Analysis of Kerr effect in resonator fiber optic gyros with triangular wave phase modulation

We present an in-depth analysis of the Kerr effect in resonator fiber optic gyros (R-FOGs) based on triangular wave phase modulation. Formulations that relate gyro output to the rotation rate, the Kerr nonlinearity, and other fiber and gyro parameters are derived and used to study the effect of Kerr nonlinearity on the gyro performance. Numerical investigation shows that the Kerr effect results in a nonzero gyro output even when the gyro is at stationary, which is interpreted as an error in the measurement of rotation rate. This error was found to increase as the frequencies of the two triangular phase modulations deviate from each other, and is not zero even if the intensities of the two counterpropagating beams are exactly the same. For fixed frequencies of the triangular phase modulations, there exists an optimal intensity splitting ratio for the two counterpropagating beams, which leads to zero gyro error. Calculation shows that the measurement error due to the Kerr effect for an R-FOG with a hollow-core photonic bandgap fiber as the fiber loop can be one to two orders of magnitude smaller than an R-FOG with a conventional single mode fiber loop.