Size-Dependent High-Order Harmonic Generation from Linear Carbon-Chain Molecules in Linearly Polarized Laser Fields

The gist The results show that increasing molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region in linear carbon-chain molecules C2H2, C6H2, and C10H2 driven by an 800 nm linearly polarized laser field.

Molecular System Investigation

This work systematically investigates the influence of molecular chain length on high-order harmonic generation (HHG) from linear carbon-chain molecules C2H2, C6H2, and C10H2 driven by an 800 nm linearly polarized laser field The research isolates the molecular-size effect from ionization potential influences by adjusting laser intensities to maintain the same Keldysh parameter for different molecules Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction

Key Findings on Chain Length Dependence

The study reveals that increasing molecular size enhances harmonic emission, with C10H2 exhibiting much stronger plateau harmonics than C2H2 The intermediate molecule C6H2 shows harmonic intensities between those of C2H2 and C10H2 Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms

Mechanisms Behind Enhanced Emission

The enhanced HHG from C10H2 is closely related to its extended molecular backbone, which provides a larger spatial region for electron acceleration along the laser polarization direction and introduces additional atomic centers for possible recombination or scattering This multi-center recollision process increases the efficiency of harmonic emission and contributes to the observed enhancement in the plateau region The dominant harmonic emission occurs during the main recollision time window, accompanied by strong charge oscillations and electron localization near the terminal carbon atoms for C10H2

Influence of Laser Intensity

The study calculated HHG spectra of C2H2 and C10H2 at different field strengths to examine robustness against laser intensity variations At relatively weak fields, the difference between C2H2 and C10H2 is modest, indicating that the molecular-size effect is not yet fully developed As the laser intensity increases, the harmonic emission from C10H2 becomes increasingly stronger than that from C2H2, especially in the plateau and high-energy regions This trend demonstrates that the size-dependent enhancement is more pronounced in stronger laser fields

Theoretical Framework

Time-dependent density functional theory (TDDFT) is employed to simulate the strong-field electron dynamics and harmonic emission The TDDFT method is based on solving the time-dependent Kohn–Sham equations for orbitals ψi(r, t) The external potential from the laser field is expressed as Vlaser(r, t) = r · E(t), where E(t) is the linearly polarized electric field The harmonic spectrum is derived from the time-dependent dipole acceleration a(t)

Conclusion

The results demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems The enhanced HHG in longer chains is closely associated with electron localization and strong charge oscillations near the terminal carbon atoms, thereby improving harmonic emission efficiency These findings establish a clear relationship between molecular size and HHG efficiency This work demonstrates that molecular-size engineering is an effective strategy for controlling HHG in extended molecular systems and may provide useful guidance for developing intense attosecond light sources The results show that the harmonic yield increases with molecular chain length and that terminal carbon atoms contribute strongly to the enhanced emission

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Size-Dependent High-Order Harmonic Generation from Linear Carbon-Chain Molecules in Linearly Polarized Laser Fields Yifan Kang, Yang Yang, Yingtan Li, Shuwen Pang, Huiwen Yang, Yingdan Zhang, and Shushan Zhou∗ School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China High-order harmonic generation from molecules is highly sensitive to molecular geometry and strong-field electron dynamics In this work we systematically investigate the influence of molecular chain length on HHG from linear carbon-chain molecules C2H2, C6H2, and C10H2 driven by an 800 nm linearly polarized laser field To isolate the molecular-size effect from the influence of different ionization potentials the laser intensities are adjusted to maintain the same Keldysh parameter for different molecules Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction The results show that increasing the molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region In particular C10H2 exhibits much stronger plateau harmonics than C2H2 while the intermediate molecule C6H2 shows harmonic intensities between those of C2H2 and C10H2 Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms These findings demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems Keywords High-order harmonic generation; Linear carbon-chain molecules; Molecular size dependence; Time-dependent density functional theory.

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FIG. 1 Schematic illustration of the molecular orientation with respect to the linearly polarized laser field The molecular axes of C2H2, C6H2, and C10H2 are aligned along the z axis parallel to the laser polarization direction The molecular lengths are 3.15 a.u., 8.01 a.u., and 12.87 a.u., respectively

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Laser early polarized laser field The molecular axis is aligned parallel to the laser polarization direction and the laser intensity is chosen to maintain the same Keldysh parameter for different molecules Time-dependent density functional theory (TDDFT) is employed to simulate the strong-field electron dynamics and harmonic emission By comparing the harmonic spectra timefrequency distributions and charge-density evolution we clarify how molecular chain length affects harmonic yield and cutoff behavior Our results show that increasing molecular size can significantly enhance the harmonic intensity and promote cutoff extension mainly due to the enlarged electron acceleration distance and enhanced multi-center recollision probability.

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Figure 2 HHG spectra of C2H2 and C10H2 driven by an 800 nm linearly polarized laser field The molecular axis is parallel to the laser polarization direction as shown in Fig. 1 The electric-field amplitude is 0.057 a.u. for C10H2 and 0.073 a.u. for C2H2 corresponding to the same Keldysh parameter γ = 0.724 The laser pulse has a trapezoidal envelope with a one-cycle ramp-on a four-cycle plateau and a one-cycle ramp-off wavelength is fixed at 800 nm and the molecular axis is parallel to the laser polarization direction

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FIG. 3 Time-frequency analysis and charge-density evolution for C2H2 and C10H2 (a,b) HHG spectra and directional components (c,d) Time-frequency distributions of the HHG spectra where the dashed lines mark the main harmonic emission times For C10H2 pronounced harmonic emission occurs during the main recollision time window Around these emission times strong charge oscillations and electron localization are observed near the terminal carbon atoms This indicates that the terminal regions of the long carbon chain play an important role in the HHG process In contrast for C2H2 the charge redistribution is spatially more confined and the electron acceleration distance is much shorter As a result the recollision probability and harmonic yield are both reduced

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FIG. 5 (a) Comparison of HHG spectra from C2H2, C6H2, and C10H2 under the same Keldysh parameter (b) Timefrequency analysis of HHG from C6H2 where the dashed line marks the main harmonic emission time (c) Time-dependent charge variation around representative atomic centers in C6H2 near the main emission time The results show that the harmonic yield increases with molecular chain length and that terminal carbon atoms contribute strongly to the enhanced emission

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FIG. 4 HHG spectra of C2H2 and C10H2 under linearly polarized laser fields with different intensities For each panel the laser amplitudes are chosen to maintain the same Keldysh parameter for the two molecules The results show that the harmonic yield of C10H2 becomes increasingly stronger than that of C2H2 as the field strength increases Notably as illustrated in Fig. 4a under relatively low field strengths the harmonic spectra of C10H2 and C2H2 exhibit almost no discernible difference

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FIG.

1. The AI system can perform molecular size-dependent HHG prediction by simulating the influence of molecular chain length on HHG from linear carbon-chain molecules C2H2, C6H2, and C10H2 by utilizing time-dependent density functional theory (TDDFT) simulations.

2. The improved AI can predict the enhancement of harmonic yield and cutoff extension by linking the enhanced HHG emission in longer chains from the enlarged electron acceleration distance and increased probability of multi-center recollision.

3. The system can optimize attosecond light source design by using the findings that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems.