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Harmonics generated in circularly polarized laser fields: a study on spin angular momentum conservation

  • Regular Article – Atomic Physics
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Abstract

Harmonics generated from the electronic transition among continuum states are studied by a quantum scattering theory. The analytical formulas of the harmonics generated in one- and two-color circularly polarized (CP) laser fields are obtained rigorously. The harmonic generation amplitude is described by a pair of phased generalized Bessel functions, by which the conservation relations of the spin angular momentum are derived in a solid base and in a straightforward way. It is found that, owing to the spin angular momentum conservation, high-order harmonics cannot be generated in the one-color CP fields, but can be generated in the bichromatic CP fields. To a given harmonic order, two generation channels exist: one generates right CP harmonic, while the other generates left CP harmonic. When the driving CP modes are of opposite helicity, the generated right CP harmonic is of the comparable strength to the left CP harmonic. When the driving CP modes are of same helicity, the harmonic with the same helicity as the driving fields is much stronger than that with the opposite helicity to the driving fields. The selection rules of harmonics are different in these two kinds of bichromatic CP driving fields.

Graphic Abstract

Figure depicts the calculated harmonic spectra generated from Ar atoms. For the counter-rotating driving fields, the harmonic spectra exhibit clear plateau and sharp cutoff structures, for both the right and left CP harmonics. The right CP harmonics are of 3n-1 series in order, while the left CP harmonics are of 3n+1 series in order. Generally, the right CP harmonics are stronger than the adjacent left CP harmonics. For the co-rotating driving fields, the harmonic rate decreases fast as the harmonic order increases, thus the plateau and the cutoff structures are not clear as their counterparts in the previous case, for both right CP and left CP harmonics. The harmonic spectra change continuously in order. Each harmonic order has its right CP and left CP components, but generally, the left CP components are much smaller than the right CP components. It is also clear that the harmonics generated from counter-rotating BCP fields are much stronger than that generated from co-rotating BCP fields.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The associated data in this manuscript can be gotten from corresponding author.]

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Acknowledgements

This work is supported by Chinese National Natural Science Foundation under Grant No. 12074261 and No.11674231, and Shanghai Natural Science Foundation under Grant No. 20ZR1441600.

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Authors and Affiliations

  1. Department of Physics, Shanghai Normal University, Shanghai, 200234, China

    Jingtao Zhang

  2. International School for Optoelectronic Engineering, QiLu University of Technology (Shandong Academy of Science), Shandong, 250353, China

    Xianghe Ren

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  1. Jingtao Zhang
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  2. Xianghe Ren
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Contributions

JTZ and XHR discussed the theoretical method. Z wrote the manuscript. XHR performed the simulations.

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Correspondence to Xianghe Ren.

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Zhang, J., Ren, X. Harmonics generated in circularly polarized laser fields: a study on spin angular momentum conservation. Eur. Phys. J. D 77, 17 (2023). https://doi.org/10.1140/epjd/s10053-023-00595-8

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