Automatic phase-matching technique for cascaded electro-optic frequency combs

Jin Wang; Feifei Yin; Zikai Yin; Zheng Wang; Haoyan Xu; Yitang Dai; Kun Xu

doi:10.3788/COL202523.013901

Journals >Chinese Optics Letters >Volume 23 >Issue 1 >Page 013901 > Article

Chinese Optics Letters
Vol. 23, Issue 1, 013901 (2025)

Automatic phase-matching technique for cascaded electro-optic frequency combs | Editors' Pick

Jin Wang, Feifei Yin^*, Zikai Yin, Zheng Wang..., Haoyan Xu, Yitang Dai and Kun Xu|Show fewer author(s)

Author Affiliations

State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

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DOI: 10.3788/COL202523.013901 Cite this Article Set citation alerts

Jin Wang, Feifei Yin, Zikai Yin, Zheng Wang, Haoyan Xu, Yitang Dai, Kun Xu, "Automatic phase-matching technique for cascaded electro-optic frequency combs," Chin. Opt. Lett. 23, 013901 (2025) Copy Citation Text

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Abstract

We propose a novel automatic phase-matching method for generating optical frequency combs using cascaded electro-optic modulators. By analyzing the power changes of different spectral lines, our method enables real-time monitoring and dynamic adjustment to achieve precise phase matching. Experiments have confirmed the fast phase matching and the adjustable spacing of a flat electro-optic frequency comb and its long-term stability. This method provides flexible and efficient light source solutions for optical communications, spectral analysis, and optical measurements.

Keywords

electro-optic frequency comb electro-optic modulator microwave photonics phase matching

E_{out 1} (t) \propto E_{0} \cdot e^{j ω_{0} t} \cdot {e^{j m_{m z m} \cos w t} + e^{j [m_{m z m} \cos (w t + π) + V_{bias}]}} \cdot e^{j m_{p} \cos (w t + φ_{1})} .

(1)

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E_{out 1} (t) \propto E_{0} e^{j w_{0} t} \cdot \sum_{n = - \infty}^{+ \infty} \sum_{k = - \infty}^{+ \infty} [(e^{j n π} + e^{j V_{bias}}) e^{j k φ_{1}} \cdot J_{n} (m_{m z m}) J_{k} (m_{p}) e^{j (n + k) w t}] .

(2)

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E_{out 1} (t) \propto E_{0} \cdot e^{j (ω_{0} + M ω) t} \cdot \sum_{n = - \infty}^{+ \infty} [(e^{j n π} + e^{j V_{bias}}) e^{j (M - n) φ_{1}} \cdot J_{n} (m_{m z m}) J_{M - n} (m_{p})] .

(3)

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I_{M} \propto E_{0}^{2} {| \sum_{n = - \infty}^{+ \infty} [(e^{j n π} + e^{j V_{bias}}) e^{j (M - n) φ_{1}} \cdot J_{n} (m_{m z m}) J_{M - n} (m_{p})] |}^{2} .

(4)

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E_{out 1} (t) \propto E_{0} e^{j w_{0} t} \cdot {e^{j m_{m z m} \cos w t} + e^{j [m_{m z m} \cos (w t + π) + V_{bias}]}} \cdot \prod_{i = 1}^{3} e^{j m_{p} \cos (w t + φ_{i})} \propto E_{0} e^{j w_{0} t} \cdot {e^{j m_{m z m} \cos w t} + e^{j [m_{m z m} \cos (w t + π) + V_{bias}]}} \cdot e^{j m_{p} \sqrt{A^{2} + B^{2}} \cos (w t + φ_{p})},

(5)

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I_{M} \propto E_{0}^{2} {| \sum_{n = - \infty}^{+ \infty} [(e^{j n π} + e^{j V_{bias}}) e^{j (M - n) φ_{p}} \cdot J_{n} (m_{m z m}) J_{M - n} (m_{p}^{'})] |}^{2},

(6)

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Jin Wang, Feifei Yin, Zikai Yin, Zheng Wang, Haoyan Xu, Yitang Dai, Kun Xu, "Automatic phase-matching technique for cascaded electro-optic frequency combs," Chin. Opt. Lett. 23, 013901 (2025)

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