The origin and characteristics of the field-off state optical properties of the general twisted nematic liquid-crystal displays (LCD) are discussed. The optical field propagating normally in a uniformly twisted nematic structure can be represented by two mutually orthogonal elliptically polarized normal modes, one with left elliptical polarization and the other with right elliptical polarization. The interference between the two normal modes explains precisely, for the first time, the working mechanism for the field-off state optical performance of all twisted nematic liquid-crystal displays. The sum of the intensities of the two modes is independent of the polarizer orientation and always constitutes one half of the total intensity. The interference between the two modes contributes the second half of the total intensity and gives rise to two separate terms, each of which can be controlled by the entrance polarizer. Each of their contributions to the transmitted intensity can be minimized or maximized by the entrance polarizer in a complementary way. In addition, the ordinary and the extraordinary waves are always excited and strongly coupled in the twisted nematic (TN) structures. We also show that the field amplitudes of the waves are, in general, nonzero. The ordinary wave is zero only at some particular spatial points when the entrance polarizer is oriented parallel to entrance LC director; the extraordinary wave is zero only at the same particular spatial points when the entrance polarizer is oriented normal to the entrance LC director. In all other spatial points, both waves are nonzero even if the entrance polarizer is oriented parallel or normal to the entrance LC director. Using the solution for the optical field, analytic expressions are obtained for the field-off state optical transmissions of the general twisted nematic liquid-crystal displays with arbitrary polarizer orientations, liquid-crystal indices of refraction, twist angle, surface pretilt angle, and cell thickness. The field-off state optical working mechanism and characteristics of various twisted nematic liquid-crystal displays, including the standard 90° twisted nematic, the lower-twisted nematic, the optical mode interference, the supertwisted nematic, and the supertwisted birefringence effects liquid-crystal displays, are discussed. All the previously reported analytic results for the TN LCDs can be shown to be special cases of our general transmission formula. However, the Gooch and Tarry approach contains a few major incorrect intermediate results, despite the correct final results. We also obtained a simple expression for the polarizer orientations, for which the field-off state transmission has an extreme value under parallel or crossed polarizers. In general, for every twist geometry, there are two possible optimized polarizer orientations for the field-off state with parallel (or crossed) polarizers configuration. In particular, for the 180° supertwisted devices, one polarizer condition describes the standard 180° supertwisted nematic display, and the second polarizer condition describes the black and white 180° optical mode interference display.