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The study of high-order harmonic generation (HHG) in confined quantum systems is essential for developing a comprehensive physical description of harmonic generation from atoms to bulk solids. Using the time-dependent density-functional theory, we demonstrate how the symmetry of the system modulates the generation of high-order harmonic in fullerene C60 molecules along different orthogonal directions, as well as the effects of amplitude and photon energy of a linearly polarized laser on high-order harmonics generation. We found that the generation of high-order harmonics perpendicular to the laser polarization direction (LPD) is related to the symmetry of molecules along the LPD and the symmetry of molecules perpendicular to the LPD. Within a certain parameter range, the cut-off energy is linearly proportional to the laser amplitude and the laser photon energy. [ABSTRACT FROM AUTHOR]

Previous studies have found that pure even harmonics are generated from oriented CO molecules in linearly polarized laser fields. In this work, we demonstrate multi-directions pure even harmonic simultaneous generation from planar molecules in linearly polarized laser fields using the time-dependent density-functional theory. The analysis reveals that pure even harmonic generation depends on the special symmetry of the planar molecule. In the linearly polarized laser field, it is found that only when the planar molecules have reflective symmetry direction and the molecules perpendicular to the reflective symmetry direction do not have reflection symmetry can the planar molecules generate pure even harmonics along such reflective symmetry direction. When the laser polarization is perpendicular to the planar molecule, if the molecule has several these directions of such reflection symmetry, pure even harmonics will be simultaneously generated along these symmetrical directions. Moreover, when the laser polarization is along the molecular plane and perpendicular to the direction of one such reflection symmetry, even harmonic is also generated along this reflection symmetry direction, whereas odd harmonic is generated along the direction of laser polarization. The phenomenon exists in all polyatomic planar molecules with such reflection symmetry. [ABSTRACT FROM AUTHOR]