Constancy of the bilayer splitting as a function of doping in $Bi_{2}Sr_{2}CaCu_{2}O_{8+delta}$

Using high energy resolution angle resolved photoemission spectroscopy, we have resolved the bilayer splitting effect in a wide range of dopings of the bilayer cuprate $Bi_{2}Sr_{2}CaCu_{2}O_{8+delta}$. This bilayer splitting is due to a nonvanishing intracell coupling $t_{perp}$, and contrary to expectations, it is not reduced in the underdoped materials. This has implications for understanding the increased c-axis confinement in underdoped materials.