  We introduce a new class of $\mathcal{PT}$-symmetric complex crystals which
are almost transparent and one-way reflectionless over a broad frequency range
around the Bragg frequency, i.e. unidirectionally invisible, regardless of the
thickness $L$ of the crystal. The $\mathcal{PT}$-symmetric complex crystal is
synthesized by a supersymmetric transformation of an Hermitian square well
potential, and exact analytical expressions of transmission and reflection
coefficients are given. As $L$ is increased, the transmittance and reflectance
from one side remain close to one and zero, respectively, whereas the
reflectance from the other side secularly grows like $ \sim L^2$ owing to
unidirectional Bragg scattering. This is a distinctive feature as compared to
the previously studied case of the complex sinusoidal $\mathcal{PT}$-symmetric
potential $V(x)=V_0 \exp(-2i k_ox)$ at the symmetry breaking point, where
transparency breaks down as $L \rightarrow \infty$.
