Researching | Singleshot terahertz polarization detection based on terahertz timedomain spectroscopy

Journals >Photonics Research >Volume 10 >Issue 6 >Page 1374 > Article

Photonics Research
Vol. 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,*|Show fewer author(s)

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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DOI: 10.1364/PRJ.449196 Cite this Article Set citation alerts

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," Photonics Res. 10, 1374 (2022) Copy Citation Text

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Abstract

This paper presents a novel design for single-shot terahertz polarization detection based on terahertz time-domain spectroscopy (THz-TDS). Its validity has been confirmed by comparing its detection results with those of the THz common-path spectral interferometer through two separate measurements for the orthogonal components. Our results also show that its detection signal-to-noise ratios (SNRs) are obviously superior to those of the 45° optical bias THz-TDS by electro-optical sampling due to its operation on common-path spectral interference rather than the polarization-sensitive intensity modulation. The setup works without need of any optical scan, which does not only save time, but also efficiently avoids the disturbances from the fluctuations of the system and environment. Its single-shot mode allows it to work well for the applications with poor or no repeatability.

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," Photonics Res. 10, 1374 (2022)

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