There is a coupling loss at the joint of the Lyot depolarizer consisting of two sections of birefringent fiber
(Polarization Maintaining fiber or PM fiber) with non-round fiber core. The contribution to the loss for the
non-roundness of the fiber core was calculated and analyzed using a method based on second moment. And the
result obtained is in agreement with the experiment and so demonstrates the exist of the loss. This also provides a
method of analyzing and calculating the coupling loss for non-round fiber core in the paper and is useful for
manufacturing the Lyot fiber depolarizer and researching on the stability of the depolarizer type of a single mode
interference fiber optic gyro (IFOG).