Optical differential operation and image edge detection have shown some unique advantages, including faster operating speeds and lower power consumption, compared to a digital image processor. Here, we examine the origin of optical differentiator in the photonic spin Hall effect. We find that the optical differentiator in x direction is related to the beam divergence when the incident angle of the central wave vector meets Brewster's, while the optical differentiator in y direction is related to the cross polarization component. By eliminating the H-H or V-V polarization component, the H-V or V-H polarization component induced the spin-dependent splitting in the photonic spin Hall effect, which can be used for the one-dimensional optical differentiator in an arbitrary direction. Furthermore, we investigate the photonic spin Hall effect and double-peak profile near Brewster angle and predict that a perfect two-dimensional optical differentiator will become a reality.

中文翻译：

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光子自旋霍尔效应中可调谐的光学空间差异

与数字图像处理器相比，光差分操作和图像边缘检测已显示出一些独特的优势，包括更快的操作速度和更低的功耗。在这里，我们研究了光子自旋霍尔效应中光微分器的起源。我们发现，当中心波矢量的入射角满足布鲁斯特定律时，x方向的光微分器与光束发散有关，而y方向的光微分器与交叉偏振分量有关。通过消除HH或VV极化分量，HV或VH偏振分量在光子自旋霍尔效应中引起自旋相关的分裂，可将其用于任意方向上的一维光学微分器。此外，我们研究了光子自旋霍尔效应和布鲁斯特角附近的双峰轮廓，并预测了一个完美的二维光学微分器将成为现实。