We derive compact representation of an extended Jones matrix (EJM) suggested by Lien [Lien A, 1997. Liq. Cryst. 22: 171-175] for the case of oblique light incidence. Our representation of the EJM is handy for analytical calculations and has the form of a general Jones matrix, with nonzero imaginary parts of its offdiagonal elements. An analogy between these two matrices is discussed. For a crystal slab with the optic axis along the slab normal, our representation of the EJM reduces to a form that yields the Jones vector identical to that obtained by the other authors in the frame of paraxial approximation.
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Nastishin, Y. A., & Nastyshyn, S. Y. (2011). Explicit representation of extended Jones matrix for oblique light propagation through a crystalline slab. Ukrainian Journal of Physical Optics, 12(4), 191–201. https://doi.org/10.3116/16091833/12/4/190/2011