The eigenmode analysis of liquid crystal optical waveguides (LCOWs) was the basis and theoretical support for the design of its devices. The accuracy of mode field analysis directly affects the performance of LCOW-based devices. We used the following procedure to accurately analyze the relationship of the eigenmode field components in the LCOW. Firstly, the magnetic field coupling equations of the nematic liquid crystals were obtained from Maxwells equations. Then, the quantitative relationship between the rotation angle of the liquid crystal director and the ratio of the magnetic field components of the eigenmodes excited by the extraordinary light wave was obtained. Additionally, the numerical simulation is carried out using OptiBPM13.1. The simulation results verify the quantitative relationship that the ratio between field components and the tangent function of director rotation angle are opposite to each other. According to this relationship, the relative order of magnitude between the transverse magnetic field components of the eigenmode field in the LCOW can be controlled by changing the applied voltage. Then, the conversion of polarization mode excited by an extraordinary light wave can be realized. This law is helpful to promote the research of polarization rotator and mode converter based on LCOW.