  We study a two-dimensional topological system driven out of equilibrium by
the application of elliptically polarized light. In particular, we analyze the
Bernevig-Hughes-Zhang model when it is perturbed using an elliptically
polarized light of frequency $\Omega$ described in general by a vector
potential ${\bf A}(t) = (A_{0x} \cos(\Omega t), A_{0y} \cos(\Omega t +
\phi_0))$. (Linear and circular polarizations can be obtained as special cases
of this general form by appropriately choosing $A_{0x}$, $A_{0y}$, and
$\phi_0$). Even for a fixed value of $\phi_0$, we can change the topological
character of the system by changing the ratio of the $x$ and $y$ components of
the drive. We therefore find a rich topological phase diagram as a function of
$A_{0x}$, $A_{0y}$ and $\phi_0$. In each of these phases, the topological
invariant given by the Chern number is consistent with the number of
spin-polarized states present at the edges of a nanoribbon.
