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Advanced Photonics
Vol. 4, Issue 6, 064001 (2022)

Silicon nitride-based Kerr frequency combs and applications in metrology

Zhaoyang Sun¹, Yang Li^1、*, Benfeng Bai^1、*, Zhendong Zhu², and Hongbo Sun^1、*

Author Affiliations

¹Tsinghua University, State Key Laboratory of Precision Measurement and Instruments, Department of Precision Instrument, Beijing, China

²National Institute of Metrology, Beijing, China

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DOI: 10.1117/1.AP.4.6.064001 Cite this Article Set citation alerts

Zhaoyang Sun, Yang Li, Benfeng Bai, Zhendong Zhu, Hongbo Sun. Silicon nitride-based Kerr frequency combs and applications in metrology[J]. Advanced Photonics, 2022, 4(6): 064001 Copy Citation Text

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Abstract

Kerr frequency combs have been attracting significant interest due to their rich physics and broad applications in metrology, microwave photonics, and telecommunications. In this review, we first introduce the fundamental physics, master equations, simulation methods, and dynamic process of Kerr frequency combs. We then analyze the most promising material platform for realizing Kerr frequency combs—silicon nitride on insulator (SNOI) in comparison with other material platforms. Moreover, we discuss the fabrication methods, process optimization as well as tuning and measurement schemes of SNOI-based Kerr frequency combs. Furthermore, we highlight several emerging applications of Kerr frequency combs in metrology, including spectroscopy, ranging, and timing. Finally, we summarize this review and envision the future development of chip-scale Kerr frequency combs from the viewpoint of theory, material platforms, and tuning methods.

Keywords

damascene process Kerr frequency comb Lgiato–Lefever equation precision measurements silicon nitride

E (t) = A (t) e^{i ω t} = \sum_{N = N_{i}}^{N_{j}} A_{N} e^{i ω_{N} t},

(1)

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f_{N} = f_{0} + N f_{r},

(2)

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f_{0} = \frac{1}{2 π} \frac{d φ_{ceo}}{d t} .

(3)

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\frac{\partial a_{μ}}{\partial τ} = - (1 + i ζ_{μ}) a_{μ} + i \sum_{μ^{'} < μ^{″}} (2 - δ_{μ^{'} μ^{″}}) a_{μ^{'}} a_{μ^{″}} a_{μ^{'} + μ^{'} - μ}^{*} + δ_{0 μ} f,

(4)

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ℏ ω_{1} + ℏ ω_{2} = ℏ ω_{3} + ℏ ω_{4},

(5)

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ℏ k_{1} + ℏ k_{2} = ℏ k_{3} + ℏ k_{4} .

(6)

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m λ = 2 π R n (λ),

(7)

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k = \frac{2 π n (λ)}{λ} = \frac{m}{R} .

(8)

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ω = \frac{2 π c}{λ} = \frac{m c}{n (λ) R}

(9)

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\frac{\partial E}{\partial t} = - (1 + i α) E + i {| E |}^{2} E - i \frac{β}{2} \frac{\partial^{2} E}{\partial θ^{2}} + F .

(10)

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\hat{D} = - (1 + i \frac{β}{2} \frac{\partial^{2}}{\partial θ^{2}}),

(11)

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\hat{N} = i {| E |}^{2} - i α .

(12)

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E (T, θ) = {F T^{- 1} [\tilde{E} (t_{0}) e^{\frac{h}{2} \hat{D}}] + \frac{h}{2} F} e^{\frac{h}{2} \hat{N}} .

(13)

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E_{cavity} = B sech \frac{ϕ}{ϕ_{τ}} e^{i ϕ} - \frac{if}{δ ω},

(14)

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\frac{\partial A_{s}}{\partial t} = - \frac{κ}{2} A_{s} - i δ ω A_{s} + i \frac{D_{2}}{2} \frac{\partial^{2} A_{s}}{\partial θ^{2}} + i \frac{κ}{2} \frac{{| A_{s} |}^{2} + 2 {| A_{B} |}^{2}}{E_{th}} A_{s} + i β \frac{κ}{2} A_{B} - \sqrt{κ_{R} κ_{L}} e^{i ϕ_{B}} A_{L},

(15)

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\frac{d A_{B}}{d t} = - \frac{κ}{2} A_{B} - i δ ω A_{B} + i \frac{κ}{2} \frac{{| A_{B} |}^{2} + 2 \int_{0}^{2 π} {| A_{s} |}^{2} d θ / (2 π)}{E_{th}} A_{s} + i β \frac{κ}{2} \bar{A_{s}},

(16)

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\frac{d A_{L}}{d t} = i δ ω_{L} A_{L} - i δ ω A_{L} + \frac{g (| A_{L}^{2} |)}{2} (1 + i α_{g}) A_{L} - \sqrt{κ_{R} κ_{L}} e^{i ϕ_{B}} A_{B} .

(17)

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\frac{\partial ψ}{\partial τ} = - (1 + i α) ψ + i \frac{D_{2}}{κ} \frac{\partial^{2} ψ}{\partial θ^{2}} + i ({| ψ |}^{2} + 2 {| ρ_{B} |}^{2}) ψ + i β^{*} ρ_{B} + z F,

(18)

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\frac{d ρ_{B}}{d τ} = - (1 + i α - 2 i P - i {| ρ_{B} |}^{2}) ρ_{B} + i β ρ,

(19)

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\frac{1}{i z} \frac{d z}{d τ} = α_{L} - α + K Im (e^{i ϕ} \frac{ρ_{B}}{i β z F}), | z | = 1,

(20)

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ω_{μ} = ω_{0} + \sum_{j = 1} \frac{D_{j} μ^{j}}{j!},

(21)

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f_{1 N} = f_{0} + N f_{r},

(22)

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f_{2 N} = f_{0} + N (f_{r} + δ f_{r}) .

(23)

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f_{N} = N δ f_{r} .

(24)

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References (163)

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Zhaoyang Sun, Yang Li, Benfeng Bai, Zhendong Zhu, Hongbo Sun. Silicon nitride-based Kerr frequency combs and applications in metrology[J]. Advanced Photonics, 2022, 4(6): 064001

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