[1] [1] Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A. 1992;45(11):8185–8189.

[2] [2] Indebetouw G. Optical vortices and their propagation. J Mod Opt. 1993;40(1):73–87.

[3] [3] Soskin MS, Vasnetsov MV. Chapter 4—Singular optics. In: Wolf E, editor. Progress in optics. Netherlands: Elsevier; 2001, p. 219–276.

[4] [4] Polynkin P, Ament C, Moloney JV. Self-focusing of ultraintense femtosecond optical vortices in air. Phys Rev Lett. 2013;111(2): Article 023901.

[5] [5] Mendis BG. On the electron vortex beam wavefunction within a crystal. Ultramicroscopy. 2015;157:1–11.

[6] [6] Zhang X, Shen B, Zhang L, Xu J, Wang X, Wang W, Yi L, Shi Y. Proton acceleration in underdense plasma by ultraintense Laguerre–Gaussian laser pulse. New J Phys. 2014;16(12): Article 123051.

[7] [7] Stillhart M, Schneider A, Günter P. Optical properties of 4-N,N-dimethylamino-4′-N′-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate crystals at terahertz frequencies. J Opt Soc Am B. 2008;25(11):1914–1919.

[8] [8] Wang H, Song Q, Cai Y, Lin Q, Lu X, Shangguan H, Ai Y, Xu S. Recent advances in generation of terahertz vortex beams and their applications*. Chinese Physics B. 2020;29(9): Article 097404.

[9] [9] Hernández-García C, Picón A, San Román J, Plaja L. Attosecond extreme ultraviolet vortices from high-order harmonic generation. Phys Rev Lett. 2013;111(8): Article 083602.

[10] [10] Gauthier D, Ribič PR, Adhikary G, Camper A, Chappuis C, Cucini R, DiMauro LF, Dovillaire G, Frassetto F, Géneaux R, et al. Tunable orbital angular momentum in high-harmonic generation. Nat Commun. 2017;8(1):14971.

[11] [11] Rego L, Dorney KM, Brooks NJ, Nguyen QL, Liao C-T, San Román J, Couch DE, Liu A, Pisanty E, Lewenstein M, et al. Generation of extreme-ultraviolet beams with time-varying orbital angular momentum. Science. 2019;364(6447):eaaw9486.10.1126/science.aaw9486

[12] [12] Chen ZK, Zheng SQ, Lu XM, Wang XL, Cai Y, Wang CY, Zheng MJ, Ai YX, Leng YX, Xu SX, et al. Forty-five terawatt vortex ultrashort laser pulses from a chirped-pulse amplification system. High Power Laser Sci Eng. 2022;10.

[13] [13] Rego L, Dorney KM, Brooks NJ, Nguyen QL, Liao CT, San Roman J, Couch DE, Liu A, Pisanty E, Lewenstein M, et al. Generation of extreme-ultraviolet beams with time-varying orbital angular momentum. Science. 2019;364(6447):1253-+.

[14] [14] Geneaux R, Camper A, Auguste T, Gobert O, Caillat J, Taieb R, Ruchon T. Synthesis and characterization of attosecond light vortices in the extreme ultraviolet. Nat Commun. 2016;7(1):12583.

[15] [15] Kong FQ, Zhang CM, Bouchard F, Li ZY, Brown GG, Ko DH, Hammond TJ, Arissian L, Boyd RW, Karimi E, et al. Controlling the orbital angular momentum of high harmonic vortices. Nat Commun. 2017;8:14970.10.1038/ncomms14970

[16] [16] Takahashi EJ, Kanai T, Ishikawa KL, Nabekawa Y, Midorikawa K. Coherent water window X ray by phase-matched high-order harmonic generation in neutral media. Phys Rev Lett. 2008;101(25): Article 253901.

[17] [17] Kerber RM, Fitzgerald JM, Oh SS, Reiter DE, Hess O. Orbital angular momentum dichroism in nanoantennas. Commun Phys. 2018;1:87.

[18] [18] Zhou YY, Alam MZ, Karimi M, Upham J, Reshef O, Liu C, Willner AE, Boyd RW. Broadband frequency translation through time refraction in an epsilon-near-zero material. Nat Commun. 2020;11(1):2180.

[19] [19] Plansinis BW, Donaldson WR, Agrawal GP. What is the temporal analog of reflection and refraction of optical beams? Phys Rev Lett. 2015;115(18):183901.

[20] [20] Vezzoli S, Bruno V, DeVault C, Roger T, Shalaev VM, Boltasseva A, Ferrera M, Clerici M, Dubietis A, Faccio D. Optical time reversal from time-dependent epsilon-near-zero media. Phys Rev Lett. 2018;120(4):043902.

[21] [21] Tirole R, Vezzoli S, Galiffi E, Robertson I, Maurice D, Tilmann B, Maier SA, Pendry JB, Sapienza R. Double-slit time diffraction at optical frequencies. Nat Phys. 2023;19:999–1002.10.1038/s41567-023-01993-w

[22] [22] Reshef O, De Leon I, Alam MZ, Boyd RW. Nonlinear optical effects in epsilon-near-zero media. Nat Rev Mater. 2019;4(8):535–551.10.1038/s41578-019-0120-5

[23] [23] Kinsey N, DeVault C, Boltasseva A, Shalaev VM. Near-zero-index materials for photonics. Nat Rev Mater. 2019;4(12):742–760.10.1038/s41578-019-0133-0

[24] [24] Alam MZ, De Leon I, Boyd RW. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science. 2016;352(6287):795–797.10.1126/science.aae0330

[25] [25] Lustig E, Sharabi Y, Segev M. Topological aspects of photonic time crystals. Optica. 2018;5(11):1390–1395.10.1364/OPTICA.5.001390

[26] [26] Yamane K, Toda Y, Morita R. Ultrashort optical-vortex pulse generation in few-cycle regime. Opt Express. 2012;20(17):18986–18993.

[27] [27] Qian J, Peng Y, Li Y, Wang P, Shao B, Liu Z, Leng Y, Li R. Femtosecond mid-IR optical vortex laser based on optical parametric chirped pulse amplification. Photon Res. 2020;8(3):421–425.10.1364/PRJ.385190

[28] [28] Jeong Y-G, Piccoli R, Ferachou D, Cardin V, Chini M, Hadrich S, Limpert J, Morandotti R, Legare F, Schmidt BE, et al. Direct compression of 170-fs 50-cycle pulses down to 1.5 cycles with 70% transmission. Sci Rep. 2018;8:11794.10.1038/s41598-018-30198-y

[29] [29] Nagy T, Hadrich S, Simon P, Blumenstein A, Walther N, Klas R, Buldt J, Stark H, Breitkopf S, Jojart P, et al. Generation of three-cycle multi-millijoule laser pulses at 318 W average power. Optica. 2019;6(11):1423–1424.

[30] [30] Shumakova V, Malevich P, Ališauskas S, Voronin A, Zheltikov AM, Faccio D, Kartashov D, Baltuška A, Pugžlys A. Multi-millijoule few-cycle mid-infrared pulses through nonlinear self-compression in bulk. Nat Commun. 2016;7(1):12877.

[31] [31] Seidel M, Brons J, Arisholm G, Fritsch K, Pervak V, Pronin O. Efficient high-power ultrashort pulse compression in self-defocusing bulk media. Sci Rep. 2017;7(1):1410.

[32] [32] Cao HB, Nagymihaly RS, Kalashnikov M. Relativistic near-single-cycle optical vortex pulses from noble gas-filled multipass cells. Opt Lett. 2020;45(12):3240–3243.

[33] [33] Schulte J, Sartorius T, Weitenberg J, Vernaleken A, Russbueldt P. Nonlinear pulse compression in a multi-pass cell. Opt Lett. 2016;41(19):4511–4514.

[34] [34] Lu CH, Tsou YJ, Chen HY, Chen BH, Cheng YC, Yang SD, Chen MC, Hsu CC, Kung AH. Generation of intense supercontinuum in condensed media. Optica. 2014;1(6):400–406.10.1364/OPTICA.1.000400

[35] [35] Qian JY, Peng YJ, Li YY, Shao BJ, Liu Z, Li WK, Feng RY, Shen LY, Leng YX, Li RX. Few-cycle mid-infrared laser based on nonlinear self-compression in solid thin plates. Opt Lett. 2021;46(19):5075–5078.10.1364/OL.442105

[36] [36] Chen BH, Huang HW, Ye RS, Lu CH, Chen K, Yang SD. Vortex beam assisted energy up-scaling for multiple-plate compression with a single spiral phase plate. Opt Lett. 2022;47(17):4423–4426.

[37] [37] Li Y, Chen Y, Li W, Wang P, Shao B, Peng Y, Leng Y. Accurate characterization of mid-infrared ultrashort pulse based on second-harmonic-generation frequency-resolved optical gating. Opt Laser Technol. 2019;120: Article 105671.

[38] [38] Denisenko V, Shvedov V, Desyatnikov AS, Neshev DN, Krolikowski W, Volyar A, Soskin M, Kivshar YS. Determination of topological charges of polychromatic optical vortices. Opt Express. 2009;17(26):23374–23379.

[39] [39] Grier DG. A revolution in optical manipulation. Nature. 2003;424(6950):810–816.10.1038/nature01935

[40] [40] Curtis JE, Koss BA, Grier DG. Dynamic holographic optical tweezers. Opt Commun. 2002;207(1):169–175.

[41] [41] Qiao Z, Kong LC, Xie GQ, Qin ZP, Yuan P, Qian LJ, Xu XD, Xu J, Fan DY. Ultraclean femtosecond vortices from a tunable high-order transverse-mode femtosecond laser. Opt Lett. 2017;42(13):2547–2550.

[42] [42] Phillips RL, Andrews LC. Spot size and divergence for LAGUERRE GAUSSIAN beams of any order. Appl Opt. 1983;22(5):643–644.

[43] [43] Zelmon DE, Small DL, Page R. Refractive-index measurements of undoped yttrium aluminum garnet from 0.4 to 5.0 μm. Appl Opt. 1998;37(21):4933–4935.

[44] [44] Xu S, Qiu J, Jia T, Li C, Sun H, Xu Z. Femtosecond laser ablation of crystals SiO2 and YAG. Opt Commun. 2007;274(1):163–166.

[45] [45] Dubietis A, Tamosauskas G, Suminas R, Jukna V, Couairon A. Ultrafast supercontinuum generation in bulk condensed media. Lith J Phys. 2017;57(3):113–157.

[46] [46] Marburger JH. Self-focusing: theory. Prog Quant Electron. 1975;4:35–110.

[47] [47] Bergé L, Skupin S, Nuter R, Kasparian J, Wolf JP. Ultrashort filaments of light in weakly ionized, optically transparent media. Rep Prog Phys. 2007;70(10):1633.10.1088/0034-4885/70/10/R03

[48] [48] Xu L, Li D, Chang J, Li D, Xi T, Hao Z. Powerful supercontinuum vortices generated by femtosecond vortex beams with thin plates. Photon Res. 2022;10(3):802–809.