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Theoretical and experimental analysis have shown that magnetic field has unavoidable effect on the performances of
ring laser gyroscopes. This kind of effect has been called the magnetic bias of ring laser gyroscopes in this article. The
affection of the mirror's phase shift on the magnetic bias in square ring resonators has been analyzed in this article. The
following parameters which have influence on the magnetic bias such as Ar, B, g and Rsp are taken into account, where
Ar is the distortion angle, B is the magnetic field, g is the phase shift of the mirror and Rsp is the difference of the
reflectivity for 's' and 'p' type polarizations of light. The affection of parameters gi (i=1, 2, 3, 4) on magnetic bias is
analyzed in detail, where gi are the phase shifts of four mirrors respectively. When g1=g2=g3=g4 and gi is near zero, the
magnetic bias will become very samll. When g1=g2=g3=g4 and gi is near π, the magnetic bias will become great. In
practice, g1≠g2≠g3≠g4, but, when g1+g2+g3+g4=0, the magnetic bias will become small. Especially, when g1+g2+g3+g4=0
and g1+g2=0, the magnetic bias is very small and can be ignored. In addition, when gi is near π and g1+g2+g3+g4=4π, the
magnetic bias is small. Especially, when gi is near π, g1+g2+g3+g4=4π and g1+g2 =2π, the magnetic bias is very small and
can be ignored. Based on these novel results, the magnetic bias can be eliminated by controlling the phase shifts of four
mirrors accurately in film coating process. The research on the magnetic bias of ring resonators is very important for
improving the performance of ring laser gyroscopes. These findings are important to the research on high precision and
super high precision ring laser gyroscopes.
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