Instantaneous Frequency Measurements Based on a Dual-Path Imbalanced Mach-Zehnder Interferometer

Cong Li; Jianming Zhang; Zhe Han

doi:10.3788/LOP222254

Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 17 >Page 1712001 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 17, 1712001 (2023)

Instantaneous Frequency Measurements Based on a Dual-Path Imbalanced Mach-Zehnder Interferometer

Cong Li^*, Jianming Zhang, and Zhe Han

Author Affiliations

Wuhan Binhu Electronic Limited Liability Company, Wuhan 430205, Hubei , China

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DOI: 10.3788/LOP222254 Cite this Article Set citation alerts

Cong Li, Jianming Zhang, Zhe Han. Instantaneous Frequency Measurements Based on a Dual-Path Imbalanced Mach-Zehnder Interferometer[J]. Laser & Optoelectronics Progress, 2023, 60(17): 1712001 Copy Citation Text

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Abstract

Instantaneous frequency measurements (IFM) are of great importance in modern electronic warfare. However, traditional methods based on electronics are facing considerable challenges because of their shortcomings. Particular attention has been paid to photon-assisted technologies owing to their large bandwidth, low loss, small size, lightweight, and electromagnetic interference immunity characteristics. In this study, the operational fundamentals of IFM are presented and analyzed based on a dual-path-imbalanced optical link. A demo system is also constructed with ordinary devices to measure the signal (0.5-18.5 GHz). It is demonstrated that the experimental and theoretical results are consistent, and we achieve excellent measurement accuracy (within ±60 MHz). This method has great potential for military applications owing to the simplicity of its front-end structure, which benefits from the use of the ordinary, phase-modulated optical link.

Keywords

amplitude comparison function imbalanced optical link instantaneous frequency measurement phase modulation

V_{i} (t) = V_{r f} s i n (ω t)

，（1）

E_{o} (t) = \sqrt[]{(2 l_{p} P_{o}) / A} {(μ / ε)}^{\frac{1}{4}} e x p \{i [2 π ν t + ϕ (t)]\} = γ_{0} e x p \{i [2 π ν t + ϕ (t)]\}

，（2）

ϕ (t) = [π V_{r f} s i n (ω t)] / V_{π} = ϕ s i n (ω t)

，（3）

\begin{matrix} E (t) = \sqrt[]{l_{b}} \cdot E_{o} (t) = \\ \sqrt[]{(2 l_{p} l_{b} P_{o}) / A} {(μ / ε)}^{\frac{1}{4}} e x p \{i [2 π ν t + ϕ (t)]\} = \\ γ e x p \{i [2 π ν t + ϕ (t)]\} \end{matrix}

，（4）

R e (E) = γ \sum_{k = - \infty}^{+ \infty} J_{k} (ϕ) c o s (2 π ν t + k ω t)

，（5）

(\begin{array}{l} E_{1} (t) \\ E_{2} (t) \end{array}) = \frac{\sqrt[]{l_{m} g_{o}}}{2} (\begin{matrix} 1 & i \\ i & 1 \end{matrix}) (\begin{matrix} Γ (τ) & 0 \\ 0 & 1 \end{matrix}) (\begin{matrix} 1 & i \\ i & 1 \end{matrix}) (\begin{array}{l} E (t) \\ 0 \end{array})

，（6）

\begin{matrix} I_{1,2} (t) = I_{d c, q} \pm (- 1) I_{d c, q} c o s (2 π ν τ) J_{0} (x) \pm \\ (- 1) \times 2 I_{d c, q} s i n (2 π ν τ) \sum_{j = 0}^{+ \infty} {(- 1)}^{j} J_{2 j + 1} \\ (x) c o s [(2 j + 1) (ω t - ω τ / 2)] \pm \\ 2 I_{d c, q} c o s (2 π ν τ) \sum_{k = 1}^{+ \infty} {(- 1)}^{k} J_{2 k} (x) c o s [2 k (ω t - ω τ / 2)] \end{matrix}

，（7）

g \equiv \frac{P_{r f, o}}{P_{r f, i}} = {[\frac{2 π I_{d c, q} s i n (π f τ)}{V_{π}}]}^{2} Z_{i} Z_{o} {|H_{p d}|}^{2}

，（8）

g_{1} = {[\frac{2 π I_{d c, q} s i n (π f τ_{1})}{V_{π}}]}^{2} Z_{i} Z_{o} {|H_{p d}|}^{2}

，（9）

g_{2} = {[\frac{2 π I_{d c, q} s i n (π f τ_{2})}{V_{π}}]}^{2} Z_{i} Z_{o} {|H_{p d}|}^{2}

。（10）

f_{A C F} \equiv \frac{P_{r f, o 1}}{P_{r f, o 2}} = \frac{g_{1}}{g_{2}} = \frac{s i n^{2} (π f τ_{1})}{s i n^{2} (π f τ_{2})}

。（11）

Cong Li, Jianming Zhang, Zhe Han. Instantaneous Frequency Measurements Based on a Dual-Path Imbalanced Mach-Zehnder Interferometer[J]. Laser & Optoelectronics Progress, 2023, 60(17): 1712001

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