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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 nobound-state. which $\mathcal{PT}$ symmetric potential was first studied in thisarticle, and the handedness effect is showed from reflection coefficients. Asthe asymptotically non-vanishing imaginary potential component, when thedirection of the incident wave is opposite, that the transmission coefficientwill emerge a complex phase factor.

Exactly solvable complex PT symmetry potential $A[\mathrm{sech}({\lambda}x) + i\tanh({\lambda}x)]$