  We investigate the effect of Rashba spin-orbit coupling and of a tunnel
barrier on the zero conduc- tance resonances appearing in a one-dimensional
conducting Aharonov-Bohm (AB) ring symmet- rically coupled to two leads. The
transmission function of the corresponding one-electron problem is derived
within the scattering matrix approach and analyzed in the complex energy plane
with focus on the role of the tunnel barrier strength on the zero-pole
structure characteristic of trans- mission (anti)resonances. The lifting of the
real conductance zeros is related to the breaking of the spin-reversal symmetry
and time-reversal symmetry of Aharonov-Casher (AC)and AB rings, as well as to
rotational symmetry breaking in presence of a tunnel barrier. We show that the
polarization direction of transmitted electrons can be controlled via the
tunnel barrier strength and discuss a novel spin-filtering design in
one-dimensional rings with tunable spin-orbit interaction.
