Conditions for the Physical Realizability of Polarization Matrices Characterizing Passive Systems |
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Authors: | Richard Barakat |
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Affiliation: | Division of Applied Sciences , Harvard University , Cambridge, MA, 02128, U.S.A. |
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Abstract: | Abstract We derive conditions for the physical realizability of polarization matrices characterizing passive systems or scattering media. By physically realizable, we mean that 0 g 1 where g ≡ (output intensity/input intensity). Using the singular-value decomposition of an arbitrary 2 × 2 complex-valued matrix, we prove that a Jones matrix T J is physically realizable if 0 det T J + T J 1. Consequently singular Jones matrices (i.e. det T J = 0) completely extinguish the output intensity irrespective of the input intensity because g ≡ 0. Corresponding results are obtained for Mueller-Jones matrices (the 4 × 4 real-valued matrices which are the four-dimensional representations of the two-dimensional 2 × 2 complex-valued Jones matrices). We also study the problem for general Mueller matrices; however because of their phenomenological character they do not admit of such criteria as do the Jones and Mueller-Jones matrices. This is because g now depends upon the matrix elements of the Mueller matrix and the input Stokes parameters; whereas for the Jones and Mueller-Jones matrices, g only depends upon the matrix elements. Finally we study the problem of relating the input and output mean randomness. |
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