Solution
= Solution
The <Poynting vector> is
$$
\boxed{
\mathbf S=\frac1{\mu_0}\mathbf E\times\mathbf B
=\frac{\omega}{\mu_0k}(B_1^2+B_2^2)
\cos^2(kz-\omega t)\,\mathbf e_z}.
$$
It is the electromagnetic energy flux in the propagation direction; its time average is $c(B_1^2+B_2^2)/(2\mu_0)$.