Cosmic Microwave Background Radiation is characterized by T, Q and U fields.
A dipole modulation in these fields has been studied in different contexts. E
and B are derived from Q and U fields with the help of the so-called `edth'
operator. In this short write-up, I do a systematic analysis to demonstrate
that a dipole modulation in E mode polarization can't be introduced. Although
the analysis has been done for the E mode, a similar exercise can be repeated
for B mode as well. It has been explicitly demonstrated that the introduction
of a dipole modulation leads to a contradiction and hence such a modulation
isn't allowed.