  We are interested by the spectral analysis of the anisotropic discrete
Maxwell operator $\hat H^D$ defined on the square lattice $\rm Z\!\!\! Z^3$. In
aim to prove that the limiting absorption principle holds we construct a
conjugate operator to the Fourier series of $\hat H^D$ at any not-zero real
value. In addition we show that at some particular thresholds the conjugate
operator is essentially self-adjoint.
