Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum

Shasha Li; Baifei Shen; Wenpeng Wang; Zhigang Bu; Hao Zhang; Hui Zhang; Shuhua Zhai

doi:doi:10.3788/COL201917.050501

Chinese Optics Letters, 2019, 17 (5): 050501, Published Online: May. 13, 2019

Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum Download： 1243次

Shasha Li ^1,2Baifei Shen ^1,3,*Wenpeng Wang ^1,**Zhigang Bu ¹Hao Zhang ^1,2Hui Zhang ¹Shuhua Zhai ^1,2

Author Affiliations

¹ State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

² University of Chinese Academy of Sciences, Beijing 100049, China

³ Department of Physics, Shanghai Normal University, Shanghai 200234, China

Figures & Tables

Fig. 1. (a) Electric field $E_{y}$ of the incident pulse in the x–y plane at $z = 0$ at $t = 14 T$ . (b) Transverse intensity distribution of the incident beam averaged for the entire pulse at $x = 5 λ$ [the black dotted line in (a)] at $t = 14 T$ . (c) Electron density distribution at $t = 22 T$ when the pulse arrives at the target surface. The black lines in (b) and (c) are the outlines of the 1/e maximum intensity of the incident beam and the hole of the target. (d) Frequency spectrum of the laser field after interaction between the input pulse and target. The field signal corresponds to $y = 2.5 λ$ and $z = 0$ at $t = 26 T$ .

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Fig. 2. Reflected transverse electric field distributions of the (a1) first, (b1) third, (c1) fifth, and (d1) seventh harmonics in the z–y plane at $x = 5 λ$ and $t = 26 T$ . Corresponding transverse intensity distributions of harmonics averaged on entire pulse are shown in (a2)–(d2).

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Fig. 3. Relation between the mode $α_{n}$ of the $n$ th harmonic and its harmonic order $n$ for the fundamental frequency beam with $α_{0} = 0.7$ . The gray dotted line is the scaling relation between $n α_{0}$ and the harmonic order $n$ .

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Fig. 4. Superposition of (a) first, (b) third, (c) fifth, and (d) seventh harmonics for different integer modes.

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Fig. 5. Fraunhofer diffraction patterns of first, third, fifth, and seventh order harmonics of fractional (first row) and integer (second row) vortex beams under different conditions. The illustrations in the bottom left of the first column are corresponding holes. (a1)–(d1) Fundamental fractional vortex beam with $α_{0} = 0.7$ diffracted by the hole shape of $α_{0} = 0.7$ . (a2)–(d2) Fundamental integer vortex beam ${LG}_{01}$ diffracted by the hole shape of ${LG}_{01}$ .

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Shasha Li, Baifei Shen, Wenpeng Wang, Zhigang Bu, Hao Zhang, Hui Zhang, Shuhua Zhai. Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum[J]. Chinese Optics Letters, 2019, 17(5): 050501.

Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum Download： 1243次

Fig. 2. Reflected transverse electric field distributions of the (a1) first, (b1) third, (c1) fifth, and (d1) seventh harmonics in the z–y plane at $x = 5 λ$ and $t = 26 T$ . Corresponding transverse intensity distributions of harmonics averaged on entire pulse are shown in (a2)–(d2).

Fig. 3. Relation between the mode $α_{n}$ of the $n$ th harmonic and its harmonic order $n$ for the fundamental frequency beam with $α_{0} = 0.7$ . The gray dotted line is the scaling relation between $n α_{0}$ and the harmonic order $n$ .

Fig. 4. Superposition of (a) first, (b) third, (c) fifth, and (d) seventh harmonics for different integer modes.

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Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum Download： 1243次

Fig. 2. Reflected transverse electric field distributions of the (a1) first, (b1) third, (c1) fifth, and (d1) seventh harmonics in the z–y plane at x=5λ and t=26T. Corresponding transverse intensity distributions of harmonics averaged on entire pulse are shown in (a2)–(d2).

Fig. 3. Relation between the mode αn of the nth harmonic and its harmonic order n for the fundamental frequency beam with α0=0.7. The gray dotted line is the scaling relation between nα0 and the harmonic order n.

Fig. 4. Superposition of (a) first, (b) third, (c) fifth, and (d) seventh harmonics for different integer modes.

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Fig. 2. Reflected transverse electric field distributions of the (a1) first, (b1) third, (c1) fifth, and (d1) seventh harmonics in the z–y plane at $x = 5 λ$ and $t = 26 T$ . Corresponding transverse intensity distributions of harmonics averaged on entire pulse are shown in (a2)–(d2).

Fig. 3. Relation between the mode $α_{n}$ of the $n$ th harmonic and its harmonic order $n$ for the fundamental frequency beam with $α_{0} = 0.7$ . The gray dotted line is the scaling relation between $n α_{0}$ and the harmonic order $n$ .