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Journals >Photonics Research >Volume 5 >Issue 6 >Page 689 > Article

Photonics Research
Vol. 5, Issue 6, 689 (2017)

Microwave frequency upconversion employing a coupling-modulated ring resonator

Yiming Zhong¹, Linjie Zhou^1、*, Yanyang Zhou¹, Yujie Xia¹, Siqi Liu¹, Liangjun Lu¹, Jianping Chen¹, and Xingjun Wang²

Author Affiliations

¹Shanghai Institute for Advanced Communication and Data Science, State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

²State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China

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DOI: 10.1364/PRJ.5.000689 Cite this Article Set citation alerts

Yiming Zhong, Linjie Zhou, Yanyang Zhou, Yujie Xia, Siqi Liu, Liangjun Lu, Jianping Chen, Xingjun Wang, "Microwave frequency upconversion employing a coupling-modulated ring resonator," Photonics Res. 5, 689 (2017) Copy Citation Text

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Abstract

We present a method to generate a frequency-doubled microwave signal by employing a coupling-modulated ring resonator. Critical coupling is achieved when the resonator intrinsic loss is perfectly balanced by the external coupling enabled by a Mach–Zehnder interferometer coupler. The high suppression of the carrier leads to a clean two-tone optical signal with the frequency interval two times larger than that of the input microwave frequency. The beating of the two-tone signal at a photodiode generates the frequency upconverted microwave signal. A theoretical model is established to analyze the modulation process and the microwave signal generation. Experimental results show that the electrical harmonic suppression ratio is around ～20 dB (29 dB) for an input microwave signal with 5 dBm (10 dBm) power.

Keywords

(130.4110) Modulators (350.4010) Microwaves.(060.5625) Radio frequency photonics

T = [\begin{matrix} t & k \\ k & - t \end{matrix}],

(1)

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t = | t | e^{i φ_{t}} = α_{1} \sin \frac{θ_{1} - θ_{2}}{2} \cdot e^{i \frac{θ_{1} + θ_{2} + π}{2}},

(2)

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k = | k | e^{i φ_{k}} = α_{1} \cos \frac{θ_{1} - θ_{2}}{2} \cdot e^{i \frac{θ_{1} + θ_{2} + π}{2}},

(3)

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φ_{t} = φ_{k} = φ = \frac{θ_{1} + θ_{2} + π}{2} .

(4)

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[\begin{matrix} b_{1} \\ b_{2} \end{matrix}] = T \cdot [\begin{matrix} a_{1} \\ a_{2} \end{matrix}] = [\begin{matrix} t & k \\ k & - t \end{matrix}] \cdot [\begin{matrix} a_{1} \\ a_{2} \end{matrix}],

(5)

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a_{2} = α_{2} \cdot e^{i θ} b_{2},

(6)

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\frac{b_{1}}{a_{1}} = \frac{α_{1}^{2} α_{2} e^{i (2 φ + θ)} + t}{1 + α_{2} t e^{i θ}} .

(7)

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π + φ + θ = 2 π m .

(8)

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{| \frac{b_{1}}{a_{1}} |}^{2} = {(\frac{| t | - α_{1}^{2} \cdot α_{2}}{1 - α_{2} | t |})}^{2} .

(9)

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| t | = α_{1}^{2} \cdot α_{2} .

(10)

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n_{eff} (v_{p n}) = n_{0} + a v_{p n} + b v_{p n}^{2},

(11)

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θ_{1} (v_{p n 1}) = θ_{0} + n_{eff} (v_{p n 1}) \cdot \frac{2 π}{λ} L,

(12)

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θ_{2} (v_{p n 2}) = n_{eff} (v_{p n 2}) \cdot \frac{2 π}{λ} L,

(13)

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\sin \frac{θ_{0} + [n_{eff} (- V_{1}) - n_{eff} (- V_{1} + V_{2})] \cdot \frac{2 π}{λ} L}{2} = α_{1} α_{2} .

(14)

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v_{p n 1} = - V_{1} + \frac{V_{m}}{2} \cos (ω_{m} t),

(15)

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v_{p n 2} = - V_{1} + V_{2} - \frac{V_{m}}{2} \cos (ω_{m} t),

(16)

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V_{m} = \sqrt{2 P_{m} R},

(17)

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| t | = α_{1}^{2} α_{2} \cos [m \cos (ω_{m} t)] + α_{1} \sqrt{1 - α_{1}^{2} α_{2}^{2}} \sin [m \cos (ω_{m} t)],

(18)

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m = ϵ [a + b (- 2 V_{1} + V_{2})] \cdot \frac{π L}{λ} V_{m},

(19)

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| t | \approx α_{1}^{2} α_{2} J_{0} (m) + 2 α_{1} \sqrt{1 - α_{1}^{2} α_{2}^{2}} J_{1} (m) \cos (ω_{m} t) - 2 α_{1}^{2} α_{2} J_{2} (m) \cos (2 ω_{m} t) .

(20)

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\frac{b_{1}}{a_{1}} = [E_{c} + E_{1} \cos (ω_{m} t) + E_{2} \cos (2 ω_{m} t)] \cdot e^{i φ},

(21)

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E_{c} = - α_{1}^{2} α_{2} + (1 - α_{1}^{2} α_{2}^{2}) α_{1}^{2} α_{2} J_{0} (m) [1 + α_{1}^{2} α_{2}^{2} J_{0} (m)] + 2 α_{1}^{2} α_{2} (1 - α_{1}^{2} α_{2}^{2}) [(1 - α_{1}^{2} α_{2}^{2}) J_{1}^{2} (m) + α_{2} J_{2}^{2} (m)],

(22)

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E_{1} = 2 (1 - α_{1}^{2} α_{2}^{2}) \sqrt{α_{1}^{2} - α_{1}^{4} α_{2}^{2}} J_{1} (m) [1 + 2 α_{1}^{2} α_{2}^{2} J_{0} (m)],

(23)

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E_{2} = 2 α_{1}^{2} α_{2} (1 - α_{1}^{2} α_{2}^{2}) [(1 - α_{1}^{2} α_{2}^{2}) J_{1}^{2} (m) - J_{2} (m) - 2 α_{1}^{2} α_{2}^{2} J_{0} (m) J_{2} (m)] .

(24)

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I_{PD} \propto {| b_{1} |}^{2} .

(25)

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I_{PD} \propto (E_{c}^{2} + \frac{E_{1}^{2}}{2} + \frac{E_{2}^{2}}{2}) + (2 E_{c} E_{1} + E_{1} E_{2}) \cos (ω t) + (\frac{E_{1}^{2}}{2} + 2 E_{c} E_{2}) \cos (2 ω t) + E_{1} E_{2} \cos (3 ω t) .

(26)

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P_{1} \propto {(2 E_{c} E_{1} + E_{1} E_{2})}^{2},

(27)

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P_{2} \propto {(\frac{E_{1}^{2}}{2} + 2 E_{c} E_{2})}^{2} .

(28)

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SR = 20 \log_{10} | \frac{\frac{E_{1}^{2}}{2} + 2 E_{c} E_{2}}{2 E_{c} E_{1} + E_{1} E_{2}} | .

(29)

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References (25)

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Yiming Zhong, Linjie Zhou, Yanyang Zhou, Yujie Xia, Siqi Liu, Liangjun Lu, Jianping Chen, Xingjun Wang, "Microwave frequency upconversion employing a coupling-modulated ring resonator," Photonics Res. 5, 689 (2017)

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