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Journals >Chinese Optics Letters >Volume 13 >Issue 2 >Page 020602 > Article

Chinese Optics Letters
Vol. 13, Issue 2, 020602 (2015)

Spin effect on a single-mode single-polarization optical fiber

Minning Ji^1、*, Gang-Ding Peng², and Yanhua Luo²

Author Affiliations

¹Institute of Fiber Optics, Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University, Shanghai 201800, China

²School of Electrical Engineering and Telecommunications, University of New South Wales, NSW 2052, Australia

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DOI: 10.3788/COL201513.020602 Cite this Article Set citation alerts

Minning Ji, Gang-Ding Peng, Yanhua Luo. Spin effect on a single-mode single-polarization optical fiber[J]. Chinese Optics Letters, 2015, 13(2): 020602 Copy Citation Text

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Abstract

The spin effect on a single-mode single-polarization optical fiber is investigated theoretically and numerically. To get a practical single elliptically polarized fiber the normalized spin rate must be in the range of 0.2–0.35. A single elliptically polarized fiber with a normalized spin rate around 0.224 is demonstrated. It has a broad band from 1.530 to 1.558 μm, in which the low-leakage elliptically polarized eigenmode loss is kept within 1.2 dB while the high-leakage elliptically polarized eigenmode loss is greater than 20 dB. This fiber can be used as an elliptical polarizer or applied in current sensing.

\frac{d E}{d z} = T E,

(1a)

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E = (\begin{matrix} E_{x} \\ E_{y} \end{matrix}),

(1b)

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T = (\begin{matrix} i \frac{δ β}{2} & τ \\ - τ & - i \frac{δ β}{2} \end{matrix}),

(1c)

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\frac{d E}{d z} = (\begin{matrix} i \frac{β_{x} - β_{y}}{2} & τ \\ - τ & - i \frac{β_{x} - β_{y}}{2} - α \end{matrix}) E .

(2)

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E = O w,

(3)

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O = [\begin{matrix} \cos (ϕ) & i \sin (ϕ) \\ i \sin (ϕ) & \cos (ϕ) \end{matrix}],

(4a)

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ϕ = \frac{1}{2} \arctan (\frac{2 τ}{δ β - i α}),

(4b)

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\tan (ϕ) = \sqrt{{(\frac{δ β - i α}{2 τ})}^{2} + 1} - \frac{δ β - i α}{2 τ},

(5)

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\frac{d w}{d z} = [\begin{matrix} i g - α / 2 & 0 \\ 0 & - i g - α / 2 \end{matrix}] w,

(6a)

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g = \sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}} .

(6b)

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w_{x} = (\begin{matrix} 1 \\ 0 \end{matrix}) e^{i g z - \frac{α}{2} z} E_{x} = [\begin{matrix} \cos (ϕ) \\ \sin (ϕ) i \end{matrix}] e^{i g z - \frac{α}{2} z},

(7a)

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w_{y} = (\begin{matrix} 0 \\ 1 \end{matrix}) e^{- i g z - \frac{α}{2} z} E_{y} = [\begin{matrix} \sin (ϕ) i \\ \cos (ϕ) \end{matrix}] e^{- i g z - \frac{α}{2} z} .

(7b)

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[\begin{matrix} \cos (ϕ) \\ \sin (ϕ) i \end{matrix}] \to [\begin{matrix} 1 \\ \tan (ϕ) i \end{matrix}] \to (\begin{matrix} 1 \\ ρ e^{i φ} \end{matrix}) \to (\begin{matrix} 1 \\ e^{i Φ} \end{matrix}),

(8a)

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ρ = | \sqrt{{(\frac{δ β - i α}{2 τ})}^{2} + 1} - \frac{δ β - i α}{2 τ} |,

(8b)

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φ = \frac{π}{2} + \arctan [\frac{Im (\sqrt{{(\frac{δ β - i α}{2 τ})}^{2} + 1} - \frac{δ β - i α}{2 τ})}{Re (\sqrt{{(\frac{δ β - i α}{2 τ})}^{2} + 1} - \frac{δ β - i α}{2 τ})}],

(8c)

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\tan (Φ) = \frac{\sin (φ)}{\sqrt{\cos {(φ)}^{2} + {(\frac{ρ^{2} - 1}{2 ρ})}^{2}}} .

(8d)

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ϵ = \frac{b}{a} = \tan \frac{Φ}{2} .

(9)

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α_{x} = Im [\sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}}] + \frac{α}{2} .

(10)

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α_{y} = - Im [\sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}}] + \frac{α}{2} .

(11)

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η = - 40 \log (e) L Im [\sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}}],

(12)

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H L = \frac{α_{y}}{α_{x}} = \frac{- Im [\sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}}] + \frac{α}{2}}{Im [\sqrt{τ^{2} + {(\frac{δ β - i α}{2})}^{2}}] + \frac{α}{2}} .

(13)

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ϵ = \sqrt{1 + {(\frac{Λ}{2 L_{b}})}^{2}} - \frac{Λ}{2 L_{b}} .

(14)

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References (14)

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Minning Ji, Gang-Ding Peng, Yanhua Luo. Spin effect on a single-mode single-polarization optical fiber[J]. Chinese Optics Letters, 2015, 13(2): 020602

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