Researching | In-band intermodulation induced by transient response of erbium-doped fiber amplifier

Journals >Chinese Optics Letters >Volume 20 >Issue 1 >Page 013901 > Article

Chinese Optics Letters
Vol. 20, Issue 1, 013901 (2022)

In-band intermodulation induced by transient response of erbium-doped fiber amplifier

Guanghao Shao^1、2、*, Xingwei Ye^1、2, Guoqiang Zhang^1、2, Yuqi Tan^1、2, Jiquan Zhai^1、2, and Yuhao Yang^1、2

Author Affiliations

¹Nanjing Research Institute of Electronics Technology, Nanjing 210039, China

²Key Laboratory of IntelliSense Technology, China Electronics Technology Group Corporation, Nanjing 210039, China

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DOI: 10.3788/COL202220.013901 Cite this Article Set citation alerts

Guanghao Shao, Xingwei Ye, Guoqiang Zhang, Yuqi Tan, Jiquan Zhai, Yuhao Yang. In-band intermodulation induced by transient response of erbium-doped fiber amplifier[J]. Chinese Optics Letters, 2022, 20(1): 013901 Copy Citation Text

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Abstract

Transient response of an erbium-doped fiber amplifier (EDFA) is studied in an externally-modulated analog link. Double tones represented as transmitted radio frequency and dither signals are introduced. Extra modulation is generated owing to the EDFA’s transient response caused by a low-frequency dither signal. Therefore, the parasitic modulation is superposed to the output signals and may significantly affect in-band electrical spectra. Analytical and numerical solutions are both given, which agree well with experimental results. This work indicates that a suitable dither signal should be selected to maximize the carrier to intermodulation ratio. In-band spurious free dynamic range is optimized in the meantime.

Keywords

carrier to intermodulation ratio dither signal erbium-doped fiber amplifier externally-modulated analog link transient response

x (t) = P_{0} {1 + \cos [φ_{d} \sin (ω_{d} t) + φ_{RF} \sin (ω_{RF} t) + φ_{dc}]},

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x (t) = P_{MZM} [1 + x_{d} (t) + x_{RF} (t) + x_{ng} (t)],

(2)

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x_{d} (t) = ψ_{d} \sin (ω_{d} t) = Re (- j ψ_{d} e^{j ω_{d} t}), x_{RF} (t) = ψ_{RF} \sin (ω_{RF} t) - ψ_{RF \pm d} {\cos [(ω_{RF} + ω_{d}) t] - \cos [(ω_{RF} - ω_{d}) t]} + ψ_{RF \pm 2 d} {\sin [(ω_{RF} + 2 ω_{d}) t] + \sin [(ω_{RF} - 2 ω_{d}) t]},

(3)

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H_{EDFA} (ω) = 1 + \frac{1}{1 + i ω τ + P_{out}^{EDFA} / P_{sat}^{EDFA}} \cdot \frac{P_{in}^{EDFA} - P_{out}^{EDFA}}{P_{sat}^{EDFA}},

(4)

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g_{d} (t) = \frac{1 + y_{d} (t)}{1 + x_{d} (t)} \approx 1 + y_{d} (t) - x_{d} (t) = 1 + ψ_{g} \cos (ω_{d} t + θ_{g}),

(5)

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ψ_{g} e^{j θ_{g}} = - j ψ_{d} [H_{EDFA} (ω_{d}) - 1]

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y_{RF} (t) = g_{d} (t) x_{RF} (t) = [1 + ψ_{g} \cos (ω_{d} t + θ_{g})] x_{RF} (t) .

(7)

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y_{RF} (t) = A_{0} \cos (ω_{RF} t + θ_{0}) + A_{+ 1} \cos [(ω_{RF} + ω_{d}) t + θ_{+ 1}] + A_{- 1} \cos [(ω_{RF} - ω_{d}) t + θ_{- 1}] + A_{+ 2} \cos [(ω_{RF} + 2 ω_{d}) t + θ_{+ 2}] + A_{- 2} \cos [(ω_{RF} - 2 ω_{d}) t + θ_{- 2}],

(8)

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A_{0} e^{j θ_{0}} = - j {ψ_{RF} + ψ_{RF \pm d} Im {j ψ_{d} [H_{EDFA} (ω_{d}) - 1]}}, A_{+ 1} e^{j θ_{+ 1}} = - ψ_{RF \pm d} - \frac{ψ_{d}}{2} ψ_{RF} [H_{EDFA} (ω_{d}) - 1] + \frac{ψ_{d}}{2} ψ_{RF \pm 2 d} [H_{EDFA}^{*} (ω_{d}) - 1], A_{- 1} e^{j θ_{- 1}} = ψ_{RF \pm d} + \frac{ψ_{d}}{2} ψ_{RF} [H_{EDFA}^{*} (ω_{d}) - 1] - \frac{ψ_{d}}{2} ψ_{RF \pm 2 d} [H_{EDFA} (ω_{d}) - 1], A_{+ 2} e^{j θ_{+ 2}} = - j ψ_{RF \pm 2 d} + j \frac{ψ_{d}}{2} ψ_{RF \pm d} [H_{EDFA} (ω_{d}) - 1], A_{- 2} e^{j θ_{- 2}} = - j ψ_{RF \pm 2 d} + j \frac{ψ_{d}}{2} ψ_{RF \pm d} [H_{EDFA}^{*} (ω_{d}) - 1] .

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{CIR}_{RF \pm d} = | \frac{ψ_{RF} + ψ_{RF \pm d} Im {j ψ_{d} [H_{EDFA} (ω_{d}) - 1]}}{ψ_{RF \pm d} + \frac{ψ_{d}}{2} {ψ_{RF} [H_{EDFA} (ω_{d}) - 1] - ψ_{RF \pm 2 d} [H_{EDFA}^{*} (ω_{d}) - 1]}} |, {CIR}_{RF \pm 2 d} = | \frac{ψ_{RF} + ψ_{RF \pm d} Im {j ψ_{d} [H_{EDFA} (ω_{d}) - 1]}}{ψ_{RF \pm 2 d} - \frac{ψ_{d}}{2} ψ_{RF \pm d} [H_{EDFA}^{*} (ω_{d}) - 1]} | .

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(1 + τ \frac{d}{d t}) \ln \frac{1 + v (t)}{1 + u (t)} = - \frac{1}{P_{sat}^{EDFA}} [v (t) - u (t)],

(11)

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References (22)

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Guanghao Shao, Xingwei Ye, Guoqiang Zhang, Yuqi Tan, Jiquan Zhai, Yuhao Yang. In-band intermodulation induced by transient response of erbium-doped fiber amplifier[J]. Chinese Optics Letters, 2022, 20(1): 013901

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