Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy
In two-color strong field ionization of atoms, dynamical characteristics such as ionization rate and electron trajectory depend heavily on the relative phase of the strong fundamental field and its second harmonic. The phase-of-the-phase spectroscopy method reveals the oscillation of the photoelectr...
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| Format: | Article |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/24/4642 |
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| author | Xunqin Huo Weifeng Yang Facheng Jin Shuai Ben Xiaohong Song |
| author_facet | Xunqin Huo Weifeng Yang Facheng Jin Shuai Ben Xiaohong Song |
| author_sort | Xunqin Huo |
| collection | DOAJ |
| description | In two-color strong field ionization of atoms, dynamical characteristics such as ionization rate and electron trajectory depend heavily on the relative phase of the strong fundamental field and its second harmonic. The phase-of-the-phase spectroscopy method reveals the oscillation of the photoelectron momentum distribution with the relative phase of the two-color field, and the relative phase contrast and its phase are usually obtained by the fitting process. Instead, we apply the generalized Bessel function to the strong field approximation and derive analytical expressions for the first- and second-order relative phase contrast and phase-of-the-phase spectra. Our analytical results are in good agreement with fitting-based ones, but calculating them is much less computationally intensive. We illustrate the advantage of using generalized Bessel functions in two-color phase-of-the-phase spectroscopy of argon. |
| first_indexed | 2024-03-09T16:08:01Z |
| format | Article |
| id | doaj.art-4b72a749829049738cff0987ac90c36f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:08:01Z |
| publishDate | 2022-12-01 |
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| spelling | doaj.art-4b72a749829049738cff0987ac90c36f2023-11-24T16:27:13ZengMDPI AGMathematics2227-73902022-12-011024464210.3390/math10244642Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase SpectroscopyXunqin Huo0Weifeng Yang1Facheng Jin2Shuai Ben3Xiaohong Song4Institute of Mathematics, College of Science, Shantou University, Shantou 515063, ChinaSchool of Science and Center for Theoretical Physics, Hainan University, Haikou 570228, ChinaInstitute of Mathematics, College of Science, Shantou University, Shantou 515063, ChinaSchool of Science and Center for Theoretical Physics, Hainan University, Haikou 570228, ChinaSchool of Science and Center for Theoretical Physics, Hainan University, Haikou 570228, ChinaIn two-color strong field ionization of atoms, dynamical characteristics such as ionization rate and electron trajectory depend heavily on the relative phase of the strong fundamental field and its second harmonic. The phase-of-the-phase spectroscopy method reveals the oscillation of the photoelectron momentum distribution with the relative phase of the two-color field, and the relative phase contrast and its phase are usually obtained by the fitting process. Instead, we apply the generalized Bessel function to the strong field approximation and derive analytical expressions for the first- and second-order relative phase contrast and phase-of-the-phase spectra. Our analytical results are in good agreement with fitting-based ones, but calculating them is much less computationally intensive. We illustrate the advantage of using generalized Bessel functions in two-color phase-of-the-phase spectroscopy of argon.https://www.mdpi.com/2227-7390/10/24/4642photoelectron momentum distributionstrong field approximationphase-of-the phasegeneralized Bessel function |
| spellingShingle | Xunqin Huo Weifeng Yang Facheng Jin Shuai Ben Xiaohong Song Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy Mathematics photoelectron momentum distribution strong field approximation phase-of-the phase generalized Bessel function |
| title | Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy |
| title_full | Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy |
| title_fullStr | Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy |
| title_full_unstemmed | Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy |
| title_short | Application of the Generalized Bessel Function to Two-Color Phase-of-the-Phase Spectroscopy |
| title_sort | application of the generalized bessel function to two color phase of the phase spectroscopy |
| topic | photoelectron momentum distribution strong field approximation phase-of-the phase generalized Bessel function |
| url | https://www.mdpi.com/2227-7390/10/24/4642 |
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