  Composite pulses, which produce ultrabroadband, ultranarrowband and
ultrapassband $x$-, $y$-) rotations by $\theta = \pi$ on the Bloch-Poincar\'e
sphere, are presented. The first class plays a role for design of achromatic
polarisation retarders, when the second class corresponds to chromatic
polarisation filters. The third class is an assortment of the above two
classes. Besides, composite pulses, which produce ultrabroadband $z$-)
rotations by $\zeta = \pi$ on the same sphere, are presented. These phasal
pulses coincide with achromatic polarisation $\pi$ rotators. On the
quantum-classical analogy, we obtain ultrarobust, ultrasensitive and
ultrasquare quantum control of a $X$ gate and ultrarobust quantum control of a
$Z$ gate.
