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Advanced Photonics
Vol. 3, Issue 1, 014002 (2021)

Generation of polarization and phase singular beams in fibers and fiber lasers

Dong Mao¹, Yang Zheng¹, Chao Zeng¹, Hua Lu¹, Cong Wang², Han Zhang², Wending Zhang^1、*, Ting Mei¹, and Jianlin Zhao¹

Author Affiliations

¹Northwestern Polytechnical University, School of Physical Science and Technology, MOE Key Laboratory of Material Physics and Chemistry Under Extraordinary Conditions, and Shaanxi Key Laboratory of Optical Information Technology, Xi’an, China

²Shenzhen University, Collaborative Innovation Centre for Optoelectronic Science and Technology, Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Shenzhen, China

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DOI: 10.1117/1.AP.3.1.014002 Cite this Article Set citation alerts

Dong Mao, Yang Zheng, Chao Zeng, Hua Lu, Cong Wang, Han Zhang, Wending Zhang, Ting Mei, Jianlin Zhao. Generation of polarization and phase singular beams in fibers and fiber lasers[J]. Advanced Photonics, 2021, 3(1): 014002 Copy Citation Text

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Abstract

Cylindrical vector beams and vortex beams, two types of typical singular optical beams characterized by axially symmetric polarization and helical phase front, possess the unique focusing property and the ability of carrying orbital angular momentum. We discuss the formation mechanisms of such singular beams in few-mode fibers under the vortex basis and show recent advances in generating techniques that are mainly based on long-period fiber gratings, mode-selective couplers, offset-spliced fibers, and tapered fibers. The performances of cylindrical vector beams and vortex beams generated in fibers and fiber lasers are summarized and compared to give a comprehensive understanding of singular beams and to promote their practical applications.

Keywords

beam shaping cylindrical vector beam fiber laser orbital angular momentum two-mode fiber vortex beam

V_{11}^{+} (r, θ) {= (HE}_{11}^{x} + i {HE}_{11}^{y}) / \sqrt{2} = (\hat{x} + i \hat{y}) F_{01} / \sqrt{2}, V_{11}^{-} (r, θ) {= (HE}_{11}^{x} - i {HE}_{11}^{y}) / \sqrt{2} = (\hat{x} - i \hat{y}) F_{01} / \sqrt{2}, V_{21}^{+} (r, θ) {= (HE}_{21}^{even} + i {HE}_{21}^{odd}) / \sqrt{2} = e^{i θ} (\hat{x} + i \hat{y}) F_{11} / \sqrt{2}, V_{21}^{-} (r, θ) {= (HE}_{21}^{even} - i {HE}_{21}^{odd}) / \sqrt{2} = e^{- i θ} (\hat{x} - i \hat{y}) F_{11} / \sqrt{2}, V_{T}^{+} (r, θ) {= (TM}_{01} - i {TE}_{01}) / \sqrt{2} = e^{- i θ} (\hat{x} + i \hat{y}) F_{11} / \sqrt{2}, V_{T}^{-} (r, θ) {= (TM}_{01} + i {TE}_{01}) / \sqrt{2} = e^{i θ} (\hat{x} - i \hat{y}) F_{11} / \sqrt{2} .

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{HE}_{11}^{x} = \hat{x} F_{01}, {HE}_{11}^{y} = \hat{y} F_{01}, {HE}_{21}^{even} = (\hat{x} \cos θ - \hat{y} \sin θ) F_{11}, {HE}_{21}^{odd} = (\hat{x} \sin θ + \hat{y} \cos θ) F_{11}, {TM}_{01} = (\hat{x} \cos θ + \hat{y} \sin θ) F_{11}, {TE}_{01} = (\hat{x} \sin θ - \hat{y} \cos θ) F_{11} .

(2)

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\frac{d A_{1} (z)}{d z} = i δ A_{1} (z) + i κ A_{2} (z), \frac{d A_{2} (z)}{d z} = i δ A_{2} (z) + i κ A_{1} (z),

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κ = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \iint E_{i} (x, y) \cdot Δ n (x, y) E_{j} (x, y) d x d y,

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κ_{1} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \iint \hat{x} F_{01} (r) Δ n (r, θ) (\hat{x} \cos θ - \hat{y} \sin θ) F_{11} (r) r d r d θ .

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κ_{1} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \cos θ d θ .

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κ_{2} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \sin θ d θ, κ_{3} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \sin θ d θ, κ_{4} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \cos θ d θ, κ_{5} = - \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \sin θ d θ, κ_{6} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \cos θ d θ, κ_{7} = - \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \cos θ d θ, κ_{8} = \frac{π}{λ} \sqrt{\frac{ε_{0}}{μ_{0}}} n_{0} \int F_{01} (r) Δ n (r) F_{11} (r) r d r \int Δ n (θ) \sin θ d θ .

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Δ n (r, θ) = n_{0} r \cos θ .

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κ_{1} = C κ_{r} \int_{0}^{2 π} \cos^{2} θ d θ = C κ_{r} π, κ_{2} = C κ_{r} \int_{0}^{2 π} \cos θ \sin θ d θ = 0, κ_{3} = C κ_{r} \int_{0}^{2 π} \cos θ \sin θ d θ = 0, κ_{4} = C κ_{r} \int_{0}^{2 π} \cos^{2} θ d θ = C κ_{r} π, κ_{5} = - C κ_{r} \int_{0}^{2 π} \cos θ \sin θ d θ = 0, κ_{6} = C κ_{r} \int_{0}^{2 π} \cos^{2} θ d θ = - C κ_{r} π, κ_{7} = - C κ_{r} \int_{0}^{2 π} \cos^{2} θ d θ = - C κ_{r} π, κ_{8} = C κ_{r} \int_{0}^{2 π} \cos θ \sin θ d θ = 0,

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\frac{d A_{1} (z)}{d z} = i δ_{1} A_{1} (z) + i κ A_{2} (z), \frac{d A_{2} (z)}{d z} = i δ_{2} A_{2} (z) + i κ A_{1} (z) .

(10)

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V_{21}^{+} (r, θ) {= (HE}_{21}^{even} + i {HE}_{21}^{odd}) / \sqrt{2} = e^{i θ} (\hat{x} + i \hat{y}) F_{11} / \sqrt{2}, V_{21}^{-} (r, θ) {= (HE}_{21}^{even} - i {HE}_{21}^{odd}) / \sqrt{2} = e^{- i θ} (\hat{x} - i \hat{y}) F_{11} / \sqrt{2}, V_{T}^{+} (r, θ) {= (TM}_{01} - i {TE}_{01}) / \sqrt{2} = e^{- i θ} (\hat{x} + i \hat{y}) F_{11} / \sqrt{2}, V_{T}^{-} (r, θ) {= (TM}_{01} + i {TE}_{01}) / \sqrt{2} = e^{i θ} (\hat{x} - i \hat{y}) F_{11} / \sqrt{2} .

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V_{x} {= V}_{21}^{+} (r, θ) + V_{T}^{-} (r, θ) = {(TM}_{01} + {HE}_{21}^{even} + i {TE}_{01} + i {HE}_{21}^{odd}) / \sqrt{2} = \hat{x} e^{i θ} F_{11} / \sqrt{2}, V_{y} {= V}_{21}^{-} (r, θ) + V_{T}^{-} (r, θ) = {(TM}_{01} + {HE}_{21}^{even} - i {TE}_{01} - i {HE}_{21}^{odd}) / \sqrt{2} = \hat{y} e^{i θ} F_{11} / \sqrt{2} .

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Dong Mao, Yang Zheng, Chao Zeng, Hua Lu, Cong Wang, Han Zhang, Wending Zhang, Ting Mei, Jianlin Zhao. Generation of polarization and phase singular beams in fibers and fiber lasers[J]. Advanced Photonics, 2021, 3(1): 014002

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