Study of the self-biasing mechanism in the double-longitudinal-mode of a laser gyro induced by Lamb dips

This paper provides a new theoretical explanation for the self-biasing effect of the dual-longitudinal-mode in laser gyro, based on Lamb's semi-classical theory. By analyzing the relationship between the number of output pulses and the power tuning curve of the laser gyro, starting from the cavity tuning frequency, we reveal that the self-biasing effect of the dual-longitudinal-mode occurs at the dual Lamb dips. To explain this phenomenon, the beat frequency equation for the dual-longitudinal-mode laser gyro is derived based on the theoretical framework of the self-consistent frequency equations for dual-longitudinal-mode, yielding the mathematical expression for the self-biasing magnitude. Theoretical analysis shows that the mode pushing coefficient, the average intensity difference of the strong mode, and the average intensity difference of the weak mode provide optical biasing for the double-longitudinal-mode self-biasing laser gyro. The key factors influencing the magnitude of the self-biasing are identified as: the average intensity difference of the weak mode (<i>i_w</i>₀), the mutual pushing coefficient of the weak mode (<i>τ</i>₄₃), the self-pushing coefficient of the weak mode (<i>ρ_w</i>), and the difference in mutual pushing coefficients of the strong modes (Δ<i>τ</i>₁). Furthermore, <i>i_w</i>₀, <i>τ</i>₄₃, <i>ρ_w</i>, and Δ<i>τ</i>₁ are all directly proportional to the relative excitation. To validate the theoretical findings, experimental verification was performed using a ring laser with a cavity length of 0.28 m. The experimental results show that increasing the relative excitation increases the average intensity difference between the strong and weak modes, which in turn increases the self-biasing magnitude. These findings provide important references for the development of an all-solid-state, zero-lock-in optical self-biasing laser gyro.