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Verdet constant is one of the key parameters to characterize the material's magneto-optical properties, along with the wavelength and temperature dependence. In order to thoroughly analyze the influence mechanisms of the incident wavelength and temperature on the Verdet constant as well as uncover its essence, both advantages and disadvantages of the classical electronic dynamics theory and quantum theory on account of basic theories and test data are discussed. By exploring the physical essences and models of the two theories, their significant associations between the medium’s polarization intensity and the molecular polarizability are determined. The former decides the medium’s permittivity and refractivity, and in turn, influences the Faraday rotation angle and Verdet constant. It should be noted that the polarizability includes not only those transition dipole moments from the electrons’ transitions between different states, but also the inductive dipole moments which is due to the non-transition electron cloud being polarized. Hence, a hypothesis is proposed which suggests that the Faraday effect results from the combination of various factors. Accordingly, a theory of wave-transition contribution to the Verdet constant is deduced. Taking the typical diamagnetic material ZF1 and the typical paramagnetic material TGG as examples, the influences of the incident wavelength and the temperature on the Verdet constant are analyzed. The deduced theory together with the corresponding models is tested and verified by analyzing the relevant parameters and the test data. The results show that the wave-transition contribution theory and its models are superior in the aspect of precisely describing the material's Verdet constant.
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