The principles behind the design and operation of polarization-based optics
for nuclear resonant scattering of synchrotron radiation are discussed. Wi
th perfect single crystals and collimated X-rays emitted from undulator-bas
ed third-generation synchrotron radiation sources, polarization-selective o
ptics with a sensitivity of parts per billion can be obtained. A general ap
proach to optical activity is introduced, and the polarization dependence o
f the index of refraction is calculated for nuclear forward scattering for
a medium with unidirectional symmetry. Some recent experimental results are
reviewed and future applications are discussed.