Data can be encoded by modulating the frequency, amplitude and phase. But I can't find any references for encoding data in the polarization of EM waves (either analog or digital). This is probably for a good reason which I do not understand. Are there any examples of such schemes?
It certainly can be done, it just isn't very useful, except in certain situations.
For example, ham radio operators sometimes like to do experiments with reflecting signals off the moon (EME, or earth-moon-earth, a.k.a. "moonbounce"). It's useful to transmit with circular polarization, because the reflection comes back with the opposite polarization, which means that the receiving antenna is better at rejecting unwanted terrestrial reflections.
However, in the general case, different polarizations have different propagation characteristics, which makes it difficult to maintain coherency in terms of demodulating a useful payload at the receiving end.
A receiver connected to a simple receiving antenna cannot distinguish between a plain carrier of polarization A and the same carrier transmitted with a different polarization and amplitude - they could look the same to the receiver.
If there was something that could re-polarize the transmission as a means of modulating the carrier, the receiver would just detect it as amplitude modulation.
Simple transmit antennas (and probably some quite complex ones too) can't be electrically made to change their polarization.
Signal reflections from objects can reorient polarization and this could muddle things up.