We derive theoretical expressions for the eigenvalues and the eigenvec
tors for a twisted-nematic liquid-crystal display (LCD) as a function
of the twist angle and the birefringence by use of the Jones-matrix fo
rmalism. These polarization eigenvectors are of particular interest fo
r phase-only transmission because they propagate unchanged through the
display. We find that the eigenvectors are elliptically polarized and
that the ellipticity changes as a function of the birefringence of th
e LCD (which is proportional to the external voltage applied to the di
splay). me can define an average eigenvector over a desired range for
the applied voltage. We show, using Jones matrices, how this average e
igenvector can be generated using a quarter-wave plate and a linear po
larizer having appropriate orientation angles. Using this average eige
nvector, we show that superior phase-only operation can be obtained ov
er a given operating range for the LCD compared with other approaches.
(C) 1998 Optical Society of America.