Orbital angular momentum mode of cylindrical spiral wave-guide
Authors: Zhao Chao-Ying , Fan Yu-Ting , Meng Yi-Chao , Guo Qi-Zhi , Tan Wei-Han ,   School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China,   State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China,   Institute of Fiber Optics, Shanghai University, Shanghai 201800, China,   Department of Physics, Shanghai University, Shanghai 200444, China
Published: December 2020

The common feature of traditional methods of preparing orbital angular momentum (OAM) light beams propagating along the <i>z</i> axis is that the wave-front phase is changed and the chief ray of beam is basically unchanged. But it is difficult to obtain a high <inline-formula><tex-math id="M5">\begin{document}$m\hbar $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M5.png"/></alternatives></inline-formula> OAM. To solve the above problem, we establish a theoretical framework based on the change of the chief ray of beam instead of the change of wave-front phase. The differential geometry theory is used to verify the theoretical assumption that the light transmitted by the cylindrical spiral wave-guide can carry high <inline-formula><tex-math id="M6">\begin{document}$m\hbar $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M6.png"/></alternatives></inline-formula> OAM. To measure the OAM optical fiber output, we use the diffraction method to detect the phase of vortex, that is, we can use a microscope to observe the phase distribution of optical fiber end face. We consider the output of linearly polarized light along the tangent direction of the fiber to observe its diffraction pattern. The transmission of optical fiber around the cylinder is the main light. The diameter of optical fiber is constant, and the light wave transmitting into the optical fiber is Bessel beam. For the linear fiber output, we need to consider only the linear fiber Bessel beam. The output cross section of the wave surface in the fiber is approximately that of plane wave. When <inline-formula><tex-math id="M7">\begin{document}$\theta > {\theta _0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M7.png"/></alternatives></inline-formula>, we use the flow coordinates <inline-formula><tex-math id="M8">\begin{document}$(\alpha,\beta, \gamma)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M8.png"/></alternatives></inline-formula> to calculate the diffraction pattern of the cross section of the optical fiber when light travels in the optical fiber around the cylinder, which shows the characteristics of vortex. The optical field distribution carries a high-order OAM mode. When <inline-formula><tex-math id="M9">\begin{document}$\theta = {\theta _0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20190997_M9.png"/></alternatives></inline-formula>, cylindrical orbital optical fibers transit to linear orbital optical fibers. We calculate the diffraction pattern of the cross section of the optical fibers propagating in a straight line. It is an Airy spot, namely a circular aperture diffraction spot. The optical field distribution has no higher-order OAM mode. When the order of the output beam is small, the output shows certain uniformity and symmetry, when the order of the output beam increases gradually, the output beam shows some inhomogeneity and asymmetry.