A new optical element that displays singular polarization eigenstates is pr
oposed. It consists of a planar stratified structure composed of alternate
gyrotropic and birefringent layers. The orthogonality of the polarization e
igenstates is lost because of anisotropic reflections at the interfaces, wh
ich are enhanced by the special condition chosen for the multiple-beam inte
rference. First we show that the anisotropic reflection at the interface be
tween the layers with linear and circular symmetries does produce strong en
ough dichroism to break the orthogonality of polarization eigenstates. Seco
nd, we investigate the behavior of these eigenstates with respect to their
Linearity and orthogonality as a function of the width of the layers. Our r
esults concretely demonstrate that it is possible to control the effective
optical parameters of such stratified structures by adjusting the thickness
of each anisotropic layer. Finally, we obtain the necessary conditions for
designing a double-layer system with singular eigenstates of linear polari
zation. (C) 2000 Optical Society of America OCIS codes: 230.4170, 230.5440,
260.1180, 260.5430.