Researching | Single-shot terahertz polarization detection based on terahertz time-domain spectroscopy

Photonics Research, Volume. 10, Issue 6, 1374(2022)

Single-shot terahertz polarization detection based on terahertz time-domain spectroscopy

Qinggang Lin^1,2, Xinming Yuan¹, Xuanke Zeng^1,3, Yatao Yang², Yi Cai¹, Xiaowei Lu¹, Maijie Zheng¹, Congying Wang¹, Wenhua Cao², and Shixiang Xu^1、*

Author Affiliations

¹Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

²College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China

³e-mail: xuankezeng@szu.edu.cn

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Equations(15)

I_{s} = \frac{I_{p} ω n^{3} γ_{41} E_{THz} L}{2 c} [2 \sin α \cdot \cos (4 φ) + \cos α \cdot \sin (4 φ)] .

(1)

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I_{s, 1} = \frac{I_{p} ω n^{3} γ_{41} L}{c} E_{THz} \sin α,

(2)

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I_{s, 2} = \frac{I_{p} ω n^{3} γ_{41} L}{2 c} E_{THz} \cos α,

(3)

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(\begin{matrix} E_{x} \\ E_{y} \end{matrix}) = \frac{\sqrt{2}}{2} (\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}) (\begin{matrix} \exp (- i \frac{φ}{2}) & 0 \\ 0 & \exp (i \frac{φ}{2}) \end{matrix}) \cdot (\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix}) (\begin{matrix} 1 & i \\ i & 1 \end{matrix}) (\begin{matrix} E_{p} \\ 0 \end{matrix}) = \frac{\sqrt{2}}{2} E_{p} (\begin{matrix} \cos (\frac{φ}{2}) - i \exp (i 2 θ) \cdot \sin (\frac{φ}{2}) \\ i \cos (\frac{φ}{2}) - \exp (i 2 θ) \cdot \sin (\frac{φ}{2}) \end{matrix}) .

(4)

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φ \approx \frac{ω n^{3} E_{THz} γ_{41} L}{2 c} [2 \sin α \cdot \sin (2 θ) - \cos α \cdot \cos (2 θ)] .

(5)

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(\begin{matrix} S_{0} \\ S_{1} \\ S_{2} \\ S_{3} \end{matrix}) = (\begin{matrix} I_{p} \\ \frac{I_{p} ω n^{3} γ_{41} L}{c} E_{THz} \sin α \\ \frac{I_{p} ω n^{3} γ_{41} L}{2 c} E_{THz} \cos α \\ - I_{p} \cos φ \end{matrix}),

(6)

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(\begin{matrix} E_{p x} \\ E_{p y} \end{matrix}) = (\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix}) (\begin{matrix} \cos 45^{o} & - \sin 45^{o} \\ \sin 45^{o} & \cos 45^{o} \end{matrix}) (\begin{matrix} \exp (- i \frac{β (λ)}{2}) & 0 \\ 0 & \exp (i \frac{β (λ)}{2}) \end{matrix}) (\begin{matrix} \cos 45^{o} & \sin 45^{o} \\ - \sin 45^{o} & \cos 45^{o} \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & i \end{matrix}) (\begin{matrix} E_{x} \\ E_{y} \end{matrix}) = i (\begin{matrix} 0 \\ E_{y} \cos (\frac{β (λ)}{2}) - E_{x} \sin (\frac{β (λ)}{2}) \end{matrix}) .

(7)

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P (λ) = {| E_{p x} |}^{2} + {| E_{p y} |}^{2} = \frac{1}{2} S_{0} (λ) - \frac{1}{4} [S_{1} (λ) - i \cdot S_{2} (λ)] \exp [i β (λ)] - \frac{1}{4} [S_{1} (λ) + i \cdot S_{2} (λ)] \exp [- i β (λ)] = \frac{1}{2} S_{0} (λ) - \frac{1}{2} | S_{12} (λ) | \cdot \cos [β (λ) + σ (λ)],

(8)

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Φ (λ) = [β (λ_{0}) + 2 π L λ_{0}] + Λ (λ),

(9a)

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L = d \frac{{Δ n_{g} |}_{λ = λ_{0}}}{λ_{0}^{2}} .

(9b)

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φ_{THz, ∥} (ω) \to φ_{THz, ∥} (λ) = \frac{- 1}{F_{0 noTHz}} \cdot {(F_{1 THz} - F_{1 noTHz}) \cdot \exp [- i β (λ)] + (F_{1 THz}^{*} - F_{1 noTHz}^{*}) \cdot \exp [i β (λ)]} \propto E_{THz, ∥} (ω),

(10a)

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φ_{THz, ⊥} (ω) \to φ_{THz, ⊥} (λ) \approx \frac{2 i}{F_{0 noTHz}} \cdot {(F_{1 THz} - F_{1 noTHz}) \cdot \exp [- i β (λ)] - (F_{1 THz}^{*} - F_{1 noTHz}^{*}) \cdot \exp [i β (λ)]} \propto E_{THz, ⊥} (ω) .

(10b)

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F_{0} = S_{0} (λ), F_{1} = \frac{1}{2} [S_{1} (λ) - i \cdot S_{2} (λ)] \exp [i β (λ)], F_{1}^{*} = \frac{1}{2} [S_{1} (λ) + i \cdot S_{2} (λ)] \exp [- i β (λ)] .

(11)

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E_{THz, ∥} (t) \propto \arg {\frac{\int_{- \infty}^{- \infty} A_{p} (ω) \exp {i [φ_{p} (ω) + φ_{THz, ∥} (ω)]} d ω}{\int_{- \infty}^{- \infty} A_{p} (ω) \exp [i φ_{p} (ω)] d ω}},

(12a)

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E_{THz, ⊥} (t) \propto \arg {\frac{\int_{- \infty}^{- \infty} A_{p} (ω) \exp {i [φ_{p} (ω) + φ_{THz, ⊥} (ω)]} d ω}{\int_{- \infty}^{- \infty} A_{p} (ω) \exp [i φ_{p} (ω)] d ω}} .

(12b)

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Qinggang Lin, Xinming Yuan, Xuanke Zeng, Yatao Yang, Yi Cai, Xiaowei Lu, Maijie Zheng, Congying Wang, Wenhua Cao, Shixiang Xu. Single-shot terahertz polarization detection based on terahertz time-domain spectroscopy[J]. Photonics Research, 2022, 10(6): 1374

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Paper Information

Category: Instrumentation and Measurements

Received: Nov. 22, 2021

Accepted: Apr. 10, 2022

Published Online: May. 12, 2022

The Author Email: Shixiang Xu (shxxu@szu.edu.cn)

DOI:10.1364/PRJ.449196

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology