Vortex beam: generation and detection of orbital angular momentum [Invited]

Yihua Bai; Haoran Lv; Xin Fu; Yuanjie Yang

doi:10.3788/COL202220.012601

Journals >Chinese Optics Letters >Volume 20 >Issue 1 >Page 012601 > Article

Chinese Optics Letters
Vol. 20, Issue 1, 012601 (2022)

Vortex beam: generation and detection of orbital angular momentum [Invited] | Editors' Pick

Yihua Bai, Haoran Lv, Xin Fu, and Yuanjie Yang^*

Author Affiliations

School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China

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DOI: 10.3788/COL202220.012601 Cite this Article Set citation alerts

Yihua Bai, Haoran Lv, Xin Fu, Yuanjie Yang. Vortex beam: generation and detection of orbital angular momentum [Invited][J]. Chinese Optics Letters, 2022, 20(1): 012601 Copy Citation Text

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Abstract

Recent advances in the research of vortex beams, structured beams carrying orbital angular momentum (OAM), have revolutionized the applications of light beams, such as advanced optical manipulations, high-capacity optical communications, and super-resolution imaging. Undoubtedly, the methods for generation of a vortex beam and detection of its OAM are of vital importance for the applications of vortex beams. In this review, we first introduce the fundamental concepts of vortex beams briefly and then summarize approaches to generating and detecting the vortex beams separately, from bulky diffractive elements to planar elements. Finally, we make a concise conclusion and outline that is yet to be explored.

Keywords

orbital angular momentum topological charge vortex beams

{LG}_{pl} (r, ϕ, z) = \sqrt{\frac{2 p!}{π (p + | l |)!}} \frac{1}{ω (z)} {[\frac{r \sqrt{2}}{ω (z)}]}^{| l |} \exp [\frac{- r^{2}}{ω^{2} (z)}] L_{p}^{| l |} [\frac{2 r^{2}}{ω {(z)}^{2}}] \exp [- \frac{r^{2}}{ω {(z)}^{2}}] \exp (i l ϕ) \exp [\frac{i k_{0} r^{2} z}{2 (z^{2} + z_{R}^{2})}] \exp [- i η \arctan (\frac{z}{z_{R}})],

(1)

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I = B_{1} (x, y) + B_{2} (x, y) \exp {i [ϕ (x, y) - l θ]} + B_{2} (x, y) \exp {- i [ϕ (x, y) - l θ]},

(2)

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Φ_{SVW} \propto \frac{\exp [2 π i k \sqrt{r^{2} + {(z - z_{1})}^{2}}]}{\sqrt{r^{2} + {(z - z_{1})}^{2}}} \exp (2 π i l ϕ),

(3)

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I_{holo} = {| \frac{\exp [2 π i k \sqrt{r^{2} + {(z - z_{1})}^{2}}]}{r^{2} + {(z - z_{1})}^{2}} \exp (2 π i l ϕ) + 1 |}^{2} .

(4)

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b (r) = {\begin{matrix} 1, & 0 \leq \sqrt{L^{2} + r_{n}^{2}} - \sqrt{L^{2} + r^{2}} < \frac{λ}{2} \\ 0, & \frac{λ}{2} \leq \sqrt{L^{2} + r_{n}^{2}} - \sqrt{L^{2} + r^{2}} < λ \end{matrix},

(5)

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{\vec{E}}_{out}^{RCP} = {\vec{E}}_{con}^{RCP} + {\vec{E}}_{res}^{RCP} = \frac{1}{\sqrt{2}} (\frac{A}{A + B} e^{i (\frac{π}{2} - 2 ϕ)} [\begin{matrix} 1 \\ - i \end{matrix}] + \frac{B}{A + B} [\begin{matrix} 1 \\ i \end{matrix}]),

(6)

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J (ϕ) = e^{i σ} [\begin{matrix} e^{i σ} μ_{1} (ϕ) & \frac{\sin 2 χ}{2} ν (ϕ) \\ \frac{\sin 2 χ}{2} ν (ϕ) & e^{- i σ} μ_{2} (ϕ) \end{matrix}],

(7)

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J_{q} = [\begin{matrix} \cos 2 α & \sin 2 α \\ \sin 2 α & - \cos 2 α \end{matrix}],

(8)

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E_{out} = J_{q} E_{in} = E_{0} [\begin{matrix} \cos 2 α & \sin 2 α \\ \sin 2 α & - \cos 2 α \end{matrix}] [\begin{matrix} 1 \\ i \end{matrix}] = E_{0} \exp (i 2 q ϕ) \exp (i 2 ϕ_{0}) [\begin{matrix} 1 \\ - i \end{matrix}] .

(9)

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Yihua Bai, Haoran Lv, Xin Fu, Yuanjie Yang. Vortex beam: generation and detection of orbital angular momentum [Invited][J]. Chinese Optics Letters, 2022, 20(1): 012601

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