  We have carried out extensive simulations of the angle-resolved photoemission
(ARPES) intensity in Bi2212 within the one-step and three-step type models
using a first-principles band theory framework. The focus is on understanding
the behavior of emissions from the antibonding and bonding bands arising from
the $CuO_2$ bilayers around the $\overline{M}(\pi,0)$ symmetry point. The
specific issues addressed include: Dependencies of the photointensity on the
energy and polarization of the incident light; character of the initial and
final states involved as well as the spectrum of the relevant final states;
and, changes in the spectral intensity as a function of the perpendicular
component, $k_\perp$, of the momentum of the photoelectron. Considerable
insight into the nature of individual transitions is adduced by examining the
momentum matrix element for bulk transitions within the solid and by further
decomposing this matrix element into contributions from various atomic sites
and angular momentum channels. These results indicate that, via remarkable
interference effects, the ARPES matrix element can in particular cases help
zoom in on the properties of electrons excited from specific sites and/or
angular momentum channels even in a complex material.
