  Existing polarization theories have mostly been concerned with Shannon's
information measures, such as Shannon entropy and mutual information, and some
related measures such as the Bhattacharyya parameter. In this work, we extend
polarization theories to a more general information measure, namely, the
R\'{e}nyi entropy. Our study shows that under conditional R\'{e}nyi entropies
of different orders, the same synthetic sub-channel may exhibit opposite
extremal states. This result reveals more insights into the polarization
phenomenon on the micro scale (probability pairs) rather than on the average
scale.
