Dynamical approximation of postsingularly finite exponentials

Given any postsingularly finite exponential function $p_{\lambda }(z)=\lambda \exp (z)$ where $\lambda \in {\text{C}}^{\ast }$, we construct a sequence of postcritically finite unicritical polynomials $p_{d,{\lambda }_d}(z)={\lambda }_d(1+\frac{z}{d}{)}^d$ that converge to $p_{\lambda }$ locally uniformly in $\text{C}$, with the same postsingular portrait as that of $p_{\lambda }$. We describe ${\lambda }_d$ in terms of parameter rays in the space of degree $d$ unicritical polynomials, and exhibit a relationship between the angles of these parameter rays as $d\to \mathrm{\infty }$ and the external addresses associated with $\lambda$ in the exponential parameter plane.