  We study the complete process \phphbbww\ using exact matrix element
computations at tree-level, at a $\sqrt s=500$ GeV \eeb\ linear collider of the
next generation. Incoming photons produced via back-scattering of laser light
are considered. Sizable effects due to the finite width of the top quark as
well as to the irreducible background to $t\bar t$ production and decay are
predicted.
