Researching | Measurement Technique for Extracting Jones Matrix of Substances Based on Longitudinal Component of Converging Terahertz Beam

Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 18 >Page 1811016 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 18, 1811016 (2023)

Measurement Technique for Extracting Jones Matrix of Substances Based on Longitudinal Component of Converging Terahertz Beam

Yunfei Liu, Xinke Wang^*, Wenfeng Sun, and Yan Zhang

Author Affiliations

Department of Physics, Capital Normal University, Beijing 100048, China

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DOI: 10.3788/LOP230638 Cite this Article Set citation alerts

Yunfei Liu, Xinke Wang, Wenfeng Sun, Yan Zhang. Measurement Technique for Extracting Jones Matrix of Substances Based on Longitudinal Component of Converging Terahertz Beam[J]. Laser & Optoelectronics Progress, 2023, 60(18): 1811016 Copy Citation Text

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Abstract

Herein, a method for extracting the Jones matrix of a material in the terahertz (THz) wave band is proposed. A THz focal-plane imaging system was utilized to coherently measure the longitudinal component of a converging THz field and to determine the THz polarization. Furthermore, the Jones matrix of the material was extracted by measuring the polarization of a reference THz field and the polarizations of the THz fields transmitted from a sample in its original position and with a 90° rotation. The proposed method was employed to measure the Jones matrices of a THz polarizer and a wave plate with different azimuthal angles, and the experimental results were consistent with theoretical calculations. This demonstrated the feasibility of the proposed method to characterize the anisotropy of materials in the THz frequency range.

Keywords

Jones matrix longitudinal component polarization terahertz

[\begin{matrix} A_{2} \\ B_{2} \end{matrix}] = [\begin{matrix} J_{11} & J_{12} \\ J_{21} & J_{22} \end{matrix}] [\begin{matrix} A_{1} \\ B_{1} \end{matrix}]

。（1）

\begin{matrix} [\begin{matrix} A_{3} \\ B_{3} \end{matrix}] = [\begin{matrix} c o s φ & - s i n φ \\ s i n φ & c o s φ \end{matrix}] [\begin{matrix} J_{11} & J_{12} \\ J_{21} & J_{22} \end{matrix}] [\begin{matrix} c o s φ & s i n φ \\ - s i n φ & c o s φ \end{matrix}] [\begin{matrix} A_{1} \\ B_{1} \end{matrix}] = \\ [\begin{matrix} c o s 90 ° & - s i n 90 ° \\ s i n 90 ° & c o s 90 ° \end{matrix}] [\begin{matrix} J_{11} & J_{12} \\ J_{21} & J_{22} \end{matrix}] [\begin{matrix} c o s 90 ° & s i n 90 ° \\ - s i n 90 ° & c o s 90 ° \end{matrix}] [\begin{matrix} A_{1} \\ B_{1} \end{matrix}] = \\ [\begin{matrix} J_{22} & - J_{21} \\ - J_{12} & J_{11} \end{matrix}] [\begin{matrix} A_{1} \\ B_{1} \end{matrix}], \end{matrix}

（2）

\{\begin{array}{l} A_{2} = J_{11} A_{1} + J_{12} B_{1} \\ B_{2} = J_{21} A_{1} + J_{22} B_{1} \\ A_{3} = J_{22} A_{1} - J_{21} B_{1} \\ B_{3} = - J_{12} A_{1} + J_{11} B_{1} \end{array}

，（3）

\{\begin{array}{l} J_{11} = \frac{A_{2} A_{1} + B_{1} B_{3}}{A_{1}^{2} + B_{1}^{2}} \\ J_{12} = \frac{A_{2} B_{1} - B_{3} A_{1}}{A_{1}^{2} + B_{1}^{2}} \\ J_{21} = \frac{B_{2} A_{1} - A_{3} B_{1}}{A_{1}^{2} + B_{1}^{2}} \\ J_{22} = \frac{B_{2} B_{1} + A_{3} A_{1}}{A_{1}^{2} + B_{1}^{2}} \end{array}

，（4）

E_{z x} (ρ, ϕ, z) = - 2 A c o s ϕ \int_{0}^{α} \sqrt[]{c o s θ} s i n^{2} θ \times J_{1} (k ρ s i n θ) e x p (j k z c o s θ) d θ

，（5）

\{\begin{array}{l} E_{a} = \sum_{x, y} E_{z} (x, y) \cdot c o s [β (x, y)] \\ E_{b} = \sum_{x, y} E_{z} (x, y) \cdot s i n [β (x, y)] \end{array}

，（6）

\begin{array}{l} [\begin{matrix} a \\ b \end{matrix}] = [\begin{matrix} c o s 45 ° & - s i n 45 ° \\ s i n 45 ° & c o s 45 ° \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}] \\ [\begin{matrix} c o s 45 ° & s i n 45 ° \\ - s i n 45 ° & c o s 45 ° \end{matrix}] [\begin{matrix} 1 \\ 0 \end{matrix}] = [\begin{matrix} 0.5 \\ 0.5 \end{matrix}] \end{array}

。（7）

\begin{matrix} [\begin{matrix} a \\ b \end{matrix}] = [\begin{matrix} c o s 45 ° & - s i n 45 ° \\ s i n 45 ° & c o s 45 ° \end{matrix}] [\begin{matrix} t_{1} & 0 \\ 0 & t_{2} e x p (j \frac{2 π v}{c} Δ n d) \end{matrix}] \times \\ [\begin{matrix} c o s 45 ° & s i n 45 ° \\ - s i n 45 ° & c o s 45 ° \end{matrix}] [\begin{matrix} 1 \\ 0 \end{matrix}] = [\begin{matrix} \frac{1}{2} [t_{1} + t_{2} e x p (j \frac{2 π v Δ n}{c} d)] \\ \frac{1}{2} [t_{1} - t_{2} e x p (j \frac{2 π v Δ n}{c} d)] \end{matrix}] \end{matrix}

，（8）

\begin{array}{l} [\begin{matrix} J_{11} & J_{12} \\ J_{21} & J_{22} \end{matrix}] = [\begin{matrix} c o s 30 ° & - s i n 30 ° \\ s i n 30 ° & c o s 30 ° \end{matrix}] [\begin{matrix} t_{1} & 0 \\ 0 & t_{2} e x p (j \frac{2 π v}{c} Δ n d) \end{matrix}] \\ [\begin{matrix} c o s 30 ° & s i n 30 ° \\ - s i n 30 ° & c o s 30 ° \end{matrix}] \end{array}

。（9）

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Yunfei Liu, Xinke Wang, Wenfeng Sun, Yan Zhang. Measurement Technique for Extracting Jones Matrix of Substances Based on Longitudinal Component of Converging Terahertz Beam[J]. Laser & Optoelectronics Progress, 2023, 60(18): 1811016

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