  We present the theoretical basis of a cavity-enhanced polarimetric scheme for
the measurement of parity-nonconserving (PNC) optical rotation. We discuss the
possibility of detecting PNC optical rotation in accessible transitions in
metastable Xe and Hg, and ground state I. In particular, the physics of the PNC
optical rotation is presented, and we explore the lineshape effects on the
expected PNC optical rotation signals. Furthermore, we present an analysis of
the eigenpolarizations of the cavity-enhanced polarimeter, which is necessary
for understanding the measurement procedure and the ability of employing robust
background subtraction procedures using two novel signal reversals. Using
recent atomic structure theoretical calculations, we present simulations of the
PNC optical rotation signals for all proposed transitions, assuming a range of
experimentally feasible parameters. Finally, the possibility of performing
sensitive measurements of the nuclear-spin-dependent PNC effects is
investigated, for the odd-neutron nuclei $^{129}$Xe and $^{199}$Hg, and the
odd-proton nucleus $^{127}$I.
