Starting from the refractive index ellipsoid equation and the electro-optic coefficient matrix of the LiNbO₃ crystal, the transverse electro-optic modulation characteristics of the LiNbO₃ crystal when an electric field is applied along the optical axis direction were calculated and analyzed. The results show that due to the presence of natural phase difference, the electro-optic modulation curve of the LiNbO₃ crystal does not necessarily pass through the coordinate origin. At the same time, the electro-optic modulation curve of the crystal is very sensitive to small deviations in the direction of light transmission within the plane determined by the y and z axes, leading to randomness in the demodulation signal waveform of the sine modulation signal at zero voltage in experiments, but this does not affect the measurement results of the half-wave voltage of the LiNbO₃ crystal. These results and conclusions can not only well answer the doubts students have in experiments but also serve as a good reference for experimental teachers and related experimental personnel.

The abnormal resonance signals in optical pumping magnetic resonance experiment were determined according to the value of g_F-factor obtained by fitting. The spectra of the abnormal resonance radio-frequency signals were measured using digital oscilloscope, and the magnitudes of the higher harmonics were calculated. The relationship between the amplitudes of normal resonance signals and the ones of radio-frequency signals was obtained by the least squares linear fitting. Using the relationship, the magnitude of the abnormal resonance signal engendered by each higher harmonic was estimated. The calculated results are basically consistent with the experimental ones. The waveforms and the spectra of the radio-frequency signals change obviously after the frequency meter is connected with the radio-frequency signal generator. The abnormal resonance signals change accordingly with the changes in the RF signal spectrum, which suggests that the abnormal resonance signals are caused by the higher harmonic resonances of the radio-frequency signals. These results show that it is not only feasible to explore the mechanism of abnormal resonance signal in optical magnetic resonance experiment by digital oscilloscope, but can also quantitatively estimate and predict the influence of radio-frequency signal waveform on the magnitude of abnormal resonance signals.