  The mid-infrared (MIR) band entangled photon source is vital for the next
generation of quantum communication, quantum imaging, and quantum sensing.
However, the current entangled states are mainly prepared in visible or
near-infrared bands. It is still lack of high-quality entangled photon sources
in the MIR band. In this work, we optimize the poling sequence of lithium
niobate to prepare two kinds of typical entangled states, the Hermit-Gaussian
state and the comb-like entangled state at 3.2 $\mu$m. We have also calculated
the photon pair rates and estimated the effect of fabrication resolution in the
schemes. Our approach will provide entangled photon sources with excellent
performance for the study of quantum information in the MIR band.
