The constraint on the Jones matrix of an optical system such that there exist two linear polarization states at its input that are mapped onto two corresponding linear states at its output is derived. These principal linear polarization (PLP) states, which characterize a broad range of systems, are also found in terms of the Jones matrix elements. Special cases when the PLP states are orthogonal, collapse onto one state, or become infinite in number are indicated. For a deterministic or nondeterministic optical system described by a Mueller matrix, the existence of two PLP states places a constraint on only 3 of the 16 matrix elements, namely, the first 3 elements of the last row. In general, the output light is partially linearly polarized. Several examples are given for demonstration.
Journal of the Optical Society of America A
R. M. A. Azzam, "Principal linear polarization states of an optical system," J. Opt. Soc. Am. A 9, 147-150 (1992)