Jones matrix analysis of frequency mixing error in three-longitudinal-mode laser heterodyne interferometer

In this study, the authors investigate theoretically a periodic non-linearity effect and its compensation in a three-longitudinal-mode heterodyne interferometer (TLMI). An analytical formula of the frequency mixing error in the TLMI is obtained based on the Jones calculus taking into account experimental parameters. We find that the non-ideal polarisation states and imperfect alignment of the optical setup play the major role to produce four- and eight-cycle non-linearities. The operation of non-linearity compensation system on the four- and eight-cycle non-linear errors is also presented.