# 瓊斯運算

## 瓊斯向量

 偏振態 瓊斯向量 偏振方向平行x軸的線偏振 ${\displaystyle {\begin{pmatrix}1\\0\end{pmatrix}}}$ 偏振方向平行y軸的線偏振 ${\displaystyle {\begin{pmatrix}0\\1\end{pmatrix}}}$ 偏振方向與x軸夾45°的線偏振 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\1\end{pmatrix}}}$ 偏振方向與x軸夾-45°的線偏振 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\-1\end{pmatrix}}}$ 偏振方向與x軸夾${\displaystyle \theta }$的線偏振 ${\displaystyle {\begin{pmatrix}\cos \theta \\\sin \theta \end{pmatrix}}}$ 右旋偏振 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\-i\end{pmatrix}}}$ 左旋偏振 ${\displaystyle {\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\i\end{pmatrix}}}$

## 瓊斯矩陣

 光學元件 瓊斯矩陣 穿透方向平行x軸的線偏振片 ${\displaystyle {\begin{pmatrix}1&0\\0&0\end{pmatrix}}}$ 穿透方向平行y軸的線偏振片 ${\displaystyle {\begin{pmatrix}0&0\\0&1\end{pmatrix}}}$ 穿透方向與x軸夾45°的線偏振片 ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&1\\1&1\end{pmatrix}}}$ 穿透方向與x軸夾-45°的線偏振片 ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&-1\\-1&1\end{pmatrix}}}$ 右旋偏振片 ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&i\\-i&1\end{pmatrix}}}$ 左旋偏振片 ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}1&-i\\i&1\end{pmatrix}}}$ 穿透方向與x軸夾${\displaystyle \Psi }$的線偏振片 ${\displaystyle {\begin{pmatrix}\cos ^{2}\Psi &\cos \Psi \sin \Psi \\\sin \Psi \cos \Psi &\sin ^{2}\Psi \end{pmatrix}}}$

 光學元件 瓊斯矩陣 光軸與x軸平行的波板 ${\displaystyle {\begin{pmatrix}e^{-i\Gamma /2}&0\\0&e^{i\Gamma /2}\end{pmatrix}}}$ 光軸與y軸平行的波板 ${\displaystyle {\begin{pmatrix}e^{i\Gamma /2}&0\\0&e^{-i\Gamma /2}\end{pmatrix}}}$ 光軸與x軸夾45°的波板 ${\displaystyle {\begin{pmatrix}\cos(\Gamma /2)&i\sin(\Gamma /2)\\i\sin(\Gamma /2)&\cos(\Gamma /2)\end{pmatrix}}}$ 光軸與x軸夾${\displaystyle \Psi }$的波板 ${\displaystyle {\begin{pmatrix}e^{-i\Gamma /2}\cos ^{2}\Psi +e^{i\Gamma /2}\sin ^{2}\Psi &-i\sin(\Gamma /2)\sin(2\Psi )\\-i\sin(\Gamma /2)\sin(2\Psi )&e^{-i\Gamma /2}\sin ^{2}\Psi +e^{i\Gamma /2}\cos ^{2}\Psi \end{pmatrix}}}$

## 旋轉元件

${\displaystyle M'(\theta )=R(\theta )\,M\,R(-\theta )}$ ,
${\displaystyle R(\theta )={\begin{pmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{pmatrix}}}$ .

## 參考

• E. Collett, Field Guide to Polarization, SPIE Field Guides vol. FG05, SPIE (2005). ISBN 0-8194-5868-6.
• E. Hecht, Optics, 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
• R. C. Jones, "New calculus for the treatment of optical systems," J. Opt. Soc. Am. 31, 488–493, (1941).
• Frank L. Pedrotti, S.J. Leno S. Pedrotti, Introduction to Optics, 2nd ed., Prentice Hall (1993). ISBN 0-13-501545-6
• A. Gerald and J.M. Burch, Introduction to Matrix Methods in Optics,1st ed., John Wiley & Sons(1975). ISBN 0-471-29685-6
• Jose Jorge Gill, Eusebio Bernabeu, Obtainment of the polarizing and retardation parameters of a non-depolarizing

optical system from the polar decomposition of its Mueller matrix, Optik, 76, 67-71, (1987).