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Based on the theory of Jones matrix and the condition of eigenmode self-consistency, we analyze the effect of linear stress birefringence of prismon the beam polarization (described with the ellipticity and loss of the eigenmodes) and null drift (described with the output frequency difference of the eigenmodes) in a TRP resonator. It is found that the linear stress birefringence of prisms can cause larger polarization ellipticity for both CW (clockwise) and CCW (counterclockwise) beams. The results may be useful for designing and optimizing the structure of super high precision TRP ring laser gyroscopes.

Differential laser gyro is an ideal equipment to solve the "lock-in" behavior. The ring cavity must be low loss and the reflectivity of mirrors in gyro must be more than 99.99%. But the insertion of a piece of quartz glass and a Faraday cell in the cavity will broaden the "lock-in" area due to additional loss, so it is very important to measure ultra-high reflectivity of mirrors and the loss of transparent glass plate used in gyro. 632.8nm He-Ne laser is the most suitable light to travel around the ring cavity in gyro, so the traditional cavity ring down spectroscopy (CRDS) must be improved by using continuous-wave (CW) He-Ne laser instead of pulsed one. The results show that the single-pass loss through the glass plate can be kept below 3.0×10 -11 cm -1 . Using combination of linear and folded cavity ring down spectroscopy, the loss such as absorption of gas in the cavity are counteracted due to the equalized length of cavity, so the reflectivity of the mirrors is measured with high accuracy. The ring down time of the cavity with and without a sample is obtained respectively, and then the total loss of the measured sample is calculated. The results show that the improved CRDS is suitable for accurately measuring low loss of medium and reflectivity of mirrors.