Circular dichroism and bilayer splitting in the normal state of underdoped (Pb,Bi)$_2$Sr$_2$(Ca$_x$Y$_{1-x}$)Cu$_2$O$_{8+δ}$ and overdoped (Pb,Bi)$_2$Sr$_2$CaCu$_2$O$_{8+δ}$

We report an ARPES investigation of the circular dichroism in the first Brillouin zone (BZ) of under- and overdoped Pb-Bi2212 samples. We show that the dichroism has opposite signs for bonding and antibonding components of the bilayer-split CuO-band and is antisymmetric with respect to reflections in both mirror planes parallel to the c-axis. Using this property of the energy and momentum intensity distributions we prove the existence of the bilayer splitting in the normal state of the underdoped compound and compare its value with the splitting in overdoped sample. In agreement with previous studies the magnitude of the interlayer coupling does not depend significantly on doping. We also discuss possible origins of the observed dichroism.