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Journals >Chinese Optics Letters >Volume 15 >Issue 12 >Page 120202 > Article

Chinese Optics Letters
Vol. 15, Issue 12, 120202 (2017)

Electron vortices in photoionization by a pair of elliptically polarized attosecond pulses | Editors' Pick

Meng Li^1、2, Guizhong Zhang^1、*, Tianqi Zhao¹, Xin Ding¹, and Jianquan Yao¹

Author Affiliations

¹College of Precision Instrument and Optoelectronics Engineering, Tianjin University, Tianjin 300072, China

²Civil Aviation Meteorological Institute, Key Laboratory of Operation Programming & Safety Technology of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China

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DOI: 10.3788/COL201715.120202 Cite this Article Set citation alerts

Meng Li, Guizhong Zhang, Tianqi Zhao, Xin Ding, Jianquan Yao. Electron vortices in photoionization by a pair of elliptically polarized attosecond pulses[J]. Chinese Optics Letters, 2017, 15(12): 120202 Copy Citation Text

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Abstract

The photoionization by two elliptically polarized, time delayed attosecond pulses is investigated to display a momentum distribution having the helical vortex or ring structures. The results are obtained by the strong field approximation method and analyzed by the pulse decomposition. The ellipticities and time delay of the two attosecond pulses are found to determine the rotational symmetry and the number of vortex arms. For observing these vortex patterns, the energy bandwidth and temporal duration of the attosecond pulses are ideal.

F (t) = F_{1} (t) + F_{2} (t - τ), F_{i} (t) = I_{0} [\frac{1}{{(1 + η_{i}^{2})}^{0.5}} \cos (ω_{i} t + θ_{i}) \hat{x} + \frac{η_{i}}{{(1 + η_{i}^{2})}^{0.5}} \sin (ω_{i} t + θ_{i}) \hat{y}] \cos^{2} (π t / T) (- T / 2 < t < T / 2, i = 1, 2) .

(1)

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f (p⃗) = - i \int_{- \infty}^{\infty} d t^{'} \exp [i \int_{t^{'}}^{\infty} d t^{''} [I_{p} + \frac{{[p⃗ + A⃗]}^{2}}{2}]] d⃗ (p⃗) \cdot E⃗,

(2)

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d⃗ (p⃗) = \frac{2^{3.5} \times {(2 I_{p})}^{5 / 4}}{π} [p⃗ / {({p⃗}^{2} + 2 I_{p})}^{3}] .

(3)

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| ψ_{8} 〉 \propto e^{- i τ E / ℏ} | f, - 4 〉 + | f, 4 〉 .

(4)

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{\begin{cases} - 1 < η_{1}, η_{2} < 1 \\ η_{1} \cdot η_{2} < 0 \\ η_{1} = - η_{2} \end{cases},

(5)

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F_{i} (t) = F_{i}^{lin} (t) + F_{i}^{cir} (t) (- T / 2 < t < T / 2), F_{i}^{lin} (t) = E_{0} [\frac{1 - η_{i}}{{(1 + η_{i}^{2})}^{0.5}} \cos (ω_{i} t + θ_{i}) \hat{x}] \cos^{2} (π t / T) (- T / 2 < t < T / 2), F_{i}^{cir} (t) = E_{0} \frac{η_{i}}{{(1 + η_{i}^{2})}^{0.5}} [\cos (ω_{i} t + θ_{i}) \hat{x} + \sin (ω_{i} t + θ_{i}) \hat{y}] \cos^{2} (π t / T) (- T / 2 < t < T / 2) .

(6)

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{\begin{cases} - 1 < η_{1}, η_{2} < 1 \\ η_{1} \cdot η_{2} < 0 \\ η_{1} \neq - η_{2} \end{cases} .

(7)

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F (t) = F_{i}^{eq} (t) + F_{i}^{lin} (t) (i = 1, 2), F_{1}^{eq} (t) = F_{1} (t) + F_{1} (t - τ), F_{1}^{lin} (t) = F_{2} (t - τ) - F_{1} (t - τ), F_{2}^{eq} (t) = F_{2} (t) + F_{2} (t - τ), F_{2}^{lin} (t) = F_{1} (t) - F_{2} (t) .

(8)

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| ψ 〉 \propto e^{- i τ E / ℏ} | g, - 4 〉 + | g, - 4 〉 .

(9)

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{\begin{cases} - 1 < η_{1}, η_{2} < 1 \\ η_{1} \cdot η_{2} > 0 \end{cases},

(10)

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References (32)

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Meng Li, Guizhong Zhang, Tianqi Zhao, Xin Ding, Jianquan Yao. Electron vortices in photoionization by a pair of elliptically polarized attosecond pulses[J]. Chinese Optics Letters, 2017, 15(12): 120202

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