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High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum Jγ, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge Jγ of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum., We thank T. Ruchon for helpful observations. E. P. acknowledges Cellex-ICFO-MPQ fellowship funding; E. P. and M. L. acknowledge the Spanish Ministry MINECO (National Plan 15 Grants: FISICATEAMO No. FIS2016-79508-P, SEVERO OCHOA No. SEV-2015-0522, FPI), European Social Fund, Fundació Cellex, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR1341 and CERCA/Program), ERC AdG OSYRIS, EU FETPRO QUIC, and the National Science Centre, Poland-Symfonia Grant No. 2016/20/W/ST4/00314. A. P. acknowledges funding from Comunidad de Madrid through TALENTO Grant No. 2017-T1/IND-5432. J. S. R., L. P., and C. H.-G acknowledge support from Junta de Castilla y León (SA046U16) and Ministerio de Economía y Competitividad (FIS2013-44174-P, FIS2016-75652-P). C. H.-G. acknowledges support from a 2017 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation and Ministerio de Ciencia, Innovación y Universidades for a Ramón y Cajal contract (RYC-2017-22745), co-funded by the European Social Fund. L. R. acknowledges support from Ministerio de Educación, Cultura y Deporte (FPU16/02591). H. C. K. and M.M.M. acknowledge support from the Department of Energy BESAwardNo.DE-FG02–99ER14982, as well as aDARPATEE Award No. D18AC00017. We thankfully acknowledge thecomputer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-AECT-2014-2-0085). This research made use of the high-performance computing resources of the Castilla yLeón Supercomputing Center (SCAYLE), financed by the European Regional Development Fund (ERDF).

High-order harmonic generation (HHG) has been recently proven to produce extreme-ultraviolet (XUV) vortices from the nonlinear conversion of infrared twisted beams. Previous works have demonstrated a linear scaling law of the vortex charge with the harmonic order. We demonstrate that this simple law hides an unexpectedly rich scenario for the buildup of orbital angular momentum (OAM) due to the nonperturbative behavior of HHG. The complexity of these twisted XUV beams appears only when HHG is driven by nonpure vortex modes, where the XUV OAM content is dramatically increased. We explore the underlying mechanisms for this diversity and derive a general conservation rule for the nonperturbative OAM buildup. The simple scaling found in previous works corresponds to the collapse of this scenario for the particular case of pure (single-mode) OAM driving fields., C.H.-G. acknowledges support by a Marie Curie International Outgoing Fellowship within the EU Seventh Framework Programme for Research and Technological Development (2007–2013), under REA Grant Agreement No. 328334. We acknowledge support from Junta de Castilla y León (Projects No. SA116U13 and No. SA046U16) and Ministerio de Economía y Competitividad (FIS2013-44174- P, FIS2016-75652-P). A. P. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Contract No. DE-AC02- 06CH11357.

We study vibrational excitations, dissociation, and ionization of H(2)(+) in few-cycle laser pulses over a broad wavelength regime. Our results of numerical simulations supported by model calculations show a many orders-of-magnitude enhancement of vibrational excitation and dissociation (over ionization) of the molecular ion at infrared wavelengths. The enhancement occurs without any chirping of the pulse, which was previously applied to take account of the anharmonicity of the molecular vibrations. The effect is related to strong-field two- and higher-order photon transitions between different vibrational states.