Attenuation characterization of multiple combinations of imperfect polarizers

Malus's law, when used to calculate the attenuation ratio of the combination of two imperfect polarizers (two-CIP), will introduce an error, especially near the crossed-axis orientation. In this paper, first, the Jones matrix of the imperfect polarizer is deduced and an exact algorithm of the attenuation ratio of the two-CIP is proposed as well as its monotonic attenuation interval. Experimental results confirm that our deduced expression is more accurate than Malus's law. Then based on this algorithm, an attenuation-ratio expression of the combination of three imperfect polarizers (three-CIP) is presented. In this three-CIP model, it is found that when the electric field amplitude ratio of the imperfect polarizer is epsilon, the attenuation ratio can change from 1 to epsilon(4) monotonically in a general model when P(1) and P(3) are rotated and P(2) is fixed, which is proved by experiment. Finally, it is deduced that the combination of n imperfect polarizers (n-CIP) can obtain a minimum attenuation ratio of epsilon(2(n-1)), which indicates the number of imperfect polarizers needed to achieve the required attenuation ratio.