  We obtained the exactly solutions of the $\mathcal{PT}$ symmetric potential
$V(x)=A[\sech(\lambda x)+i \tanh(\lambda x)]$, and found this system has no
bound-state. which $\mathcal{PT}$ symmetric potential was first studied in this
article, and the handedness effect is showed from reflection coefficients. As
the asymptotically non-vanishing imaginary potential component, when the
direction of the incident wave is opposite, that the transmission coefficient
will emerge a complex phase factor.
