The Jones matrix of a quarter-wave plate is studied theoretically and experimentally, taking into account internal reflections, the ellipsoid of the indices, geometric defects, the tilt angle, and the characteristics of the incident Gaussian beam. The influence of the different parameters is isolated, and large discrepancies are observed with respect to results obtained from the Jones matrix that are usually given in textbooks. It is shown that the effective Jones matrix of the plate does not depend on the longitudinal position of the plate on the Gaussian beam but only on the beam-waist size. This leads to a method of characterization of the defects of a quarter-wave plate that is more precise than the usual methods. Different procedures to optimize the efficiency of a given plate are discussed, taking the plate defects into account. In all cases, a good agreement between experiments and theory is obtained.
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