Abstract Using the Richards–Wolf formula focusing of a circularly polarized plane wave with wavelength 532 nm by an aplanatic lens with high numerical aperture was investigated numerically. We have investigated the behavior of the spin angular momentum (SAM) and the Poynting vector at the focal spot. It was shown that the direction of rotation of the transverse component of the SAM at the focus does not depend on the direction of the input polarization: for both the left and right circular polarization the transverse component of the SAM is rotated counterclockwise. For the transverse component of the Poynting vector, the direction of rotation will depend on the direction of the input polarization: for the left polarization — clockwise; for the right — counterclockwise. When moving away from the focus plane, the maxima of the transverse components of the Poynting vector and SAM behave identically: for the right circular polarization, they rotate counterclockwise; for the left circular polarization — clockwise. It is interesting that for the focused light with left circular polarization the longitudinal component of the SAM is negative, and for right-hand circular polarization the longitudinal component SAM is positive. The longitudinal component of the energy flow is always positive: for left and right circular polarization.

中文翻译：

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焦点处横向自旋角动量的不变性

摘要 利用Richards-Wolf公式对高数值孔径消球差透镜对波长为532 nm的圆偏振平面波的聚焦进行了数值研究。我们已经研究了焦点处的自旋角动量 (SAM) 和坡印廷矢量的行为。结果表明，焦点处 SAM 横向分量的旋转方向不取决于输入偏振的方向：对于左圆偏振和右圆偏振，SAM 的横向分量都逆时针旋转。对于坡印廷矢量的横向分量，旋转方向将取决于输入极化的方向：对于左极化 — 顺时针；右边——逆时针。当远离焦平面时，坡印廷矢量和 SAM 的横向分量的最大值表现相同：对于右圆偏振，它们逆时针旋转；对于左圆极化 - 顺时针。有趣的是，对于左旋圆偏振的聚焦光，SAM 的纵向分量为负，而对于右旋圆偏振，纵向分量 SAM 为正。能量流的纵向分量始终为正：对于左圆极化和右圆极化。对于右旋圆极化，纵向分量 SAM 为正。能量流的纵向分量始终为正：对于左圆极化和右圆极化。对于右旋圆极化，纵向分量 SAM 为正。能量流的纵向分量始终为正：对于左圆极化和右圆极化。