  The optical effects due to the loop-current order parameter in under-doped
cuprates are studied in order to understand the recent observation of unusual
birefringence in electromagnetic propagation in under-doped cuprates. It is
shown why birefringence occurs even in multiple domains of order with size of
domains much smaller than the wave-length and in twinned samples. Not only is
there a rotation of polarization of incident light but also a rotation of the
principal optical axis from the crystalline axes. Both are calculated in
relative agreement with experiments in terms of the same parameters. The
magnitude of the effect is orders of magnitude larger than the unusual Kerr
effect observed in under-doped cuprates earlier. The new observations,
including their comparison with the Kerr effect, test the symmetry of the
proposed order decisively and confirm the conclusions from polarized neutron
scattering.
