Optomagnetics emerges as a growing field of research cross-linking optics, magnetism, and material science. Here we provide a microscopic quantum-mechanical and a macroscopic classical model to describe an optomagnetic medium, i.e., optical gyration coefficient from a nonlinear optics point of view. Our self-consistent quantum-mechanical formulation considers all orders of perturbing field and results not only in finding generalized Pitaevskii's relationship, where photoinduced magnetization can be expanded in terms of light power, but also provides compact and analytical expressions for optical gyration vector coefficients. Classical treatment is then developed based on the anharmonic Drude-Lorentz model showing that the photoinduced DC magnetization is proportional to odd harmonics of the light power. The difference in quantum and classical results is revealed and discussed. Having a pump-probe setup in mind, we describe how a probe light signal can propagate down an optomagnetic medium, i.e., a medium that is magnetized by intense circularly polarized pump light, via its permittivity tensor and find light propagation characteristics. Inverse Faraday and Cotton-Mouton effects are discussed as a result of circular and linear birefringences and their Verdet constants have been analytically found.

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光磁非线性光学：量子和经典处理

光电学作为交叉链接光学，磁性和材料科学的研究领域不断发展。在这里，我们提供了一个微观的量子力学和宏观的经典模型来描述光磁介质，即从非线性光学的角度来看的光学回转系数。我们自洽的量子力学公式考虑了扰动场的所有阶数，不仅导致发现了广义的Pitaevskii关系，其中光感应磁化强度可以在光功率方面扩展，而且还为旋光矢量系数提供了紧凑和解析的表达式。然后，基于非谐波Drude-Lorentz模型开发了经典处理方法，该模型表明光感应DC磁化强度与光功率的奇次谐波成比例。揭示和讨论了量子和经典结果的差异。考虑到泵浦探针的设置，我们描述了探针光信号如何通过其介电常数张量沿着光磁介质（即被强圆偏振泵浦光磁化的介质）向下传播，并找到光传播特性。由于圆形和线性双折射的缘故，讨论了法拉第逆效应和棉花木顿效应，并已通过分析找到了它们的维尔德常数。