Quantum-orbit theory of low-energy above-threshold ionization on and off axis

W. Becker; D. B. Milošević

doi:10.3788/COL201513.070006

Journals >Chinese Optics Letters >Volume 13 >Issue 7 >Page 070006 > Article

Chinese Optics Letters
Vol. 13, Issue 7, 070006 (2015)

Quantum-orbit theory of low-energy above-threshold ionization on and off axis

W. Becker^1、* and D. B. Milošević^1、2、3

Author Affiliations

¹Max-Born-Institut, Max-Born-Str. 2a, 12489 Berlin, Germany

²Faculty of Science, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo, Bosnia and Herzegovina

³Academy of Sciences and Arts of Bosnia and Herzegovina, Bistrik 7, 71000 Sarajevo, Bosnia and Herzegovina

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DOI: 10.3788/COL201513.070006 Cite this Article Set citation alerts

W. Becker, D. B. Milošević. Quantum-orbit theory of low-energy above-threshold ionization on and off axis[J]. Chinese Optics Letters, 2015, 13(7): 070006 Copy Citation Text

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Abstract

Intense-laser-induced above-threshold ionization of a bound electron into continuum states with low energy is investigated in the context of the strong-field approximation that allows for one act of rescattering of the revisiting electron. The quantum orbits for forward and backward scattering are evaluated and generalized to arbitrary scattering angles. The velocity map of the liberated electron exhibits the well-known low-energy structure as well as other features off the polarization axis.

T_{p i}^{R} \propto \sum_{s} Δ_{s}^{- 1 / 2} M_{{pk}_{st}} (t_{s}) M_{k_{st} i} (t_{0 s}) e^{i S_{s}} .

(1)

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\frac{1}{2} {[k_{st} + A (t_{0})]}^{2} = - I_{p},

(2)

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\frac{1}{2} {[k_{st} + A (t)]}^{2} = \frac{1}{2} {[p + A (t)]}^{2},

(3)

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Δ (t_{0}, t) = {[\frac{i (t - t_{0})}{2 π}]}^{3} [{(\frac{\partial^{2} S}{\partial t_{0} \partial t})}^{2} - \frac{\partial^{2} S}{\partial t_{0}^{2}} \frac{\partial^{2} S}{\partial t^{2}}] .

(4)

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M_{{pk}_{st}}^{LFA} (t) = 〈 ψ_{p + A (t)}^{(-)} | V | k_{st} + A (t) 〉,

(5)

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k = - A_{0} \frac{\sin ω t - \sin ω t_{0}}{ω τ}, \frac{k}{A_{0}} = - \frac{\sin σ \cos ψ}{σ},

(6)

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k + A (t_{0}) = 0,

(7)

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{[k + A (t)]}^{2} = {[p + A (t)]}^{2} .

(8)

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a \cos ψ - b \sin ψ = 0,

(9)

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\sin ψ = s a / \sqrt{a^{2} + b^{2}}, \cos ψ = s^{'} b / \sqrt{a^{2} + b^{2}},

(10)

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\frac{E_{p}}{2 U_{p}} = \frac{b^{2}}{a^{2} + b^{2}} (2 c^{2} + d \pm 2 c \sqrt{c^{2} + d}),

(11)

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W. Becker, D. B. Milošević. Quantum-orbit theory of low-energy above-threshold ionization on and off axis[J]. Chinese Optics Letters, 2015, 13(7): 070006

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