Why do optical isomers rotate polarized light?

The propagation of electromagnetic waves in crystals is much more complex than in an isotropic or amorphous medium. To start with, the electric displacement #D# is not necessarily in the same direction as #E#. Analyzing this is possible by extending Maxwell's Equations using a "dielectric tensor" with nine quantities in a matrix (only six independent) instead of the single scalar permitivity #epsilon#.

The pattern of this tensor is dependent on the crystal pattern. In some crystals, it is diagonal and there is no optical effect. In crystals of lithium niobate, or in solutions of only one handedness (like dextrose or laevose, or optically-selected butan-2-ol), the effect of the non-zero off-diagonal elements is to cause various optical effects. These include slightly different propagation speeds depending on the direction of the beam, and the splitting of polarized light (other than along special directions) into circularly polarized light, because the speed of propagation of the two components is slightly different.

In organic chemistry an important consideration is whether each carbon atom has a plane of symmetry, as determined by seeing if has (for example) four bonds to four distinctly different structures. If it has this property, its solution may well exhibit optical isomerism.

If you try to solve the upgraded Maxwell's Equations assuming that the waves propagate like plane waves, you find that this cannot be done except for certain angles relative to the crystal axis. If you split an incoming wave into two components at those angles, the two components propagate at different speeds, so that instead of a plane wave you get various degrees of circular polarization.