The Fe-K$\alpha$ fluorescence lines are commonly observed in AGNs and X-ray binaries. The lines are believed to be originated from the reflection of the hard X-ray continuum near the inner-most region of the accretion disks of black holes. The geometry of the accretion disk is usually assumed to be infinitely thin, but this assumption is not appropriate when the accretion rate is moderately super-Eddington. With the increase of the accretion rate, the disk becomes thick, which will significantly affect the properties of the fluorescence lines. For instance, the polarized radiation is strongly depended on the geometry of the accretion disk. In this work, based on the lamp-post model, we study the polarization properties of the relativistic Fe-K$\alpha$ lines from thick disks in the framework of fully general relativity. We find that with the increase of the disk thickness, the polarization degree (PD) at the blue edge of the iron line increase significantly, and there appears a peak at the profile of the PD of the iron emission line, which at most is one order higher that of the line from the thin disk. Thus, the polarization properties of relativistic broad Fe-K$\alpha$ lines can be used to as a tool to diagnose the disk thickness.

Fe-K$\alpha$荧光线通常在 AGN 和 X 射线双星中观察到。这些线条被认为源自黑洞吸积盘最内部区域附近的硬 X 射线连续谱的反射。吸积盘的几何形状通常被假设为无限薄，但当吸积率中等超爱丁顿时，这种假设是不合适的。随着吸积率的增加，圆盘变厚，这将显着影响荧光线的性质。例如，偏振辐射强烈依赖于吸积盘的几何形状。在这项工作中，基于灯柱模型，我们研究了相对论性 Fe-K 的偏振特性$\alpha$在完全广义相对论的框架中，来自厚圆盘的线条。我们发现随着圆盘厚度的增加，铁线蓝色边缘的极化度（PD）显着增加，并且在铁发射线的PD轮廓处出现一个峰值，最多为1顺序高于从薄盘开始的线。因此，相对论宽 Fe-K 的极化性质$\alpha$ 线可用作诊断磁盘厚度的工具。