for coherent free-space optical communications," Optica, Vol. 12, No. 2, 158-167, 2025.
doi:10.1364/optica.541823        Google Scholar

122. Sánchez-Montes, Adriana R., Sachleen Singh, Andrés Márquez, Jorge Francés, Andrew Forbes, and Angela Dudley, "Nonlinear modal decomposition of structured light," Optics Express, Vol. 33, No. 19, 41261-41270, 2025.
doi:10.1364/oe.567825        Google Scholar

123. Moon, Jungho, Ye-Chan Cho, Sungsam Kang, Mooseok Jang, and Wonshik Choi, "Measuring the scattering tensor of a disordered nonlinear medium," Nature Physics, Vol. 19, No. 11, 1709-1718, 2023.
doi:10.1038/s41567-023-02163-8        Google Scholar

124. Sohmen, Maximilian, Maria Borozdova, Monika Ritsch-Marte, and Alexander Jesacher, "Complex-valued scatter compensation in nonlinear microscopy," Physical Review Applied, Vol. 22, No. 4, 044036, 2024.
doi:10.1103/physrevapplied.22.044036        Google Scholar

125. Buono, W. T., J. Santiago, L. J. Pereira, D. S. Tasca, K. Dechoum, and A. Z. Khoury, "Polarization-controlled orbital angular momentum switching in nonlinear wave mixing," Optics Letters, Vol. 43, No. 7, 1439-1442, 2018.
doi:10.1364/ol.43.001439        Google Scholar

126. Pereira, Leonardo J., Wagner T. Buono, Daniel S. Tasca, Kaled Dechoum, and Antonio Z. Khoury, "Orbital-angular-momentum mixing in type-II second-harmonic generation," Physical Review A, Vol. 96, No. 5, 053856, 2017.
doi:10.1103/physreva.96.053856        Google Scholar

127. Wu, Hai-Jun, Bo Zhao, Carmelo Rosales-Guzmán, Wei Gao, Bao-Sen Shi, and Zhi-Han Zhu, "Spatial-polarization-independent parametric up-conversion of vectorially structured light," Physical Review Applied, Vol. 13, No. 6, 064041, 2020.
doi:10.1103/PhysRevApplied.13.064041        Google Scholar

128. Pinheiro da Silva, B., G. Dos Santos, A. De Oliveira, N. Rubiano da Silva, W. Buono, R. Gomes, W. Soares, A. Jesus-Silva, E. Fonseca, P. Souto Ribeiro, et al. "Observation of a triangular-lattice pattern in nonlinear wave mixing with optical vortices," Optica, Vol. 9, No. 8, 908-912, 2022.
doi:10.1364/OPTICA.459812        Google Scholar

129. Wu, H.-J., B.-S. Yu, Z.-H. Zhu, W. Gao, D.-S. Ding, Z.-Y. Zhou, X.-P. Hu, C. Rosales-Guzmán, Y. Shen, and B.-S. Shi, "Conformal frequency conversion for arbitrary vectorial structured light," Optica, Vol. 9, No. 2, 187-196, 2022.
doi:10.1364/optica.444685        Google Scholar

130. Menshikov, Evgenii, Paolo Franceschini, Kristina Frizyuk, Ivan Fernandez-Corbaton, Andrea Tognazzi, Alfonso Carmelo Cino, Denis Garoli, Mihail Petrov, Domenico de Ceglia, and Costantino De Angelis, "Light structuring via nonlinear total angular momentum addition with flat optics," Light: Science & Applications, Vol. 14, No. 1, 381, 2025.
doi:10.1038/s41377-025-02004-8        Google Scholar

131. Zhang, Yong, Yan Sheng, Shining Zhu, Min Xiao, and Wieslaw Krolikowski, "Nonlinear photonic crystals: From 2D to 3D," Optica, Vol. 8, No. 3, 372-381, 2021.
doi:10.1364/optica.416619        Google Scholar

132. Chen, P., C. Wang, D. Wei, Y. Hu, X. Xu, J. Li, D. Wu, J. Ma, S. Ji, L. Zhang, et al. "Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal," Light: Science & Applications, Vol. 10, No. 1, 146, 2021.
doi:10.1038/s41377-021-00588-5        Google Scholar

133. Olarte, Omar E., Jacob Licea-Rodriguez, Jonathan A. Palero, Emilio J. Gualda, David Artigas, Jürgen Mayer, Jim Swoger, James Sharpe, Israel Rocha-Mendoza, Raul Rangel-Rojo, and Pablo Loza-Alvarez, "Image formation by linear and nonlinear digital scanned light-sheet fluorescence microscopy with Gaussian and Bessel beam profiles," Biomedical Optics Express, Vol. 3, No. 7, 1492-1505, 2012.
doi:10.1364/boe.3.001492        Google Scholar

134. Vettenburg, Tom, Heather I. C. Dalgarno, Jonathan Nylk, Clara Coll-Lladó, David E. K. Ferrier, Tomáš Čižmár, Frank J. Gunn-Moore, and Kishan Dholakia, "Light-sheet microscopy using an Airy beam," Nature Methods, Vol. 11, No. 5, 541-544, 2014.
doi:10.1038/nmeth.2922        Google Scholar

135. Valle, Andres Flores and Johannes D. Seelig, "Two-photon Bessel beam tomography for fast volume imaging," Optics Express, Vol. 27, No. 9, 12147-12162, 2019.
doi:10.1364/oe.27.012147        Google Scholar

136. Chen, Xin, Suyi Zhong, Yiwei Hou, Ruijie Cao, Wenyi Wang, Dong Li, Qionghai Dai, Donghyun Kim, and Peng Xi, "Superresolution structured illumination microscopy reconstruction algorithms: A review," Light: Science & Applications, Vol. 12, No. 1, 172, 2023.
doi:10.1038/s41377-023-01204-4        Google Scholar

137. Zhang, Chenshuang, Bin Yu, Fangrui Lin, Soham Samanta, Huanhuan Yu, Wei Zhang, Yingying Jing, Chunfeng Shang, Danying Lin, Ke Si, Wei Gong, and Junle Qu, "Deep tissue super-resolution imaging with adaptive optical two-photon multifocal structured illumination microscopy," PhotoniX, Vol. 4, No. 1, 38, 2023.
doi:10.1186/s43074-023-00115-2        Google Scholar

138. Lee, Hongki, Hajun Yoo, Gwiyeong Moon, Kar-Ann Toh, Kentaro Mochizuki, Katsumasa Fujita, and Donghyun Kim, "Super-resolved Raman microscopy using random structured light illumination: Concept and feasibility," The Journal of Chemical Physics, Vol. 155, No. 14, 144202, 2021.
doi:10.1063/5.0064082        Google Scholar

139. Wang, Feifei, Yeteng Zhong, Oliver Bruns, Yongye Liang, and Hongjie Dai, "In vivo NIR-II fluorescence imaging for biology and medicine," Nature Photonics, Vol. 18, No. 6, 535-547, 2024.
doi:10.1038/s41566-024-01391-5        Google Scholar

140. Badrodien, Imraan, Pieter H. Neethling, and Gurthwin W. Bosman, "Improved image contrast in nonlinear light-sheet fluorescence microscopy using i2PIE Pulse compression," Scientific Reports, Vol. 14, No. 1, 12770, 2024.
doi:10.1038/s41598-024-63429-6        Google Scholar

141. Barsi, Christopher, Wenjie Wan, and Jason W. Fleischer, "Imaging through nonlinear media using digital holography," Nature Photonics, Vol. 3, No. 4, 211-215, 2009.
doi:10.1038/nphoton.2009.29        Google Scholar

142. Jia, Shu, Joyce Lee, Jason W. Fleischer, Georgios A. Siviloglou, and Demetrios N. Christodoulides, "Diffusion-trapped Airy beams in photorefractive media," Physical Review Letters, Vol. 104, No. 25, 253904, 2010.
doi:10.1103/physrevlett.104.253904        Google Scholar

143. Cao, Jianjun, Dongyi Shen, Yaming Feng, and Wenjie Wan, "Nonlinear negative refraction by difference frequency generation," Applied Physics Letters, Vol. 108, No. 19, 191101, 2016.
doi:10.1063/1.4948974        Google Scholar

144. Xu, Xiaoyi, Pengcheng Chen, Taxue Ma, Jianan Ma, Chao Zhou, Yawen Su, Mingxin Lv, Weiwen Fan, Bohan Zhai, Yuyang Sun, et al. "Large field-of-view nonlinear holography in lithium niobate," Nano Letters, Vol. 24, No. 4, 1303-1308, 2024.
doi:10.1021/acs.nanolett.3c04286        Google Scholar

145. Shen, Feiyang, Weiwen Fan, Yong Zhang, Xianfeng Chen, and Yuping Chen, "3D orbital angular momentum nonlinear holography," Advanced Optical Materials, Vol. 13, No. 9, 2402836, 2025.
doi:10.1002/adom.202402836        Google Scholar

146. Chen, Yi-Zhe, Ding Yan, Tong Qi, Xiang-Wei Wang, and Wei Gao, "Observation of spatial differentiation in structured nonlinear optics," Laser & Photonics Reviews, Vol. 19, No. 20, e00595, 2025.
doi:10.1002/lpor.202500595        Google Scholar

147. Sun, Xuhui, Hao Wu, Bing Gao, Chenglong Wang, Yibing Ma, Xuhao Hong, Chao Zhang, Yiqiang Qin, and Yongyuan Zhu, "Observation of ferroelectric domain walls using nonlinear spiral interferometry," Applied Physics Letters, Vol. 125, No. 7, 071111, 2024.
doi:10.1063/5.0201387        Google Scholar

148. Wang, Cheng, Zhaoyi Li, Myoung-Hwan Kim, Xiao Xiong, Xi-Feng Ren, Guang-Can Guo, Nanfang Yu, and Marko Lončar, "Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides," Nature Communications, Vol. 8, No. 1, 2098, 2017.
doi:10.1038/s41467-017-02189-6        Google Scholar

149. Dutt, Avik, Aseema Mohanty, Alexander L. Gaeta, and Michal Lipson, "Nonlinear and quantum photonics using integrated optical materials," Nature Reviews Materials, Vol. 9, No. 5, 321-346, 2024.
doi:10.1038/s41578-024-00668-z        Google Scholar

150. Gao, Jiannan, Maria Antonietta Vincenti, Jesse Frantz, Anthony Clabeau, Xingdu Qiao, Liang Feng, Michael Scalora, and Natalia M. Litchinitser, "Near-infrared to ultra-violet frequency conversion in chalcogenide metasurfaces," Nature Communications, Vol. 12, No. 1, 5833, 2021.
doi:10.1038/s41467-021-26094-1        Google Scholar

151. Zheng, Ze, Daria Smirnova, Gabriel Sanderson, Ying Cuifeng, Demosthenes C. Koutsogeorgis, Lujun Huang, Zixi Liu, Rupert Oulton, Arman Yousefi, Andrey E. Miroshnichenko, et al. "Broadband infrared imaging governed by guided-mode resonance in dielectric metasurfaces," Light: Science & Applications, Vol. 13, No. 1, 249, 2024.
doi:10.1038/s41377-024-01535-w        Google Scholar

152. Gao, J., H. Barati Sedeh, D. Tsvetkov, D. G. Pires, M. A. Vincenti, Y. Xu, I. Kravchenko, R. George, M. Scalora, L. Feng, et al. "Topology-imprinting in nonlinear metasurfaces," Science Advances, Vol. 11, No. 24, eadv5190, 2025.
doi:10.1126/sciadv.adv5190        Google Scholar

153. Vabishchevich, Polina and Yuri Kivshar, "Nonlinear photonics with metasurfaces," Photonics Research, Vol. 11, No. 2, B50-B64, 2023.
doi:10.1364/prj.474387        Google Scholar

154. Yesharim, O., S. Izhak, and A. Arie, "Pseudo-spin light circuits in nonlinear photonic crystals," Nature Communications, Vol. 16, No. 1, 6508, 2025.
doi:10.1038/s41467-025-61918-4        Google Scholar

155. Autere, Anton, Henri Jussila, Yunyun Dai, Yadong Wang, Harri Lipsanen, and Zhipei Sun, "Nonlinear optics with 2D layered materials," Advanced Materials, Vol. 30, No. 24, 1705963, 2018.
doi:10.1002/adma.201705963        Google Scholar

156. Norden, T., L. M. Martinez, N. Tarefder, K. W. Kwock, L. M. McClintock, N. Olsen, L. N. Holtzman, J. H. Yeo, L. Zhao, X. Zhu, et al. "Twisted nonlinear optics in monolayer van der Waals crystals," ACS Nano, Vol. 19, No. 34, 30919-30929, 2025.
doi:10.1021/acsnano.5c06908        Google Scholar

157. Dang, Junhui, Dajiang Mei, and Yuandong Wu, "Review of growth method for typical nonlinear optical crystal," Journal of Synthetic Crystals, Vol. 49, No. 7, 1308, 2020.        Google Scholar

158. Borghi, M., C. Castellan, S. Signorini, A. Trenti, and L. Pavesi, "Nonlinear silicon photonics," Journal of Optics, Vol. 19, No. 9, 093002, 2017.
doi:10.1088/2040-8986/aa7a6d        Google Scholar

159. Shen, D., J. Cao, and W. Wan, "Wavefront shaping with nonlinear four-wave mixing," Scientific Reports, Vol. 13, No. 1, 2750, 2023.
doi:10.1038/s41598-023-29621-w        Google Scholar

160. Keren-Zur, Shay, Lior Michaeli, Haim Suchowski, and Tal Ellenbogen, "Shaping light with nonlinear metasurfaces," Advances in Optics and Photonics, Vol. 10, No. 1, 309-353, 2018.
doi:10.1364/aop.10.000309        Google Scholar

161. Santiago-Cruz, T., S. D. Gennaro, O. Mitrofanov, S. Addamane, J. Reno, I. Brener, and M. V. Chekhova, "Resonant metasurfaces for generating complex quantum states," Science, Vol. 377, No. 6609, 991-995, 2022.
doi:10.1126/science.abq8684        Google Scholar

162. Dekkers, Kiki, Mwezi Koni, Vagharshak Hakobyan, Sachleen Singh, Jonathan Leach, Etienne Brasselet, Isaac Nape, and Andrew Forbes, "Wavelength-adaptive spin-orbit orbital angular momentum management in three-wave mixing," Journal of Optics, Vol. 27, No. 11, 115501, 2025.
doi:10.1088/2040-8986/ae184b        Google Scholar

163. Bashan, Gil, Avishay Eyal, Moshe Tur, and Ady Arie, "Optically programable quasi phase matching in four-wave mixing," Nature Communications, Vol. 16, No. 1, 6855, 2025.
doi:10.1038/s41467-025-62025-0        Google Scholar

164. Vasilets, V. N., A. V. Kuznetsov, and V. I. Sevastianov, "Vacuum ultraviolet treatment of polyethylene to change surface properties and characteristics of protein adsorption," Journal of Biomedical Materials Research Part A: An Official Journal of The Society for Biomaterials, The Japanese Society for Biomaterials, and The Australian Society for Biomaterials and the Korean Society for Biomaterials, Vol. 69, No. 3, 428-435, 2004.
doi:10.1002/jbm.a.30005        Google Scholar

165. Mao, Y., D. Zhao, S. Yan, H. Zhang, J. Li, K. Han, X. Xu, C. Guo, L. Yang, C. Zhang, et al. "A vacuum ultraviolet laser with a submicrometer spot for spatially resolved photoemission spectroscopy," Light: Science & Applications, Vol. 10, No. 1, 22, 2021.
doi:10.1038/s41377-021-00463-3        Google Scholar

166. Wang, J., Z. Wang, F. Liu, L. Cai, J.-b. Pan, Z. Li, S. Zhang, H.-Y. Chen, X. Zhang, and Y. Mo, "Vacuum ultraviolet laser desorption/ionization mass spectrometry imaging of single cells with submicron craters," Analytical Chemistry, Vol. 90, No. 16, 10 009-10 015, 2018.
doi:10.1021/acs.analchem.8b02478        Google Scholar

167. Semmlinger, M., M. L. Tseng, J. Yang, M. Zhang, C. Zhang, W.-Y. Tsai, D. P. Tsai, P. Nordlander, and N. J. Halas, "Vacuum ultraviolet light-generating metasurface," Nano Letters, Vol. 18, No. 9, 5738-5743, 2018.
doi:10.1021/acs.nanolett.8b02346        Google Scholar

168. Tseng, M. L., M. Semmlinger, M. Zhang, C. Arndt, T.-T. Huang, J. Yang, H. Y. Kuo, V.-C. Su, M. K. Chen, C. H. Chu, et al. "Vacuum ultraviolet nonlinear metalens," Science Advances, Vol. 8, No. 16, eabn5644, 2022.
doi:10.1126/sciadv.abn5644        Google Scholar

169. Reintjes, J. and R. C. Eckardt, "Efficient harmonic generation from 532 to 266 nm in ADP and KD*P," Applied Physics Letters, Vol. 30, No. 2, 91-93, 1977.
doi:10.1063/1.89300        Google Scholar

170. Sakuma, Jun, Yuichi Asakawa, and Minoru Obara, "Generation of 5-W deep-UV continuous-wave radiation at 266 nm by an external cavity with a CsLiB6O10 crystal," Optics Letters, Vol. 29, No. 1, 92-94, 2004.
doi:10.1364/ol.29.000092        Google Scholar

171. Zhang, Jin-Wei, Hai-Nian Han, Lei Hou, Long Zhang, Zi-Jiao Yu, De-Hua Li, and Zhi-Yi Wei, "Frequency doubled femtosecond Ti:sapphire laser with an assisted enhancement cavity," Chinese Physics B, Vol. 25, No. 1, 014205, 2016.
doi:10.1088/1674-1056/25/1/014205        Google Scholar

172. Ghorui, Chandan, A. M. Rudra, Udit Chatterjee, A. K. Chaudhary, and D. Ganesh, "Efficient second-harmonic and terahertz generation from single BiB3O6 crystal using nanosecond and femtosecond lasers," Applied Optics, Vol. 60, No. 19, 5643-5651, 2021.
doi:10.1364/AO.424241        Google Scholar

173. Kang, Lei, Huaguang Bao, and Douglas H. Werner, "Efficient second-harmonic generation in high Q-factor asymmetric lithium niobate metasurfaces," Optics Letters, Vol. 46, No. 3, 633-636, 2021.
doi:10.1364/ol.413764        Google Scholar

174. Liu, Sheng, Michael B. Sinclair, Sina Saravi, Gordon A. Keeler, Yuanmu Yang, John Reno, Gregory M. Peake, Frank Setzpfandt, Isabelle Staude, Thomas Pertsch, and Igal Brener, "Resonantly enhanced second-harmonic generation using III-V semiconductor all-dielectric metasurfaces," Nano Letters, Vol. 16, No. 9, 5426-5432, 2016.
doi:10.1021/acs.nanolett.6b01816        Google Scholar

175. Vabishchevich, Polina P., Sheng Liu, Michael B. Sinclair, Gordon A. Keeler, Gregory M. Peake, and Igal Brener, "Enhanced second-harmonic generation using broken symmetry III-V semiconductor Fano metasurfaces," ACS Photonics, Vol. 5, No. 5, 1685-1690, 2018.
doi:10.1021/acsphotonics.7b01478        Google Scholar

176. Li, Junhao, Guangwei Hu, Lina Shi, Nan He, Daqian Li, Qiuyu Shang, Qing Zhang, Huange Fu, Linlin Zhou, Wei Xiong, et al. "Full-color enhanced second harmonic generation using rainbow trapping in ultrathin hyperbolic metamaterials," Nature Communications, Vol. 12, No. 1, 6425, 2021.
doi:10.1038/s41467-021-26818-3        Google Scholar

177. Brown, Andrew J. W., Mark S. Bowers, Ken W. Kangas, and Charles H. Fisher, "High-energy, high-efficiency second-harmonic generation of 1064-nm radiation in KTP," Optics Letters, Vol. 17, No. 2, 109-111, 1992.
doi:10.1364/ol.17.000109        Google Scholar

178. Kumar, S. Chaitanya, G. K. Samanta, Kavita Devi, and M. Ebrahim-Zadeh, "High-efficiency, multicrystal, single-pass, continuous-wave second harmonic generation," Optics Express, Vol. 19, No. 12, 11152-11169, 2011.
doi:10.1364/oe.19.011152        Google Scholar

179. Liu, Hua-Yu, Zi-Han Zhou, Qi Bian, Yong Bo, Yang Kou, Lei Yuan, Da-Fu Cui, and Qin-Jun Peng, "High-efficiency nanosecond green laser based on extra-cavity second-harmonic generation of a Nd:YAG MOPA system," IEEE Photonics Journal, Vol. 15, No. 5, 1-5, 2023.
doi:10.1109/jphot.2023.3309390        Google Scholar

180. Gwo, Shangjr, Chun-Yuan Wang, Hung-Ying Chen, Meng-Hsien Lin, Liuyang Sun, Xiaoqin Li, Wei-Liang Chen, Yu-Ming Chang, and Hyeyoung Ahn, "Plasmonic metasurfaces for nonlinear optics and quantitative SERS," ACS Photonics, Vol. 3, No. 8, 1371-1384, 2016.
doi:10.1021/acsphotonics.6b00104        Google Scholar

181. Suntsov, Sergiy, Christian E. Rüter, Dominik Brüske, and Detlef Kip, "Watt-level 775 nm SHG with 70% conversion efficiency and 97% pump depletion in annealed/reverse proton exchanged diced PPLN ridge waveguides," Optics Express, Vol. 29, No. 8, 11386-11393, 2021.
doi:10.1364/oe.416723        Google Scholar

182. Gili, V. F., L. Carletti, A. Locatelli, D. Rocco, M. Finazzi, L. Ghirardini, I. Favero, C. Gomez, A. Lemaître, M. Celebrano, C. de Angelis, and G. Leo, "Monolithic AlGaAs second-harmonic nanoantennas," Optics Express, Vol. 24, No. 14, 15965-15971, 2016.
doi:10.1364/oe.24.015965        Google Scholar

183. Fedotova, Anna, Mohammadreza Younesi, Jürgen Sautter, Aleksandr Vaskin, Franz J. F. Löchner, Michael Steinert, Reinhard Geiss, Thomas Pertsch, Isabelle Staude, and Frank Setzpfandt, "Second-harmonic generation in resonant nonlinear metasurfaces based on lithium niobate," Nano Letters, Vol. 20, No. 12, 8608-8614, 2020.
doi:10.1021/acs.nanolett.0c03290        Google Scholar

184. Yuan, Shuai, Yunkun Wu, Zhongzhou Dang, Cheng Zeng, Xiaozhuo Qi, Guangcan Guo, Xifeng Ren, and Jinsong Xia, "Strongly enhanced second harmonic generation in a thin film lithium niobate heterostructure cavity," Physical Review Letters, Vol. 127, No. 15, 153901, 2021.
doi:10.1103/physrevlett.127.153901        Google Scholar

185. Tu, Xu, Siqi Feng, Jiajun Li, Yangguang Xing, Feng Wu, Tingting Liu, and Shuyuan Xiao, "Enhanced second-harmonic generation in high-Q all-dielectric metasurfaces with backward frequency conversion," Physical Review A, Vol. 109, No. 6, 063522, 2024.
doi:10.1103/PhysRevA.109.063522        Google Scholar

186. Hu, B., X. Yang, J. Wu, S. Lu, H. Yang, Z. Long, L. He, X. Luo, K. Tian, W. Wang, et al. "Highly efficient octave-spanning long-wavelength infrared generation with a 74% quantum efficiency in a χ(2) waveguide," Nature Communications, Vol. 14, No. 1, 7125, 2023.
doi:10.1038/s41467-023-42912-0        Google Scholar