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Abstract
We explored an equivalent Mueller matrix method for analyzing 3-D axial errors in 2-D polarization state measurements for the first time, to the best of our knowledge. The method treats 2-D devices with 3-D errors as a closed system, within which the transformation of a 3-D polarization field is described using a $3 \times 3$ coherency matrix and generalized Jones matrix (GJM). The equivalent $4 \times 4$ Mueller matrix of the component is numerically evaluated from the 2-D polarization field information at the input and output ports. Furthermore, our research has identified that any 3-D axial error within the polarization state analyzer (PSA) can be classified into two categories: axial alignment error (AAE) and wave-vector alignment error (WAE). For the latter case, we have introduced a concept of equal weight variance of a wave-vector as an alternative to the spiral sampling method to estimate the upper-bound of relative state of polarization (SoP) error. A simulation result shows that for the ideal bi-plate PSA, the upper-bound remains below 3% when the deviation value is less than 17.7 deg. The equivalent Mueller matrix method can be applied to analyze the 3-D errors in an arbitrary sort of PSA, and the description of 3-D transformation in this paper is simpler than a $9 \times 9$ generalized Mueller matrix and nine-element generalized Stokes vector, which has potential value in the research of vector beam generation.
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